APPSC Group 1 · Screening Paper II · Topic 1
1 APPSC Group 1 General Mental and Psychological Abilities questions with answers
115 questions from APPSC G1 Paper II Mock 1 with answers and APPSC G1 Paper II 2024 question paper with answers. Try each one, then tap Show answer.
Previous-paper questions are as in the original paper. Medha AI wrote the answers and explanations.
1.1.1Reasoning: series, coding, relations and Venn diagramsNotes
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What is the greatest number of pieces into which a cube-shaped cake can be cut with 4 straight plane cuts, if the pieces are not moved between cuts?
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Answer D. 15
With plane cuts the maximum pieces are 2, 4, 8 for 1, 2, 3 cuts. A fourth plane meets the first three planes in 3 lines, which divide it into at most 7 regions; so it adds 7 pieces: 8 + 7 = 15.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-I build script)
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Statements:
1. All engineers are graduates.
2. Raju is an engineer.
Conclusions:
I. Raju is a graduate.
II. All graduates are engineers.
Considering the statements to be true even if they appear to be at variance with commonly known facts, which of the conclusions logically follow(s)?
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Answer A. Only I follows
Only I follows. Raju is an engineer and every engineer is a graduate, so Raju is a graduate. An 'All' statement cannot be reversed.
Source: Standard reasoning method; answer and every option checked in Python (arrangements, syllogisms and truth puzzles brute-forced for a unique answer)
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Take the given statements to be true even if they seem to differ from commonly known facts. Decide which of the given conclusions logically follow(s) from the statements. ('Only a few X are Y' means that some X are Y and some X are not Y.)
Statements:
1. All lakes are ponds.
2. Only a few ponds are wells.
Conclusions:
I. All lakes being wells is a possibility.
II. Some wells are not ponds.
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Answer A. Only I follows
Only I follows. The lakes may all lie inside the part of the ponds that are wells, so the possibility exists. All wells may be ponds, so II is not definite.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-I build script)
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Draw a rectangle, join its opposite corners by both diagonals, and join the mid-points of its top and bottom sides by a vertical line. How many triangles can be counted?
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Answer D. 12
The rectangle with both diagonals has 8 triangles (4 small ones and 4 made of two small ones). The vertical line through the centre splits the top and bottom small triangles into right triangles with a vertex at the centre, adding 4 triangles: two on top (each half of the top triangle) and two at the bottom. Total = 12.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-I build script)
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Which letter comes seventh? A, Z, C, X, E, V, ?
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Answer A. G
Two series alternate: A, C, E, ? (+2) and Z, X, V (-2). The 7th term belongs to the first series: G.
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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Which number should come in place of the question mark? 2, 4, 10, 28, 82, ?
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Answer C. 244
Rule: x 3 - 2. 2 -> 4 -> 10 -> 28 -> 82 -> 82 x 3 - 2 = 244.
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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Take the three statements below to be true even if they seem to differ from commonly known facts.
1. Some actors are singers.
2. All singers are dancers.
3. No dancer is a painter.
Which one of the following conclusions can be drawn from them with certainty?
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Answer D. Some actors are not painters
Some actors are singers, all singers are dancers, and no dancer is a painter; so the actors who are singers are not painters, i.e. some actors are not painters.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-I build script)
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If P means '+', Q means '-', R means 'x' and S means '÷', what is the value of 36 S 4 R 3 P 8 Q 5?
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Answer B. 30
Replace the letters: 36 ÷ 4 x 3 + 8 - 5. Left to right for ÷ and x: 9 x 3 = 27. Then 27 + 8 - 5 = 30.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-C build script)
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A window of a school in Eluru was broken by one of four students, Anil, Bala, Chandra and Durga. Anil says, 'Bala broke it.' Bala says, 'Durga broke it.' Chandra says, 'I did not break it.' Durga says, 'Bala is lying.' If only one of the four statements is true, who broke the window?
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Answer B. Chandra
Check each culprit and count the true statements: Anil 2, Bala 3, Chandra 1, Durga 2. Only 'Chandra' gives exactly one true statement.
Source: Standard reasoning method; answer and every option checked in Python (arrangements, syllogisms and truth puzzles brute-forced for a unique answer)
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Find the next letter in the series: B, E, H, K, N, ?
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Answer C. Q
Positions are 2, 5, 8, 11, 14 (step +3), so the next is 17 = Q.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-C build script)
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Which letter group comes next? DKM, FJN, HIO, ?
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Answer B. JHP
Letter by letter: D -> F -> H -> J (+2); K -> J -> I -> H (-1); M -> N -> O -> P (+1). Next term: JHP.
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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If A @ B means A is the father of B, A # B means A is the daughter of B, A $ B means A is the sister of B and A % B means A is the husband of B, then in the expression P @ Q $ R # S, how is S related to P?
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Answer A. Wife
P @ Q: P is Q's father. Q $ R: Q and R are sisters, so P is R's father too. R # S: R is S's daughter. R's two parents are P (father) and S, so S is P's wife.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-C build script)
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A five-pointed star (a pentagram) is drawn with five straight lines, each line joining two points of the star; there is no outer border. How many triangles are there in the figure?
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Answer B. 10
The 5 tips of the star are 5 small triangles. There are also 5 larger triangles, each with two points of the star (joined by one line) as two vertices and a crossing point of the other lines as the third. Total = 5 + 5 = 10.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-E build script)
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Statements:
1. All mobiles are phones.
2. No phones are laptops.
3. Some laptops are tablets.
Conclusions:
I. Some tablets are not phones.
II. No mobiles are laptops.
Considering the statements to be true even if they appear to be at variance with commonly known facts, which of the conclusions logically follow(s)?
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Answer C. Both I and II follow
Both I and II follow. The tablets that are laptops are not phones, so some tablets are not phones. Mobiles lie inside phones and phones are separate from laptops, so no mobile is a laptop.
Source: Standard reasoning method; answer and every option checked in Python (arrangements, syllogisms and truth puzzles brute-forced for a unique answer)
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Find the next letter in the series: A, C, F, J, O, ?
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Answer A. U
Positions 1, 3, 6, 10, 15 increase by 2, 3, 4, 5. Next is 15 + 6 = 21 = U.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-C build script)
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Find the wrong term in the series: 10, 18, 34, 66, 130, 256, 514
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Answer C. 256
Rule: next = previous x 2 - 2 (10, 18, 34, 66, 130, 258, 514). The term 256 should be 258.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-C build script)
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The numbers 5, 7, 11, 19, 35 follow a rule. Which number follows 35?
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Answer B. 67
Differences: 2, 4, 8, 16. Next difference 32: 35 + 32 = 67. (Equivalently, each term is 2 x previous - 3.)
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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Read the information and answer the question.
A family in Kurnool has eight members P, Q, R, S, T, U, V and W in three generations. There are three married couples.
(i) P is married to Q, and R is the only son of P and Q.
(ii) Q is the mother of S.
(iii) U is the son-in-law of Q.
(iv) R is the husband of T.
(v) V is a girl and T is her mother.
(vi) W is the son of S.
How is U related to R?
