Puzzle Test Questions and Answers

Q: Read the given passage and answer the questions that follow. Seven boxes 1, 2, 3, 4, 5, 6 and 7 are kept one over the other, but not necessarily in the same order. Boxes 4 and 7 are always kept together, with 4 immediately above 7. Box 3 is kept second from the bottom and above box 5. Only one box is kept between 2 and 6, with box 6 always above box 2. Box 7 is always kept above box 2. Which box is at the fourth position from the bottom?

The box fourth from the bottom is 1.Box 3 is second from the bottom and above box 5, so 5 is at the bottom and 3 is second. Box 7 is just below box 4, and 7 is above 2. Box 6 is above 2 with exactly one box between them. The only arrangement that works from the bottom is 5, 3, 2, 1, 6, 7, 4: 6 is two places above 2, 7 is above 2 and 4 is directly above 7.The fourth place from the bottom therefore holds box 1. Boxes 5, 2 and 7 sit at the first, third and sixth places.Placing the fixed facts first makes it quick: 5 at the bottom, 3 second, then the pair 4 over 7 as a block, with 2 below 7, and 6 two places above 2. Trying 2 in the fourth place from the bottom leaves no room for 6, so 2 must be in the third place and box 1 fills the fourth.

Q: Four people, A, B, C and D, live in a four storey building, where the ground floor is numbered 1, the floor above it is numbered 2, and so on, till the top floor is numbered 4. All are living on different floors. Each of the persons living on the four floors likes a different phone, i.e. Samsung, iPhone, Redmi and Nokia, but not necessarily in the same order. A lives on an odd numbered floor greater than 2, and does not like iPhone, Samsung or Nokia. C lives above B and like iPhone. D does not like Nokia. The number of persons above A is the same as the number of persons below D. Which of the following statements is true?

The true statement is B likes Nokia.A lives on an odd floor above 2, so on floor 3, and likes Redmi (not iPhone, Samsung or Nokia). One person lives above A, so one person is below D, which puts D on floor 2. B is then on floor 1 and C, who lives above B and likes iPhone, is on floor 4. D does not like Nokia and the iPhone and Redmi are taken, so D likes Samsung, leaving Nokia for B.D likes Samsung, C lives on the 4th floor and A lives on the 3rd floor, so the other statements are false.Check the answer against the other statements: D likes Samsung, not Redmi, so the statement 'D likes Redmi' is false. C lives on the top floor, the 4th, and not the 2nd. A lives on the 3rd floor, not the 1st. Only 'B likes Nokia' is true.

Q: A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.i. If the house number is a multiple of 3, then it is a number from 50 to 59.ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.What is the house number?

The house number is 76.Each statement is an 'if ... then' rule, so a number passes a rule automatically when the 'if' part is false. Test the options:76: not a multiple of 3, so rule i does not apply; a multiple of 4, so rule ii does not apply; not a multiple of 6, so rule iii requires 70 to 79, and 76 is. All three hold.54: not a multiple of 4, so rule ii demands 60 to 69. It fails.65: not a multiple of 6, so rule iii demands 70 to 79. It fails.66: a multiple of 3, so rule i demands 50 to 59. It fails.

Q: Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them:i. Neither H2 nor H3 is the easternmost hill.ii. Neither H2 nor H3 is the westernmost hill.iii. Neither the easternmost hill nor the westernmost hill is the southernmost hill.iv. Two hills are located to the west of H2.v. The southernmost hill has at least two hills to its east.The southernmost hill is ________.

The southernmost hill is H3.By (i) and (ii), neither H2 nor H3 is at either end of the west-east order, so H1 and H4 occupy the two ends and H2 and H3 the middle two places. By (iv), two hills lie west of H2, so H2 is third from the west and H3 is second from the west.By (iii), the southernmost hill is not at either end, so it is H2 or H3. By (v), it has at least two hills to its east. H2, third from the west, has only one hill to its east, while H3 has two. So H3 is the southernmost.H1 and H4 are ruled out by (iii), and H2 by (v).

