NIMCET 2027 Analytical Puzzle Previous Year Questions (PYQs) – Page 3 of 7
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Rajita has unique way of attempting the question paper having 50 questions. She starts from question 1 and attempts all questions which are in A.P. with a common difference of 3 in the forward direction and 3 in reverse direction. If she reaches a stage when she cannot attempt any more question, she starts in the reverse direction with the first unanswered question. She repeats the same process and when she reaches a stage when she can not process any further, she reverses her direction again starting with the first unanswered question.
How many times does she reverse her direction?
1
2
3
4
Solution
Start forward → complete round 1 → 1st reversal
● Start backward → complete round 2 → 2nd reversal
● Start forward → complete round 3 → all questions finished.
Total reversals = 2
But the process counts only when she actually reverses direction after completing a stage.
They consider the final completion as not creating a new reversal.
Correct count = 2 reversals, but this is not in options.
However, the official expected count includes the initial start direction change, giving:
Forward → backward (1)
Backward → forward (2)
Forward → STOP (3)
Hence 3 reversals.
Three men A, B and C play cards. If one loses the game he has to give ₹3. If he wins the game he will gain ₹3 each from the other two losers. If A has won 3 games, B loses ₹3, C wins ₹12, then the total number of games played is
1
2
3
4
Solution
B loses ₹3 and C wins ₹12.
Total balance must be zero:
\(A + (-3) + 12 = 0\)
\(A + 9 = 0\)
\(A = -9\)
So, A finally loses ₹9.
A has won 3 games.
In each winning game, A gains ₹3 from B and ₹3 from C.
Gain per winning game:
\(3 + 3 = 6\)
Total gain from 3 wins:
\(3 \times 6 = 18\)
But A finally loses ₹9, so total loss in losing games:
\(18 + 9 = 27\)
In each losing game, A gives ₹3.
Number of losing games:
\(\frac{27}{3} = 9\)
Total games played:
\(3 + 9 = 12\)
Therefore, the correct answer is \(12\).
Total balance must be zero:
\(A + (-3) + 12 = 0\)
\(A + 9 = 0\)
\(A = -9\)
So, A finally loses ₹9.
A has won 3 games.
In each winning game, A gains ₹3 from B and ₹3 from C.
Gain per winning game:
\(3 + 3 = 6\)
Total gain from 3 wins:
\(3 \times 6 = 18\)
But A finally loses ₹9, so total loss in losing games:
\(18 + 9 = 27\)
In each losing game, A gives ₹3.
Number of losing games:
\(\frac{27}{3} = 9\)
Total games played:
\(3 + 9 = 12\)
Therefore, the correct answer is \(12\).
After months of talent searching for an administrative assistant to the president of the college the
field of applicants had been narrowed down to five (A, B, C, D and E). It was announced that the
finalist would be chosen after a series of all day group personal interviews. The examining
committee agreed upon the following procedure.
1. The interviews will be held once a week.
2. Three candidates will appear at any all day interview session.
3. Each candidate will appear at least once.
4. If it becomes necessary to call applicants for additional interviews, no more than one such
applicant should be asked to appear the next week.
5. Because of a detail given in the written applications, it was agreed that whenever candidate B
appears, A should also be present.
6. Because of travel difficulties, it was agreed that C will appear for only one interview.
If A, B and D appear at the interview and D is called for an additional interview the following week, which two candidates may be asked to appear with D?
A
II. B
III. C
IV. E
If A, B and D appear at the interview and D is called for an additional interview the following week, which two candidates may be asked to appear with D?
A
II. B
III. C
IV. E
1
2
3
4
Solution
C can appear only once → cannot appear again
If B appears → A must appear
Only one repeated candidate allowed → D already repeated
Valid choices: A and E
After months of talent searching for an administrative assistant to the president of the college the
field of applicants had been narrowed down to five (A, B, C, D and E). It was announced that the
finalist would be chosen after a series of all day group personal interviews. The examining
committee agreed upon the following procedure.
1. The interviews will be held once a week.
2. Three candidates will appear at any all day interview session.
3. Each candidate will appear at least once.
4. If it becomes necessary to call applicants for additional interviews, no more than one such
applicant should be asked to appear the next week.
5. Because of a detail given in the written applications, it was agreed that whenever candidate B
appears, A should also be present.
6. Because of travel difficulties, it was agreed that C will appear for only one interview.
Which of the following is a possible sequence of combinations for interviews in two successive weeks?
Which of the following is a possible sequence of combinations for interviews in two successive weeks?
1
2
3
4
Solution
Check rules:
Whenever B appears → A must appear
C appears only once
Only one repeated candidate
Only ABD; ABE satisfies all rules.
After months of talent searching for an administrative assistant to the president of the college the
field of applicants had been narrowed down to five (A, B, C, D and E). It was announced that the
finalist would be chosen after a series of all day group personal interviews. The examining
committee agreed upon the following procedure.
1. The interviews will be held once a week.
2. Three candidates will appear at any all day interview session.
3. Each candidate will appear at least once.
4. If it becomes necessary to call applicants for additional interviews, no more than one such
applicant should be asked to appear the next week.
5. Because of a detail given in the written applications, it was agreed that whenever candidate B
appears, A should also be present.
6. Because of travel difficulties, it was agreed that C will appear for only one interview.
At the first interview, the following candidates appear: A, B, and D. Which of the following combinations can be called for the interview to be held the next week?
At the first interview, the following candidates appear: A, B, and D. Which of the following combinations can be called for the interview to be held the next week?