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Answer B. Brother-in-law
U is Q's son-in-law, and Q's only daughter is S (R is the only son). So U is the husband of R's sister: R's brother-in-law.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-C build script)
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Six friends, Gita, Hari, Indu, Jagan, Kavya and Lokesh, sit around a circular table at a family function in Ongole, all facing the centre. They are a doctor, an engineer, a lawyer, a teacher, a farmer and a pilot, one profession each. The doctor sits immediately to the left of Gita. Jagan is the lawyer. Indu sits between the doctor and the lawyer, next to both of them. The pilot sits immediately to the right of Gita. The teacher sits immediately to the left of Jagan. Kavya is neither the teacher nor the pilot. Lokesh is an immediate neighbour of Jagan. Gita is not the engineer.
Who sits second to the right of the teacher?
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Answer D. Indu
Clockwise (towards each person's left) from Gita: Gita (farmer), Kavya (doctor), Indu (engineer), Jagan (lawyer), Lokesh (teacher), Hari (pilot). Facing the centre, right = anticlockwise: from Lokesh, one seat right is Jagan, two seats right is Indu.
Source: Standard reasoning method; answer and every option checked in Python (arrangements, syllogisms and truth puzzles brute-forced for a unique answer)
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(Directions for questions 2 - 3)
There are two series given below, of which one is complete and follows a certain pattern. Based on the pattern of the complete series, find the answering term in the other series with missing terms marked by alphabets.
Which number will come in place of D in the following ?
4 25 169 1009 5041 20161
6 A B C D E
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Answer C. 8401
The complete series follows ×8−7, ×7−6, ×6−5, ×5−4, ×4−3. Starting from 6: A = 41, B = 281, C = 1681, D = 1681×5−4 = 8401.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q2, final key
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(Directions for questions 2 - 3)
There are two series given below, of which one is complete and follows a certain pattern. Based on the pattern of the complete series, find the answering term in the other series with missing terms marked by alphabets.
Which number will come in place of E in the following ?
4 7·5 21·25 77·875 354·9375 1957·65625
5 A B C D E
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Answer C. 2282·5
Each term = previous × k + k with k = 1.5, 2.5, 3.5, 4.5, 5.5. From 5: A = 9, B = 25, C = 91, D = 414, E = 414 × 5.5 + 5.5 = 2282.5.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q3, final key
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If pKq means p + q
pLq means p – q
pMq means p % q
pNq means p ÷ q
which of the following equation is incorrect ?
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Answer D. 30N10K4M2L2 = 15
Reading % (M) as multiplication makes options 1-3 true: 5+3−4×6÷2 = −4; 56×12−2÷1 = 670; 5+6−3×4÷8 = 9.5. Option 4 gives 30÷10+4×2−2 = 9, not 15.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q5, final key
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If E * F means 'E is the son of F'
E + F means 'E is the father of F'
E > F means 'E is the daughter of F'
E < F means 'E is the wife of F'
which of the following pair of people represents first cousins with regard to the relation given in the expressions, if it is provided that H is the sister of P ?
Q > R < P + S and M * H < I + J < K + L
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Answer B. MS
Q and S are children of R and her husband P. M is the son of H, and H is P's sister, so M and S are children of siblings: first cousins.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q8, final key
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In a hostel room, five people P, Q, R, S and T read a novel. The one who reads the novel first gives it to R. The one who reads the novel last has taken it from P. T is not the first or the last to read the novel. There are two readers between Q and P. Identify those two readers between Q and P in the same order.
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Answer B. R and T
R is 2nd and P is 4th. T is neither 1st nor 5th, so T is 3rd; Q must be two places from P, so Q is 1st and S is 5th. Order: Q, R, T, P, S.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q9, final key
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There are 5 members in the family by the names Ravi, Madhu, Mahesh, Raghu and Praveen. Praveen is taller than Raghu but not as fat as Raghu. Mahesh is taller than Ravi but shorter than Madhu. Ravi is fatter than Raghu but not as fat as Madhu. Praveen is thinner than Mahesh, who is thinner than Raghu. If they are arranged in an ascending order, i.e., fattest to thinnest, who will come in the middle ?
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Answer B. Raghu
Fattest to thinnest: Madhu > Ravi > Raghu > Mahesh > Praveen. The height clues are not needed; Raghu is in the middle.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q18, final key
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(Directions for questions 19 - 21)
On the eve of Bathukamma festival, the association of Greenfield Apartments had organized games for children. As a part of that, Keerthi, Joshna, Pallavi, Rama and Swetha participated in a race. They got different ranks from 1 to 5 in the race (1 being the fastest and 5 being the slowest).
The following information is also known :
I. Keerthi is not the person who finished the race first.
II. Pallavi didn't get the 5th rank, but she finished the race after Keerthi.
III. Rama finished the race after Joshna.
IV. The sum of ranks of Keerthi and Swetha was equal to the sum of ranks of Pallavi and Rama.
Among the five girls that participated in the race, who was the last to finish the race ?
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Answer A. Swetha
Keerthi and Joshna cannot be last (someone finishes after each), nor can Pallavi. If Rama were 5th, K + S = P + 5 with P > K forces S > 5, impossible. So Swetha is last.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q19, final key
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(Directions for questions 19 - 21)
On the eve of Bathukamma festival, the association of Greenfield Apartments had organized games for children. As a part of that, Keerthi, Joshna, Pallavi, Rama and Swetha participated in a race. They got different ranks from 1 to 5 in the race (1 being the fastest and 5 being the slowest).
The following information is also known :
I. Keerthi is not the person who finished the race first.
II. Pallavi didn't get the 5th rank, but she finished the race after Keerthi.
III. Rama finished the race after Joshna.
IV. The sum of ranks of Keerthi and Swetha was equal to the sum of ranks of Pallavi and Rama.
If the sum of the ranks of Swetha and Pallavi is 8, then who got the 4th rank ?
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Answer B. Rama
Swetha is 5th, so Pallavi is 3rd. Then Keerthi is 2nd, Joshna 1st and, from K + S = P + R (2 + 5 = 3 + R), Rama is 4th.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q20, final key
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(Directions for questions 19 - 21)
On the eve of Bathukamma festival, the association of Greenfield Apartments had organized games for children. As a part of that, Keerthi, Joshna, Pallavi, Rama and Swetha participated in a race. They got different ranks from 1 to 5 in the race (1 being the fastest and 5 being the slowest).
The following information is also known :
I. Keerthi is not the person who finished the race first.
II. Pallavi didn't get the 5th rank, but she finished the race after Keerthi.
III. Rama finished the race after Joshna.
IV. The sum of ranks of Keerthi and Swetha was equal to the sum of ranks of Pallavi and Rama.
Among the five girls, who could not have finished the race after Pallavi ?
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Answer A. Keerthi
Statement II says Pallavi finished after Keerthi, so Keerthi can never be behind Pallavi. The two possible orders are J-K-P-R-S and J-K-R-P-S.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q21, final key
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In a kitchen rack, six boxes are kept one on top of another. The red box is just above the blue box. The purple box is between the black and the green box. The yellow box is between the red and the black box. If the boxes are numbered from 1 to 6 from top to bottom, then the difference between the position of the green and the red box is D. What is the value of D³/2 ?