Q: Four people P, Q, R, and S, of different ages, make the following observations.P - I am younger than S.Q - I am neither the youngest nor the oldest.R - P is older than me.Based on these observations, the youngest person is ______.

The youngest person is R.Write ages with \(\lt\) meaning 'younger than'. P's statement gives \(P \lt S\). R's statement, that P is older than R, gives \(R \lt P\). Together, \(R \lt P \lt S\). Q is neither the youngest nor the oldest, so Q falls somewhere between R and S, and the order from youngest is R, then P and Q in some order, then S.Either way R is the youngest. P cannot be youngest because R is younger than P; Q's own statement rules Q out; and S is older than P, so S is if anything the oldest.

Q: Consider the following statements relating to the level of poker play of four players P, Q, R and S.I. P always beats QII. R always beats SIII. S loses to P only sometimesIV. R always loses to QWhich of the following can be logically inferred from the above statements?(i) P is likely to beat all the three other players(ii) S is the absolute worst player in the set

Neither can be inferred, so the answer is neither (i) nor (ii).From the statements: P always beats Q, Q always beats R, and R always beats S. P beats S only sometimes, so S sometimes beats P.(i) is not certain: P always beats Q, but nothing says P ever plays R or how often P beats R, and P loses to S part of the time, so 'likely to beat all three' is not established. (ii) is not certain either: S always loses to R, but S sometimes beats P, who always beats Q, so S is not simply the worst player. The chain of 'always' results is broken by statement III, which is the point of the question.

Important Instructions

11.

Six boxes, C, D, E, F, G and H, are kept one above another. The topmost position is the first and bottom-most position is the last. Three boxes are between D and C, where D is placed at the second last position. Four boxes are kept between C and G. One box is kept between D and E. Box F is above H. How many boxes are between F and D?

A.One
B.Two
C.Three
D.Zero

Exam Year(s)

DSSSB PGT - 2023,

Answer: B

Two boxes lie between F and D. Number the positions 1 to 6 from the top. D is second last, so D is 5. Three boxes are between D and C, so C is 1. Four boxes are between C and G, so G is 6. One box is between D and E, so E is 3. The remaining positions 2 and 4 go to F and H, and F is above H, so F is 2 and H is 4.

Between F (2) and D (5) are positions 3 and 4, so two boxes. One and three miscount that gap, and zero would need F and D to be adjacent.

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12.

Six students, Divya, Monika, Nitu, Saanvi, Tania and Yashika, are born in different years - 1990, 1993, 1997, 2000, 2002 and 2004. Their ages are with respect to the current year, i.e. 2023, same month and same date. There is a 14-year difference between Nitu and Monika. Monika was born before 1993. Divya is 5 years older than Tania. Saanvi is 3 years younger than Monika. Yashika was born in which year?

A.2000
B.1993
C.2002
D.1997

Exam Year(s)

DSSSB PGT - 2023,

Answer: A

Yashika was born in 2000. Nitu and Monika are 14 years apart and Monika was born before 1993, so Monika is 1990 and Nitu is 2004. Saanvi is 3 years younger than Monika, so Saanvi is 1993. The years left are 1997, 2000 and 2002. Divya is 5 years older than Tania, which fits only 1997 and 2002, so Divya is 1997 and Tania is 2002. That leaves 2000 for Yashika.

1993 is Saanvi's year, 2002 is Tania's and 1997 is Divya's.

A check on the years: Nitu (2004) is 14 years younger than Monika (1990), Saanvi (1993) is 3 years younger than Monika, and Divya (1997) is 5 years older than Tania (2002).

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13.

Six people, Aarush, Bindu, Cheema, Deepanshu, Gopal and Harish, live on the different floors of a building but not necessarily in the same order. The bottom-most floor is numbered 1 and the topmost floor is numbered 6. All are living on different floors. Bindu lives just below Cheema and both are living above floor number 4. Cheema lives three floors above Aarush, who is not adjacent to Deepanshu. Gopal lives two floors below Harish. Which of the following statements is true?