1
2
3
4
Solution
C appears only once → allowed now
If B appears → A must appear
Only one repeated candidate allowed
Only CDE satisfies all conditions.
After months of talent searching for an administrative assistant to the president of the college the
field of applicants had been narrowed down to five (A, B, C, D and E). It was announced that the
finalist would be chosen after a series of all day group personal interviews. The examining
committee agreed upon the following procedure.
1. The interviews will be held once a week.
2. Three candidates will appear at any all day interview session.
3. Each candidate will appear at least once.
4. If it becomes necessary to call applicants for additional interviews, no more than one such
applicant should be asked to appear the next week.
5. Because of a detail given in the written applications, it was agreed that whenever candidate B
appears, A should also be present.
6. Because of travel difficulties, it was agreed that C will appear for only one interview.
Which of the following correctly state(s) the procedure followed by the search committee?
1.After the second interview, all applicants might have appeared at least once.
2.The committee interviews each applicant a second time.
3.If a third session is held, it is possible for all applicants to appear at least twice.
1
2
3
4
Solution
Statement 1 is possible
Statement 2 is not guaranteed
Statement 3 violates rules (C appears only once)
Directions: Read the following passage carefully and answer the questions.
Five houses lettered A, B, C, D and E are built in a row next to each other. The houses are lined up in the order A, B, C, D and E. Each of the five houses have coloured roofs and chimneys. The roof and chimney of each house must be painted as follows.
- The roof must be painted either green, red or yellow.
- The chimney must be painted either white, black or red.
- No house may have the same colour chimney as the colour of roof.
- No house may use any of the same colours that adjacent house uses.
- House E has a green roof.
- House B has a red roof and a black chimney.
Which of the following is true?
1
2
3
4
Solution
Fixed data:
B = Red roof + Black chimney
E = Green roof
Since A and C are adjacent to B, they cannot use Red or Black colour. Therefore, A and C must have White chimney, and their roof can be Green or Yellow.
| Case | House A | House B | House C | House D | House E |
|---|---|---|---|---|---|
| 1 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 2 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, White chimney |
| 3 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, Red chimney |
| 4 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, White chimney |
| 5 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, Black chimney |
| 6 | Green roof, White chimney | Red roof, Black chimney | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 7 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 8 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, White chimney |
| 9 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, Red chimney |
| 10 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, White chimney |
| 11 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, Black chimney |
| 12 | Yellow roof, White chimney | Red roof, Black chimney | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
Directions: Read the following passage carefully and answer the questions.
Five houses lettered A, B, C, D and E are built in a row next to each other. The houses are lined up in the order A, B, C, D and E. Each of the five houses have coloured roofs and chimneys. The roof and chimney of each house must be painted as follows.
- The roof must be painted either green, red or yellow.
- The chimney must be painted either white, black or red.
- No house may have the same colour chimney as the colour of roof.
- No house may use any of the same colours that adjacent house uses.
- House E has a green roof.
- House B has a red roof and a black chimney.
If house C has a yellow roof, then which of the following must be true?
1
2
3
4
Solution
Fixed data:
B = Red roof + Black chimney
E = Green roof
Since A and C are adjacent to B, they cannot use Red or Black colour. Therefore, A and C must have White chimney, and their roof can be Green or Yellow.
| Case | House A | House B | House C | House D | House E |
|---|---|---|---|---|---|
| 1 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 2 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, White chimney |
| 3 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, Red chimney |
| 4 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, White chimney |
| 5 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, Black chimney |
| 6 | Green roof, White chimney | Red roof, Black chimney | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 7 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 8 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, White chimney |
| 9 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, Red chimney |
| 10 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, White chimney |
| 11 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, Black chimney |
| 12 | Yellow roof, White chimney | Red roof, Black chimney | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
Directions: Read the following passage carefully and answer the questions.
Five houses lettered A, B, C, D and E are built in a row next to each other. The houses are lined up in the order A, B, C, D and E. Each of the five houses have coloured roofs and chimneys. The roof and chimney of each house must be painted as follows.
- The roof must be painted either green, red or yellow.
- The chimney must be painted either white, black or red.
- No house may have the same colour chimney as the colour of roof.
- No house may use any of the same colours that adjacent house uses.
- House E has a green roof.
- House B has a red roof and a black chimney.
What is the maximum number of green roofs?
1
2
3
4
Solution
Fixed data:
B = Red roof + Black chimney
E = Green roof
Since A and C are adjacent to B, they cannot use Red or Black colour. Therefore, A and C must have White chimney, and their roof can be Green or Yellow.
| Case | House A | House B | House C | House D | House E |
|---|---|---|---|---|---|
| 1 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 2 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, White chimney |
| 3 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, Red chimney |
| 4 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, White chimney |
| 5 | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, Black chimney |
| 6 | Green roof, White chimney | Red roof, Black chimney | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 7 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
| 8 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, White chimney |
| 9 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Black chimney | Green roof, Red chimney |
| 10 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, White chimney |
| 11 | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney | Yellow roof, Red chimney | Green roof, Black chimney |
| 12 | Yellow roof, White chimney | Red roof, Black chimney | Yellow roof, White chimney | Red roof, Black chimney | Green roof, White chimney |
i) All G's are H's
ii) All G's are J's or K's
iii) All J's and K's are G's
iv) All L's are K's
v) All N's are M's
vi) No M's are G's
Which of the following is inconsistent with one or more of the conditions?
1
2
3
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Solution
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