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Answer D. 32
Top to bottom the order is Green, Purple, Black, Yellow, Red, Blue. Green is 1st and Red 5th, so D = 4 and D³/2 = 64/2 = 32.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q31, final key
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Pointing at a boy in the photograph Bhargav said, "The boy sitting on the left is the son of the wife of the only son of the grandmother of my younger brother." What is the relation between the boy in the photograph and Bhargav ?
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Answer A. Brothers
The only son of the younger brother's grandmother is their father; his wife is their mother; her son (other than Bhargav) is Bhargav's brother.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q32, final key
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Umesh is standing in a bus stand facing the North-west direction. He turns 135° anti-clockwise. After that he turns 45° anti-clockwise. He finally turns 90° clockwise. Which direction is he facing now ?
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Answer B. South-west
Net turn = 135° + 45° − 90° = 90° anti-clockwise. 90° anti-clockwise from North-west is South-west.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q40, final key
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Find the incorrect term in the given series :
193 140 97 62 35 16 5
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Answer D. 193
Working back from the end, the differences 11, 19, 27, 35, 43 rise by 8, so the next difference should be 51 and the first term 140 + 51 = 191, not 193.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q46, final key
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Find the number of triangles in the following figure :
[Figure: a square divided into a 4 × 4 grid with both diagonals drawn]
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Answer C. 48
Each diagonal with one horizontal and one vertical grid line forms a right triangle: 10 pairs of points on a diagonal × 2 orientations = 20 per diagonal, 40 in all. Add 8 triangles with apex at the centre whose base lies on grid lines 1 or 3 units, or the outer edges, from the centre: 40 + 8 = 48.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q49, final key
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Each of seven boys named A, B, C, D, E, F and G has an exam on a different day of a week, starting from Sunday and ending on Saturday of the same week. Only two persons have their exam between C and A. B has his exam immediately before E. C has his exam immediately before F. Only G has his exam after A. Which of the following options represents the correct match of a boy and the day of his exam ?
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Answer C. C : Tuesday
Only G is after A, so A is Friday and G Saturday. Two people between C and A puts C on Tuesday and F on Wednesday. B and E take Sunday and Monday, leaving Thursday for D.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q50, final key
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Choose the correct suitable figure among the four alternatives A, B, C and D given below that would complete the given figure matrix.
[Figure: 3 × 3 figure matrix of squares with diagonal and V-shaped lines, the last cell marked '?', and answer figures A, B, C, D]
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Answer A. B
The lines in the matrix join up across cells to form a continuous pattern; the missing cell must continue the lines from its neighbours, which only figure B does (as per the final key).
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q52, final key
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Read the below given statements followed by conclusions. Choose the conclusion which logically follows from the given statements :
Statements :
All professors are doctors.
All doctors are engineers.
Some professors are lawyers.
Conclusions :
I. All professors are engineers.
II. All engineers are lawyers.
III. Some doctors are lawyers.
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Answer B. Only conclusions I and III follow
Professors ⊂ doctors ⊂ engineers gives I. The professors who are lawyers are also doctors, so some doctors are lawyers (III). Nothing says all engineers are lawyers.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q55, final key
1.2.1Clocks, calendars, ages and the number systemNotes
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A two-digit number is four times the sum of its digits. If 18 is added to the number, its digits are reversed. What is the number?
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Answer A. 24
10a + b = 4(a + b) gives b = 2a. Adding 18 reverses the digits, so 9(b - a) = 18 and b = a + 2. Then a = 2, b = 4; the number is 24.
Source: Standard arithmetic / number-theory method; every option computed and checked in Python (puzzles brute-forced for a unique answer)
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Mahatma Gandhi's date of birth is 2 October 1869. Find the day of the week of his birth.
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Answer A. Saturday
Odd days: 1600 years = 0 and 200 years = 3, so 1800 years = 3; 1801-1868 = 68 years with 17 leap years = 85 = 1 odd day; 1 January to 2 October 1869 = 275 days = 2 odd days. Total = 3 + 1 + 2 = 6, i.e. Saturday.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-I build script)
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A number leaves a remainder of 47 when divided by 342. What remainder will it leave when divided by 18?
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Answer C. 11
N = 342k + 47 and 342 is a multiple of 18 (18 x 19). So N mod 18 = 47 mod 18 = 11.
Source: Standard arithmetic / number-theory method; every option computed and checked in Python (puzzles brute-forced for a unique answer)
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Add up the factorials 1!, 2!, 3!, ..., 50!. Which digit is in the units place of the total?
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Answer C. 3
From 5! onwards each factorial ends in 0. 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33, so the unit digit is 3.
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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How many three-digit numbers have the sum of their digits equal to 5?
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Answer C. 15
Let the digits be a, b, c with a at least 1. Put a = a' + 1: a' + b + c = 4 has C(6, 2) = 15 solutions, all with digits below 10. (Checked by listing all three-digit numbers.)
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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A number leaves a remainder of 24 when divided by a certain divisor. Twice the number leaves a remainder of 11 when divided by the same divisor. What is the divisor?
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Answer A. 37
If N = Dk + 24, then 2N = 2Dk + 48. This leaves 11, so 48 - 11 = 37 is a multiple of D bigger than 24: D = 37.
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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Let x = (√3 + 1)/(√3 - 1). Then x + 1/x equals
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Answer D. 4
x = (√3 + 1)^2/(3 - 1) = (4 + 2√3)/2 = 2 + √3. Then 1/x = 2 - √3, so x + 1/x = 4.
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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How many zeros are there at the end of 125! (125 factorial)?
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Answer A. 31
Trailing zeros = number of factors of 5 in 125! = 25 + 5 + 1 = 31 (factors of 2 are more plentiful).
Source: Standard arithmetic / number-theory method; every option computed and checked in Python (puzzles brute-forced for a unique answer)
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Find the reflex angle formed by the hands of a clock when the time is 5:15.
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Answer B. 292.5 degrees
Angle = |30 x 5 - 5.5 x 15| = |150 - 82.5| = 67.5 degrees. The reflex angle is 360 - 67.5 = 292.5 degrees.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-I build script)
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How many days are there from 26 January 2025 to 15 August 2025, counting both the days?
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Answer C. 202
Days: January 26-31 = 6, February 28, March 31, April 30, May 31, June 30, July 31, August 1-15 = 15. Total = 6+28+31+30+31+30+31+15 = 202.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-E build script)
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At what time between 7 o'clock and 8 o'clock will the hands of a clock be 10 degrees apart for the first time?
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Answer A. 36 4/11 minutes past 7
At 7:00 the minute hand is 210 degrees behind the hour hand and gains 5.5 degrees per minute. The gap first becomes 10 degrees when it has gained 200 degrees: M = 200/5.5 = 400/11 = 36 4/11 minutes past 7. (The second time, 10 degrees past the hour hand, is at 40 minutes past 7.)
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-E build script)
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If 808 × 8008 × 80008 = A and the sum of all the digits in the A is M, what will be the value of √M ?