A.Harish lives just above to Gopal.
B.Only three persons live between Aarush and Bindu.
C.Aarush lives just above to Bindu.
D.Only four persons live between Cheema and Deepanshu.

Exam Year(s)

DSSSB PGT - 2023,

Answer: D

Only four persons live between Cheema and Deepanshu. Bindu is just below Cheema and both are above floor 4, so Bindu is on 5 and Cheema on 6. Cheema is three floors above Aarush, so Aarush is on 3. Gopal is two floors below Harish; of the free floors 1, 2 and 4 the only pair two apart is Gopal on 2 and Harish on 4, which leaves Deepanshu on 1, not adjacent to Aarush as required. Floors 2, 3, 4 and 5 lie between 1 and 6, so four persons live between Cheema and Deepanshu. Harish is two floors, not one, above Gopal. Aarush (3) is not just above Bindu (5), and only one person (on floor 4) lives between Aarush and Bindu.

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14.

Six people A, B, C, D, E, and F are living in a six-storey building, but not necessarily in the same order. C’s floor is lower than D but immediately higher than A’s floor. B’s floor is higher than E’s floor but immediate lower than F’s floor. If A’s floor is immediately higher than F’s floor, then who amongst the six is on the top floor?

Exam Year(s)

DSSSB - 2023,

Answer: C

Take the conditions one at a time. A's floor is immediately higher than F's, and C's floor is immediately higher than A's, so F, A and C occupy three consecutive floors in that order going up. B is immediately below F, so B comes just under F. E is lower than B, so E is at the bottom. From the bottom the order is E, B, F, A, C, and since C is lower than D, D must be above C on the sixth floor. D is therefore on the top floor, option (C). F, E and C all lie below D, so they cannot be on the top floor.

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15.

Read the given passage and answer the questions that follow. Seven boxes 1, 2, 3, 4, 5, 6 and 7 are kept one over the other, but not necessarily in the same order. Boxes 4 and 7 are always kept together, with 4 immediately above 7. Box 3 is kept second from the bottom and above box 5. Only one box is kept between 2 and 6, with box 6 always above box 2. Box 7 is always kept above box 2. Which box is at the fourth position from the bottom?

Exam Year(s)

DSSSB - 2023,

Answer: B

The box fourth from the bottom is 1.

Box 3 is second from the bottom and above box 5, so 5 is at the bottom and 3 is second. Box 7 is just below box 4, and 7 is above 2. Box 6 is above 2 with exactly one box between them. The only arrangement that works from the bottom is 5, 3, 2, 1, 6, 7, 4: 6 is two places above 2, 7 is above 2 and 4 is directly above 7.

The fourth place from the bottom therefore holds box 1. Boxes 5, 2 and 7 sit at the first, third and sixth places.

Placing the fixed facts first makes it quick: 5 at the bottom, 3 second, then the pair 4 over 7 as a block, with 2 below 7, and 6 two places above 2. Trying 2 in the fourth place from the bottom leaves no room for 6, so 2 must be in the third place and box 1 fills the fourth.

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16.

Four people, A, B, C and D, live in a four storey building, where the ground floor is numbered 1, the floor above it is numbered 2, and so on, till the top floor is numbered 4. All are living on different floors. Each of the persons living on the four floors likes a different phone, i.e. Samsung, iPhone, Redmi and Nokia, but not necessarily in the same order. A lives on an odd numbered floor greater than 2, and does not like iPhone, Samsung or Nokia. C lives above B and like iPhone. D does not like Nokia. The number of persons above A is the same as the number of persons below D. Which of the following statements is true?

A.D likes Redmi.
B.B likes Nokia.
C.C lives on the 2nd floor.
D.A lives on the 1st floor.

Exam Year(s)

DSSSB - 2023,

Answer: B

The true statement is B likes Nokia.