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Answer A. 8
808 × 8008 = 6,470,464 and × 80008 gives A = 517,688,883,712. Its digits add to M = 64, so √M = 8.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q1, final key
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Rajani has a digital watch that shows time in a 24-hour format. The time on the watch shows 23:45. After passing 'A' minutes the watch shows the time in such a way that the four whole numbers are again arranged in ascending order from left to right. Then what will be the value of A × A ?
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Answer D. 9604
Read 'arranged in ascending order' as four consecutive ascending digits, as at 23:45 (2-3-4-5). The next such time is 01:23 (0-1-2-3): from 23:45 that is 15 + 83 = 98 minutes, so A × A = 98² = 9604.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q7, final key
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The sum of all the three-digit natural numbers, which on being divided by 5, leave a remainder equal to 4 is XXYZA. What is the value of Y + Z ?
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Answer A. 9
The numbers are 104, 109, ..., 999: 180 terms. Sum = 180 × (104 + 999)/2 = 99,270, so X = 9, Y = 2, Z = 7 and Y + Z = 9.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q11, final key
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The ratio of Pooja's age to Ajay's age is 1 : 3. The ratio of their ages after 8 years will be 1 : 2. How many years ago was the ratio of their ages 1 : 5 ?
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Answer B. 4 years
(x + 8)/(3x + 8) = 1/2 gives x = 8: ages 8 and 24. (8 − t)/(24 − t) = 1/5 gives t = 4.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q22, final key
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Bhaskar bought a piggy bank for his daughter Kavitha. Kavitha started saving her money. On 1st March, 2024 she saved ₹ 1 and every day starting from 2nd March she saved ₹ 1 more than the previous day. Find the first date after 1st March, 2024 at the end of which her total savings will be a perfect square.
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Answer D. 8th March, 2024
After n days the total is n(n + 1)/2. After day 1 it is 1; the next perfect square is at n = 8: 36. So 8 March.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q23, final key
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In a classroom, a teacher asked, "How many 2-digit numbers exist which have the property that the product of factorials of its digits > the sum of factorials of its digits ?" Then what will be the answer of the students present there ?
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Answer B. 63
a!·b! > a! + b! fails when a digit is 0 or 1 (product ≤ sum) and for 22 (4 = 4). Digits 2-9 give 8 × 8 = 64 numbers; removing 22 leaves 63.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q26, final key
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If 12th June, 2024 will be a Wednesday, then what day of week will it be on 19th November, 2024 ?
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Answer D. Tuesday
Days from 12 June to 19 November = 18 + 31 + 31 + 30 + 31 + 19 = 160 = 22 weeks + 6 days. Wednesday + 6 = Tuesday.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q39, final key
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If 8·92 × 4·15 × 7·69 × ? = 1565·67631, what will come in the place of '?' ?
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Answer D. 5·5
8.92 × 4.15 = 37.018 and 37.018 × 7.69 = 284.66842; 1565.67631 ÷ 284.66842 = 5.5.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q41, final key
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Chandra is a confused typist. While typing the numbers from 600 to 799 (both included), he typed 8 wherever he was supposed to type 6. Then the total number of times he had typed 8 is :
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Answer A. 180
From 600 to 799 the digit 6 occurs 100 (hundreds) + 20 (tens) + 20 (units) = 140 times, and the digit 8 occurs 20 (tens) + 20 (units) = 40 times. All of these are typed as 8: 140 + 40 = 180.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q45, final key
1.3.1Arithmetic: ratio, percentage, interest, time, work and distanceNotes
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Read the information and answer the question.
An electronics shop in Vijayawada buys a mixer-grinder for Rs 4,000 and marks it 40% above the cost price. During a festival sale it gives two successive discounts of 15% and 10% on the marked price.
Instead of the two discounts, what single discount on the marked price would give the shop a profit of exactly 12%?
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Answer A. 20%
Required SP = 4,000 x 1.12 = 4,480. Discount = (5,600 - 4,480)/5,600 x 100 = 20%.
Source: Standard arithmetic method; every option computed and checked in Python
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A train crosses a pole in 15 seconds and a 150 m long platform in 24 seconds. What is the length of the train?
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Answer B. 250 m
The extra 9 seconds are for the 150 m platform, so speed = 150/9 = 50/3 m/s. Length = 50/3 x 15 = 250 m.
Source: Standard arithmetic method; every option computed and checked in Python
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Read the information and answer the question.
A cashew trader in Palasa buys 250 kg of cashew kernels at Rs 640 per kg and pays transport charges equal to 5% of the purchase cost. During grading, 10 kg is found unfit for sale. He fixes the marked price of the remaining kernels at 25% above his total cost per saleable kg. He sells half of the saleable kernels at the marked price and the other half at a discount of 10% on the marked price.
What is the trader's total cost per saleable kg?
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Answer B. Rs 700
Total cost = 250 x 640 = 1,60,000 plus 5% transport = Rs 1,68,000. Saleable kernels = 240 kg, so cost per saleable kg = 1,68,000/240 = Rs 700.
Source: Standard arithmetic method; every option computed and checked in Python
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Rs 7,800 is divided among Anitha, Bharathi and Chaitanya in the ratio 1/2 : 1/3 : 1/4. What is Bharathi's share?
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Answer C. Rs 2,400
Multiply 1/2 : 1/3 : 1/4 by 12 to get 6 : 4 : 3 (13 parts). Bharathi's share = 7,800 x 4/13 = Rs 2,400.
Source: Standard arithmetic method; every option computed and checked in Python
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Read the information and answer the question.
In a test at a school in Visakhapatnam, five students A, B, C, D and E scored marks out of 100. The average of A and B is 64, of B and C is 71, of C and D is 76, of D and E is 72, and of A and E is 61.
What is the average mark of all five students?
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Answer A. 68.8
Pair totals: 128, 142, 152, 144, 122; their sum 688 counts each student twice, so the total = 344. Average = 344/5 = 68.8.
Source: Standard arithmetic / number-theory method; every option computed and checked in Python (puzzles brute-forced for a unique answer)
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Pipes A and B can fill a tank in 12 minutes and 18 minutes respectively. Both are opened together. After how many minutes should B be closed so that the tank is full exactly 9 minutes after the start?
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Answer A. 4.5 minutes
A works for all 9 minutes: 9/12 = 3/4. B must fill 1/4, which takes 18/4 = 4.5 minutes.
Source: Standard arithmetic method; every option computed and checked in Python
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A trader sells a bicycle at a loss. The loss is equal to one-third of the selling price. What is his loss percentage?
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Answer A. 25%
Loss = S/3, so CP = S + S/3 = 4S/3. Loss% = (S/3)/(4S/3) x 100 = 25%.
Source: Standard arithmetic method; every option computed and checked in Python
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Read the information and answer the question.
Three teams P, Q and R are lining a canal near Polavaram. Working alone, P can finish the job in 30 days, Q in 40 days and R in 60 days. In the actual plan, P and Q start the work together; after 8 days P leaves and R joins Q, and Q and R finish the job together. The total payment of Rs 60,000 is shared in proportion to the work done by each team.
Under the actual plan, for how many days do Q and R work together?
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Answer A. 12.8 days
In 8 days P and Q do 8 x (4 + 3)/120 = 56/120. Left: 64/120. Q and R do (3 + 2)/120 per day, so they need 64/5 = 12.8 days.
Source: Standard mental-ability method; answer and every option computed and checked in Python (MA-G build script)
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In a 1 km race, A beats B by 40 m, and B beats C by 50 m. By how many metres does A beat C?
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Answer D. 88 m
When A runs 1,000 m, B runs 960 m. C runs 950 m for every 1,000 m of B, so C runs 960 x 0.95 = 912 m. A beats C by 88 m.
Source: Standard arithmetic method; every option computed and checked in Python
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Read the information and answer the question.
A cashew trader in Palasa buys 250 kg of cashew kernels at Rs 640 per kg and pays transport charges equal to 5% of the purchase cost. During grading, 10 kg is found unfit for sale. He fixes the marked price of the remaining kernels at 25% above his total cost per saleable kg. He sells half of the saleable kernels at the marked price and the other half at a discount of 10% on the marked price.
What is the trader's overall profit percentage on his total outlay?
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Answer B. 18.75%
Receipts = 120 x 875 + 120 x 787.50 = 1,05,000 + 94,500 = Rs 1,99,500. Profit = 1,99,500 - 1,68,000 = Rs 31,500, which is 31,500/1,68,000 x 100 = 18.75%.
Source: Standard arithmetic method; every option computed and checked in Python
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Ramesh's salary is 40% more than Bhaskar's salary. Chandu's salary is 20% less than Ramesh's salary. By what percentage is Chandu's salary more than Bhaskar's salary?
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Answer D. 12%
Take Bhaskar = 100. Ramesh = 140. Chandu = 140 x 0.80 = 112. So Chandu earns 12% more than Bhaskar.
Source: Standard arithmetic method; every option computed and checked in Python
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A boat goes 36 km downstream in 3 hours and 20 km upstream in 4 hours on the Godavari. What is the speed of the stream?
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Answer A. 3.5 km/h
Downstream = 36/3 = 12 km/h, upstream = 20/4 = 5 km/h. Stream = (12 - 5)/2 = 3.5 km/h.
Source: Standard arithmetic method; every option computed and checked in Python
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A loan grows at 10% a year with interest added yearly. The interest charged in the second year alone is Rs 1,320. Find the amount originally borrowed.
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Answer C. Rs 12,000
Interest for the 2nd year = 10% of the amount after 1 year = 0.10 x 1.10P = 0.11P. So 0.11P = 1,320 and P = Rs 12,000.
Source: Standard arithmetic method; every option computed and checked in Python
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₹3,600 is divided among A, B and C so that A gets 2/3 of what B and C together get, and B gets 1/4 of what A and C together get. What is B's share?
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Answer D. ₹720
A = 2/(2+3) x 3,600 = 1,440. B = 1/(1+4) x 3,600 = 720. C = 3,600 - 1,440 - 720 = 1,440. Check: 720 = (1,440 + 1,440)/4.
Source: Standard arithmetic / number-theory method; every option computed and checked in Python (puzzles brute-forced for a unique answer)
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A pipe can fill a tank in 8 hours. Because of a leak at the bottom, it takes 10 hours to fill. In how many hours can the leak alone empty the full tank?
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Answer B. 40 hours
Leak rate = 1/8 - 1/10 = 1/40 of the tank per hour, so the leak empties it in 40 hours.
Source: Standard arithmetic method; every option computed and checked in Python
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Ajay can do a job in 10 days and Vijay in 15 days. They do it together and receive Rs 4,500. What is Ajay's share if payment is in proportion to work done?
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Answer A. Rs 2,700
Rates 1/10 : 1/15 = 3 : 2. Ajay's share = 4,500 x 3/5 = Rs 2,700.
Source: Standard arithmetic method; every option computed and checked in Python
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An employee's salary is first increased by 20% and then the new salary is decreased by 20%. What is the net effect on the original salary?
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Answer A. 4% decrease
Net change = a + b + ab/100 = 20 + (-20) + (20 x -20)/100 = -4%, i.e. a 4% decrease (1.20 x 0.80 = 0.96).
Source: Standard arithmetic method; every option computed and checked in Python
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A and B together can do a work in 12 days, B and C together in 15 days, and C and A together in 20 days. In how many days can A alone do it?
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Answer C. 30 days
2(A + B + C) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5, so A + B + C = 1/10. A = 1/10 - (B + C) = 1/10 - 1/15 = 1/30, i.e. 30 days.
Source: Standard arithmetic method; every option computed and checked in Python
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The population of a village is 50,000. The annual birth rate is 4.5% and the annual death rate is 2.5% of the population at the start of each year. What will the population be after 2 years?
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Answer A. 52,020
Net growth = 4.5% - 2.5% = 2% per year. Population = 50,000 x (1.02)^2 = 52,020.
Source: Standard arithmetic method; every option computed and checked in Python
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Rs 20,000 is invested for 2 1/2 years at 10% a year. Interest is added to the principal at the end of each full year, and simple interest is paid for the remaining half-year. How much interest is earned in all?
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Answer B. Rs 5,410
For the last half-year, interest is simple at 5% on the amount after 2 years. Amount = 20,000 x 1.1 x 1.1 x 1.05 = Rs 25,410, so CI = Rs 5,410.
Source: Standard arithmetic method; every option computed and checked in Python
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Rs 24,000 is deposited at compound interest at 10% for the first year and 12% for the second year, compounded annually. What is the compound interest for 2 years?
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Answer D. Rs 5,568
Amount = 24,000 x 1.10 x 1.12 = Rs 29,568, so CI = 29,568 - 24,000 = Rs 5,568.
Source: Standard arithmetic method; every option computed and checked in Python
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Amit has to travel distances of 66 km, 88 km and 110 km on three consecutive days. He travels with the greatest possible constant speed (in km/hr) on all the three days so that he covers the respective distances in an integer number of hours on each day. How many hours will it take him to complete the journey ?
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Answer B. 12 hours
The greatest speed that divides 66, 88 and 110 exactly is their HCF, 22 km/h. Time = 3 + 4 + 5 = 12 hours.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q4, final key
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(Directions for questions 12 - 15)
Read the following instructions carefully and answer the questions given below :
Nandu and Mohan decided to sell their Apple 6 Series watches each at ₹ 42,000 to Karthik and Ganesh respectively. In each case the selling price of ₹ 42,000 was arrived at by increasing the cost price by 25%. While Nandu gives a discount of 10% on the first ₹ 12,000, 8% on the next ₹ 16,000 and 5% on the rest to the buyer Karthik, Mohan gives a discount of 8% on the first ₹ 16,000, 7% on the next ₹ 8,000 and 5% on the rest to his buyer Ganesh. These discounts were however subject to the condition, that the buyers make the payment on time, failing which the discount gets reduced by 1% for every delay of a week.
If Nandu and Mohan got all the payments on time, what is the approximate percentage of profit of the person getting the higher profit ?