A lives on an odd floor above 2, so on floor 3, and likes Redmi (not iPhone, Samsung or Nokia). One person lives above A, so one person is below D, which puts D on floor 2. B is then on floor 1 and C, who lives above B and likes iPhone, is on floor 4. D does not like Nokia and the iPhone and Redmi are taken, so D likes Samsung, leaving Nokia for B.

D likes Samsung, C lives on the 4th floor and A lives on the 3rd floor, so the other statements are false.

Check the answer against the other statements: D likes Samsung, not Redmi, so the statement 'D likes Redmi' is false. C lives on the top floor, the 4th, and not the 2nd. A lives on the 3rd floor, not the 1st. Only 'B likes Nokia' is true.

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17.

A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

A.54
B.65
C.66
D.76

Exam Year(s)

GATE Mathematics - 2018, GATE ME - 2018, GATE AE - 2018,

Answer: D

The house number is 76.

Each statement is an 'if ... then' rule, so a number passes a rule automatically when the 'if' part is false. Test the options:

76: not a multiple of 3, so rule i does not apply; a multiple of 4, so rule ii does not apply; not a multiple of 6, so rule iii requires 70 to 79, and 76 is. All three hold.
54: not a multiple of 4, so rule ii demands 60 to 69. It fails.
65: not a multiple of 6, so rule iii demands 70 to 79. It fails.
66: a multiple of 3, so rule i demands 50 to 59. It fails.

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18.

Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them:

i. Neither H2 nor H3 is the easternmost hill.
ii. Neither H2 nor H3 is the westernmost hill.
iii. Neither the easternmost hill nor the westernmost hill is the southernmost hill.
iv. Two hills are located to the west of H2.
v. The southernmost hill has at least two hills to its east.

The southernmost hill is ________.

A.H1
B.H2
C.H3
D.H4

Exam Year(s)

GATE Chemistry - 2026, GATE Physics - 2026, GATE AE - 2026,

Answer: C

The southernmost hill is H3.

By (i) and (ii), neither H2 nor H3 is at either end of the west-east order, so H1 and H4 occupy the two ends and H2 and H3 the middle two places. By (iv), two hills lie west of H2, so H2 is third from the west and H3 is second from the west.

By (iii), the southernmost hill is not at either end, so it is H2 or H3. By (v), it has at least two hills to its east. H2, third from the west, has only one hill to its east, while H3 has two. So H3 is the southernmost.

H1 and H4 are ruled out by (iii), and H2 by (v).

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19.

Four people P, Q, R, and S, of different ages, make the following observations.
P - I am younger than S.
Q - I am neither the youngest nor the oldest.
R - P is older than me.

Based on these observations, the youngest person is ______.

Exam Year(s)

GATE Mathematics - 2026, GATE Life Sciences - 2026, GATE AG - 2026, GATE XE - 2026,

Answer: C

The youngest person is R.

Write ages with \(\lt\) meaning 'younger than'. P's statement gives \(P \lt S\). R's statement, that P is older than R, gives \(R \lt P\). Together, \(R \lt P \lt S\). Q is neither the youngest nor the oldest, so Q falls somewhere between R and S, and the order from youngest is R, then P and Q in some order, then S.

Either way R is the youngest. P cannot be youngest because R is younger than P; Q's own statement rules Q out; and S is older than P, so S is if anything the oldest.

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20.

Consider the following statements relating to the level of poker play of four players P, Q, R and S.

I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q

Which of the following can be logically inferred from the above statements?

(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set

A.(i) only
B.(ii) only
C.(i) and (ii)
D.neither (i) nor (ii)

Exam Year(s)

GATE CS - 2016,

Answer: D

Neither can be inferred, so the answer is neither (i) nor (ii).

From the statements: P always beats Q, Q always beats R, and R always beats S. P beats S only sometimes, so S sometimes beats P.

(i) is not certain: P always beats Q, but nothing says P ever plays R or how often P beats R, and P loses to S part of the time, so 'likely to beat all three' is not established. (ii) is not certain either: S always loses to R, but S sometimes beats P, who always beats Q, so S is not simply the worst player. The chain of 'always' results is broken by statement III, which is the point of the question.

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