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Answer C. 17%
Cost price = 42,000/1.25 = ₹33,600. Nandu's discount = 1,200 + 1,280 + 700 = ₹3,180 (profit ₹5,220); Mohan's = 1,280 + 560 + 900 = ₹2,740 (profit ₹5,660). Mohan earns more: 5,660/33,600 ≈ 16.8% ≈ 17%.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q12, final key
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(Directions for questions 12 - 15)
Read the following instructions carefully and answer the questions given below :
Nandu and Mohan decided to sell their Apple 6 Series watches each at ₹ 42,000 to Karthik and Ganesh respectively. In each case the selling price of ₹ 42,000 was arrived at by increasing the cost price by 25%. While Nandu gives a discount of 10% on the first ₹ 12,000, 8% on the next ₹ 16,000 and 5% on the rest to the buyer Karthik, Mohan gives a discount of 8% on the first ₹ 16,000, 7% on the next ₹ 8,000 and 5% on the rest to his buyer Ganesh. These discounts were however subject to the condition, that the buyers make the payment on time, failing which the discount gets reduced by 1% for every delay of a week.
If Karthik defaults to make payment by 1 and 2 weeks in the second and third payments respectively, what would be the profit of Nandu on the sale of a watch ?
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Answer C. ₹ 5,660
Discounts become 10% of 12,000 = 1,200, 7% of 16,000 = 1,120 and 3% of 14,000 = 420: total ₹2,740. Selling price = ₹39,260, so profit = 39,260 − 33,600 = ₹5,660.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q13, final key
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(Directions for questions 12 - 15)
Read the following instructions carefully and answer the questions given below :
Nandu and Mohan decided to sell their Apple 6 Series watches each at ₹ 42,000 to Karthik and Ganesh respectively. In each case the selling price of ₹ 42,000 was arrived at by increasing the cost price by 25%. While Nandu gives a discount of 10% on the first ₹ 12,000, 8% on the next ₹ 16,000 and 5% on the rest to the buyer Karthik, Mohan gives a discount of 8% on the first ₹ 16,000, 7% on the next ₹ 8,000 and 5% on the rest to his buyer Ganesh. These discounts were however subject to the condition, that the buyers make the payment on time, failing which the discount gets reduced by 1% for every delay of a week.
If Ganesh defaults in each payment by 2 weeks, what would be the profit of Mohan on the sale of a watch ?
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Answer C. ₹ 6,500
Each rate drops by 2%: 6% of 16,000 = 960, 5% of 8,000 = 400, 3% of 18,000 = 540, total ₹1,900. Selling price ₹40,100, profit = 40,100 − 33,600 = ₹6,500.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q14, final key
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(Directions for questions 12 - 15)
Read the following instructions carefully and answer the questions given below :
Nandu and Mohan decided to sell their Apple 6 Series watches each at ₹ 42,000 to Karthik and Ganesh respectively. In each case the selling price of ₹ 42,000 was arrived at by increasing the cost price by 25%. While Nandu gives a discount of 10% on the first ₹ 12,000, 8% on the next ₹ 16,000 and 5% on the rest to the buyer Karthik, Mohan gives a discount of 8% on the first ₹ 16,000, 7% on the next ₹ 8,000 and 5% on the rest to his buyer Ganesh. These discounts were however subject to the condition, that the buyers make the payment on time, failing which the discount gets reduced by 1% for every delay of a week.
What would be the difference in the profits of Nandu and Mohan if both the buyers default in each payment by a week ?
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Answer A. ₹ 440
Nandu: 9%, 7%, 4% give 1,080 + 1,120 + 560 = ₹2,760 (profit ₹5,640). Mohan: 7%, 6%, 4% give 1,120 + 480 + 720 = ₹2,320 (profit ₹6,080). Difference = ₹440.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q15, final key
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Madhu purchased a bike in the year 2024 at the cost of ₹ 78,000. It depreciates in value, 10% the first year, 9·5% the next year, 9% the third year and so on, with all the percentages applied on the original cost of the bike. What will be its value in the year 2029 ?
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Answer D. ₹ 42,900
2024 to 2029 is 5 years: 10 + 9.5 + 9 + 8.5 + 8 = 45% of the original cost. Value = 78,000 × 0.55 = ₹42,900.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q16, final key
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Neelima places an order for 'p' number of sweets from Agarwal Sweet Shop that produces 'q' number of sweets every day. r% of the total number of sweets produced in a day fail quality check and are discarded. What will be the number of days in which the order will be completed ?
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Answer C. 100p/((100 – r)q)
Good sweets per day = q(100 − r)/100. Days = p ÷ that = 100p/((100 − r)q).
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q17, final key
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Jaya, a shopkeeper, initially had 'n' pens. A customer bought 10% pens from n, then another customer bought 20% of the remaining pens, after that one more customer purchased 25% of the remaining pens. Finally, Jaya was left with 270 pens in her shop. How many pens were there initially in her shop ?
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Answer D. 500
n × 0.9 × 0.8 × 0.75 = 0.54n = 270, so n = 500.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q24, final key
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A preliminary test was conducted by a recruiting agency which consisted of 100 questions. Madhuri takes that test and attempts all the questions in it. For every correct answer 1 mark is awarded, while a wrong answer is penalized as follows :
I. One-fifth of the questions carry 1/10 negative marking.
II. One-tenth of the questions carry 1/5 negative marking.
III. Remaining questions will carry 1/2 negative marking.
Unattempted questions carry 0 marks. If maximum and minimum possible marks scored by Madhuri are X and Y respectively, then (X – Y)/17·375 is :
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Answer D. 8
X = 100 (all correct). Y = −(20 × 0.1 + 10 × 0.2 + 70 × 0.5) = −39 (all wrong). (100 + 39)/17.375 = 139/17.375 = 8.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q25, final key
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Krishna, Suresh and Raghava together started a business with the initial investments of ₹ 15,000, ₹ 18,000 and ₹ 20,000 respectively. After a year, Krishna and Suresh increased their investments by ₹ 5,000 and ₹ 2,000 respectively, while Raghava withdrew ₹ 5,000. After one more year, Krishna, Suresh and Raghava increased their investments by 20%, 25% and 40% respectively. It was decided that Raghava would receive 20% of the total profit received by them for his extra work and the rest of the profit would be distributed according to their investments. After 3 years, the total profit received by them was ₹ 53,400. If the extra profit received by Raghava was excluded, then find the ratio of profit shares of Krishna, Suresh and Raghava :
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Answer C. 59 : 63 : 56
Capital-years: Krishna 15,000 + 20,000 + 24,000 = 59,000; Suresh 18,000 + 20,000 + 25,000 = 63,000; Raghava 20,000 + 15,000 + 21,000 = 56,000. Ratio 59 : 63 : 56.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q27, final key
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John has a piggy bank which contains 25-paise, 50-paise and 1-rupee coins. There are 220 coins in all and the total amount in the piggy bank is ₹ 160. If there are thrice as many 1-rupee coins as there are 25-paise coins, then what is the number of 50-paise coins in the piggy bank ?
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Answer C. 60
Let 25-paise coins = x, 1-rupee coins = 3x, 50-paise = 220 − 4x. Value: 0.25x + 3x + 0.5(220 − 4x) = 160 gives 1.25x = 50, x = 40, so 50-paise coins = 60.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q28, final key
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Sekhar delivered a 20 litre solution of milk and water in the ratio 3 : 2 to Bhaskar. Bhaskar removed 10 litres from this, replaced it with pure milk and delivered it to Karthik and Karthik repeated this process and delivered it to Varun. What is the ratio of milk and water in the solution received by Varun ?
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Answer D. 9 : 1
Start: 12 L milk, 8 L water. Each step removes half the mixture and adds 10 L milk, halving the water: 8 → 4 → 2 L. Varun gets 18 L milk and 2 L water, i.e. 9 : 1.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q29, final key
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In a new year party, out of the total guests, 60% are women. If 80% of the guests are married couples (form a pair of husband and wife) and the rest are unmarried, then which of the following statements are correct ?
I. All men are married.
II. More than 30% of women are unmarried.
Select the correct answer using the codes given below :
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Answer C. Both I and II
Of 100 guests, 60 are women and 40 men. 80 married guests form 40 couples, so all 40 men are married and 40 women are married. The other 20 women (33.3% of women) are unmarried.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q30, final key
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An electrical lineman has to climb on a pole of height 50 meters to fix the wires. In the first one minute he climbed up 5 meters, in the next one minute he slipped down by 2 meters. Further, he repeated the same process till he reached the top of the pole. Then at what height was he at the 24th minute and how many times did he have to go upwards to reach the top of the pole ?
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Answer C. 36 meters, 16
Each 2-minute cycle gains 3 m, so after 24 minutes (12 cycles) he is at 36 m. After 15 cycles he is at 45 m and the 16th climb of 5 m takes him to 50 m.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q34, final key
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Sandeep invested a certain amount in Reliance Infra Private Limited which offers compound interest (compounded annually) at 5% p.a. and an amount equal to 50% of that amount was invested in Reliance Jio, which offers compound interest (compounded annually) at 10% p.a. The duration of investment for both the companies was 2 years. If the difference between the amount received from both the companies is ₹ 6,965, what is the difference between the sums invested in the two companies ?
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Answer A. ₹ 7,000
With P in the first company: 1.1025P − 0.5P × 1.21 = 0.4975P = 6,965, so P = ₹14,000. The sums are ₹14,000 and ₹7,000; their difference is ₹7,000.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q35, final key
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Kalpana's project report consists of 40 pages, each of 75 lines with 80 characters in each line. The lines are reduced to 70, but the number of characters is increased to 95 per line. What is the approximate change in the number of pages ?
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Answer B. – 10%
Total characters = 40 × 75 × 80 = 2,40,000. New page holds 70 × 95 = 6,650, so pages ≈ 36.1, a change of about −9.8% ≈ −10%.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q36, final key
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A, B and C are hired for a painting job. Working together, A and B can do a job in 12 days, B and C can do the same job in 8 days, while A and C can do it in 16 days. Then how long will it take, if all of them work together to complete the job ?
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Answer D. 7 5/13 days
2(A + B + C) = 1/12 + 1/8 + 1/16 = 13/48, so A + B + C = 13/96 per day and the time is 96/13 = 7 5/13 days.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q37, final key
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Pawan appeared for examination in 5 subjects. The maximum marks are the same for each subject. His marks in these 5 subjects are in the proportion 4 : 5 : 6 : 7 : 8 and overall he scored 60%. In how many subjects did he score less than 50% of the maximum marks ?
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Answer A. 1
Total 30x = 60% of 5M, so x = M/10. The marks are 40%, 50%, 60%, 70% and 80% of the maximum, so only one subject (40%) is below 50%.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q42, final key
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It takes Madhu 2t minutes to complete Form-A which has k questions and 3t minutes to complete Form-B which has k/2 questions. If Madhu answers all the questions, how much more time does he take on an average to answer a Form-B question than he takes to answer a Form-A question ?
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Answer C. 4t/k
Form-A: 2t/k minutes per question. Form-B: 3t ÷ (k/2) = 6t/k per question. Difference = 6t/k − 2t/k = 4t/k.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q43, final key
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A professor of pharmaceutical sciences in his classroom defines that the 'half-life of a drug substance is the time period in which the drug substance becomes just half of it'. If it is known that the half-life of a drug Adrenaline is 800 years, then after 3200 years, 1200 gm of Adrenaline becomes X. Which of the following is a possible value for the sum of all digits in X ?
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Answer A. 12
3200 years is 4 half-lives, so X = 1200 ÷ 2⁴ = 75 gm. The digit sum of 75 is 7 + 5 = 12.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q44, final key
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Ganesh donated 50% of his saving of ₹ 1,26,588 to Ayodhya Trust and he invested the rest of the amount at 10% compound interest per annum, separately for his children Krishna and Veda in such a way that when they attain the age of 18 years, they would receive the same amount. The age of Krishna is 13 years and that of Veda is 11 years. Then the amount invested for Veda must be :
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Answer B. ₹ 28,640
₹63,294 is invested for 5 years (Krishna) and 7 years (Veda). K(1.1)⁵ = V(1.1)⁷ gives K = 1.21V, so 2.21V = 63,294 and V = 28,639.8 ≈ ₹28,640.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q47, final key
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Vande Bharat Express travelling at 63 kmph can cross a platform of Visakhapatnam railway station which is 199·5 m long in 21 seconds. How much time would Vande Bharat Express take to completely cross (from the moment they meet) Duronto Express 157 m long and travelling at 54 kmph in the opposite direction to it ?
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Answer B. 10 seconds
63 kmph = 17.5 m/s, so train + platform = 367.5 m and the train is 168 m. Relative speed 117 kmph = 32.5 m/s; (168 + 157) ÷ 32.5 = 10 s.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q53, final key
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In a recreation club, Sam, Gautham, Nagesh, Deepak and Anup were playing cards. Sam says to Gautham, "If you give me three cards, you will have as many as Anup has and if I give you three cards, you will have as many as Deepak has." Sam and Gautham together have 10 cards more than what Deepak and Anup together have. If Gautham has two cards more than what Nagesh has and the total number of cards be 133, how many cards does Gautham have ?
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Answer D. 25
A = G − 3 and D = G + 3, so D + A = 2G and S = G + 10. N = G − 2. Total 5G + 8 = 133, so G = 25.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q58, final key
1.4.1Mensuration and geometryNotes
- Q101 Paper II Mock 1, Q52
What is the area of a triangle whose sides are 13 cm, 14 cm and 15 cm?
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Answer D. 84 cm²
s = (13 + 14 + 15)/2 = 21. By Heron's formula, area = √(21 × 8 × 7 × 6) = √7056 = 84 cm².
Source: NCERT Mathematics Class IX (Ch. 10 Heron's Formula, Ch. 11 Surface Areas and Volumes) and Class X (Ch. 11 Areas Related to Circles, Ch. 12 Surface Areas and Volumes); every number computed and checked in Python
- Q102 Paper II Mock 1, Q53
A cylindrical pillar has a radius of 7 cm and a height of 10 cm. Taking π = 22/7, what is its curved surface area?
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Answer D. 440 cm²
CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².
Source: NCERT Mathematics Class IX (Ch. 10 Heron's Formula, Ch. 11 Surface Areas and Volumes) and Class X (Ch. 11 Areas Related to Circles, Ch. 12 Surface Areas and Volumes); every number computed and checked in Python
- Q103 Paper II Mock 1, Q54
Rain falls to a depth of 2 cm on a flat roof measuring 22 m × 20 m. All the water is collected in a cylindrical tank with a base diameter of 2 m. To what height does the water rise in the tank? (Take π = 22/7.)
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Answer C. 2.8 m
Volume of water = 22 × 20 × 0.02 = 8.8 m³. Tank base area = (22/7) × 1² = 22/7 m². Height = 8.8 × 7/22 = 2.8 m.
Source: NCERT Mathematics Class IX (Ch. 10 Heron's Formula, Ch. 11 Surface Areas and Volumes) and Class X (Ch. 11 Areas Related to Circles, Ch. 12 Surface Areas and Volumes); every number computed and checked in Python
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Consider the following statements :
I. An equilateral triangle in a circle will have the maximum area compared to other triangles inside the same circle.
II. If the height of an equilateral triangle is 10 cm, its area will be equal to 100√3/3 cm².
III. If three sides of a triangle are 5, 12 and 13 cm, then the circumradius of the triangle is 2·5 cm.
IV. Scalene triangle is a triangle with none of the sides equal to any other sides.
Which among the above given statements are correct ?
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Answer B. I, II and IV only
The inscribed equilateral triangle has the largest area. Height 10 gives side 20/√3 and area h²/√3 = 100√3/3. A 5-12-13 triangle is right-angled, so its circumradius is 13/2 = 6.5 cm, not 2.5 cm.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q10, final key
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Consider the following statements :
I. A Parallelogram having all the sides equal is a Rhombus.
II. All the Rhombuses are Parallelograms, but the reverse is not true.
III. A Rhombus may or may not be a Square, but all Squares are Rhombuses.
Which among the above given statements are correct ?
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Answer D. All the above
A rhombus is a parallelogram with all sides equal, so I and II hold. A square is a rhombus with right angles, so every square is a rhombus but not every rhombus is a square.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q33, final key
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If a circle touching all the n sides of a polygon of perimeter 2p has radius r, then the area of the polygon is :
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Answer D. pr
Joining the centre to the vertices splits the polygon into n triangles of height r, so area = ½ × r × perimeter = ½ × r × 2p = pr.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q57, final key
1.5.1Data interpretation, central tendency and probabilityNotes
- Q107 Paper II Mock 1, Q55
A student of a Kurnool school scored 68, 74, 81, 59 and 78 marks in five subjects. How many marks must she score in the sixth subject so that her average over the six subjects is exactly 75?
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Answer B. 90
Required total = 6 x 75 = 450. Present total = 68 + 74 + 81 + 59 + 78 = 360. Marks needed = 450 - 360 = 90.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-E build script)
- Q108 Paper II Mock 1, Q56
Number of tourists (in thousands) who visited Araku Valley in three years (hypothetical data): 2021 - 40, 2022 - 55, 2023 - 66. What was the percentage increase in tourists from 2022 to 2023?
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Answer A. 20%
Increase = 66 - 55 = 11 thousand; percentage increase = 11/55 x 100 = 20%.
Source: Standard reasoning method; answer and every option computed and checked in Python (MA-E build script)
- Q109 Paper II Mock 1, Q57
From the frequency table below, find the mean.
x: 1, 2, 3, 4
f: 3, 5, 8, 4
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Answer B. 2.65
Mean = Σfx / Σf = (1×3 + 2×5 + 3×8 + 4×4) / 20 = 53 / 20 = 2.65.
Source: Standard statistics method; answer and every option computed and checked in Python
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The letters of the word 'ENTRANCE' are arranged in such a way that all vowels are always written together. How many such ways of writing the word is possible ?
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Answer A. 1080
Vowels E, A, E form one block; with consonants N, T, R, N, C that is 6 units with N repeated: 6!/2! = 360. Inside the block 3!/2! = 3. Total 360 × 3 = 1080.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q38, final key
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Study the following bar chart and answer the question that is given below. The chart shows the number of students that appeared for and passed B.Tech. examination from different IITs in 2024.
[Bar chart: Number of students who appeared for and passed B.Tech. exam from different IITs in India]
IIT Appeared Passed Kanpur 210 160 Madras 250 180 Pune 270 225 Tirupati 200 150 Bombay 300 250 The number of students who passed the examination from IIT Kanpur and IIT Pune is what percentage of the average number of students who appeared for the examination from IIT Madras, IIT Tirupati and IIT Bombay respectively ?
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Answer B. 64% and 90%
Average appeared at Madras, Tirupati and Bombay = (250 + 200 + 300) ÷ 3 = 250. Kanpur passed 160 ÷ 250 = 64%; Pune passed 225 ÷ 250 = 90%.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q54, final key
1.6.1Emotional and social intelligence, decision making and personalityNotes
- Q112 Paper II Mock 1, Q58
Consider the following statements about the Myers-Briggs Type Indicator (MBTI):
1. Its four dichotomies include Thinking-Feeling and Judging-Perceiving.
2. It is a projective technique in which the person makes up stories about ambiguous pictures.
Which of the statements given above is/are correct?
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Answer A. 1 only
The MBTI, based on Carl Jung's theory of psychological types, is a self-report questionnaire that sorts people into 16 types using four dichotomies: Extraversion-Introversion, Sensing-Intuition, Thinking-Feeling and Judging-Perceiving. Telling stories about ambiguous pictures describes the TAT.
Source: The Myers-Briggs Company, MBTI Manual (3rd ed., 1998); C. G. Jung, Psychological Types (1921)
- Q113 Paper II Mock 1, Q59
Consider the following statements about the assessment of personality:
1. The reliability of a test refers to the consistency of its results when it is administered repeatedly.
2. The validity of a test refers to whether it measures what it claims to measure.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Reliability is the consistency (stability) of scores over time or across items; validity is the extent to which a test measures what it is meant to measure. Both are basic requirements of a good psychological test.
Source: NCERT Psychology Class XI, ch. 2 'Methods of Enquiry in Psychology' (reliability and validity)
- Q114 Paper II Mock 1, Q60
Which one of the following pairs (problem-solving tool - main purpose) is NOT correctly matched?
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Answer D. SWOT analysis - scheduling project activities along the critical path
SWOT analysis examines Strengths, Weaknesses, Opportunities and Threats for planning; scheduling activities along a critical path is done with CPM/PERT. The other three pairs are correct.
Source: K. Ishikawa, Guide to Quality Control (1968); J. M. Juran, Quality Control Handbook; S. R. Covey, The 7 Habits of Highly Effective People (1989)
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Assume that you are the polling officer of a polling station for the general elections 2024 and the polling booth is in an area where Maoist prevalence is high. During the day of polling a group of Maoists come and try to disrupt proceedings by terrorizing the voters and firing guns. What will you do ?
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Answer C. Inform the police force stationed there and ask them to ensure safety of important documents and EVMs.
The polling officer's first duty in an armed disruption is to alert the security force on duty and protect the EVMs and election records; the police handle the attackers, and the officer reports to superiors.
Source: APPSC Group 1 Paper II 2024 (Notification 12/2023), Q56, final key
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