NIMCET 2027 Puzzle Previous Year Questions (PYQs) – Page 10 of 12
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John, Johny and Janardan participated in a race and each won a different medal among Gold, Silver and Bronze, not necessarily in that order. Each person among them gives two replies to any question, one of which is true and the other is false (in any order). When asked about the details of the medals obtained by them, the following were their replies:
John: I won the Gold medal.Johny won the Bronze medal.
Johny: John won the Silver medal.I won the Gold medal.
Janardan: Johny won the Silver medal.I won the Gold medal.
Which among the following is the correct order of the persons who won the Gold medal, the Silver medal and the Bronze medal respectively?
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Solution
Solution (One True & One False per person)
- Assumption rule: From each pair of statements, exactly one is true.
- Check Johny’s pair:
- S₁: “John won Silver.”
- S₂: “I (Johny) won Gold.”
- Assign Gold: With John already Silver, Gold must be either John or Janardan. John can’t be Gold now ⇒ Janardan = Gold.
- Remaining Bronze: goes to Johny.
John’s statements:
- “I won Gold.” → False
- “Johny won Bronze.” → True
Johny’s statements:
- “John won Silver.” → True
- “I won Gold.” → False
Janardan’s statements:
- “Johny won Silver.” → False
- “I won Gold.” → True
✅ Final Order (Gold, Silver, Bronze): Janardan, John, Johny
Read the information given below and answer the following question: Who among the following is one of the couples?
- In a family of six persons A,B,C,D,E and F, there are two married couples.
- D Is grandmother of A and mother of B.
- C is wife of B and mother of F.
- F is the granddaughter of E.
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Solution
A woman took a certain number of eggs to the market and sold some of them.
Next day the number left over was doubled and she sold the same number as the previous day.
On the third day the remainder was tripled, on the fourth day quadrupled, and on the fifth day quintupled.
Each day she sold exactly the same number and finally disposed of her entire stock.
What is the smallest number of eggs she could have taken on the first day and how many did she sell daily?
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Solution
Let the number of eggs sold each day be $x$
and the number of eggs remaining after the first day be $a_1$.
Day 1:
Initial eggs $= x + a_1$
Day 2:
Leftover doubled, then sold $x$
$a_2 = 2a_1 - x$
Day 3:
Leftover tripled, then sold $x$
$a_3 = 3a_2 - x$
Day 4:
Leftover quadrupled, then sold $x$
$a_4 = 4a_3 - x$
Day 5:
Leftover quintupled and all sold
$5a_4 - x = 0$
$\Rightarrow x = 5a_4$
Working backward
From $x = 5a_4$
$a_4 = \dfrac{x}{5}$
From $a_4 = 4a_3 - x$
$\dfrac{x}{5} = 4a_3 - x$
$4a_3 = \dfrac{6x}{5}$
$a_3 = \dfrac{3x}{10}$
From $a_3 = 3a_2 - x$
$\dfrac{3x}{10} = 3a_2 - x$
$3a_2 = \dfrac{13x}{10}$
$a_2 = \dfrac{13x}{30}$
From $a_2 = 2a_1 - x$
$\dfrac{13x}{30} = 2a_1 - x$
$2a_1 = \dfrac{43x}{30}$
$a_1 = \dfrac{43x}{60}$
Initial number of eggs
Initial eggs
$= a_1 + x$
$= \dfrac{43x}{60} + x$
$= \dfrac{103x}{60}$
For this to be an integer, smallest possible value is
$x = 60$
So initial eggs
$= \dfrac{103 \times 60}{60} = 103$Initial number of eggs $= 103$
Number sold daily $= 60$
Read the information given below and answer the following question: Which of the following is true?
- In a family of six persons A,B,C,D,E and F there are two married couples.
- D Is grandmother of A and mother of B.
- C is wife of B and mother of F.
- F is the granddaughter of E.
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Solution
Read the information given below and answer the following question: What is C to A?
- In a family of six persons A,B,C,D,E and F there are two married couples.
- D Is grandmother of A and mother of B.
- C is wife of B and mother of F.
- F is the granddaughter of E.
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Solution
A, B, C, D, E are a group of 7 friends from a club. There are two houses wives, one lecturer, one architect, one accountant and one lawyer in the group. There are two married couples. The lawyer is married to D, who is a housewife. No lady is either an architect or an accountant. C, the accountant is married to F, who is a lecturer. If E is not a housewife, what is the profession of E?
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Solution
There were two men standing on a street.
One says: “I have 3 daughters; the product of their ages is 36.”
The other says: “I need more information.”
First adds: “The sum of their ages is equal to the house number across the street.”
Second still needs more information.
Then the first says: “My oldest daughter wears a red dress.”
What is the age of the oldest daughter?
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Solution
Triples with product $36$:
$(1,1,36),(1,2,18),(1,3,12),(1,4,9),(1,6,6),(2,2,9),(2,3,6),(3,3,4)$
Only sums that repeat are $13$: $(1,6,6)$ and $(2,2,9)$.
Since there is a unique oldest daughter, ages must be $(2,2,9)$.
There are five books A, B, C, D, and E placed on a table. If A is placed below E, C is placed above D, B is placed below A and D is placed above E, then which of the following books touches the surface of the table.
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Solution
In a remote research outpost, five scientists (Dr. Anand, Dr. Beena, Dr. Chirag, Dr. Dinesh,
and Dr. Elango) are studying a rare phenomenon. They communicate through a secure,
text-based system. Over the course of an hour, the following exchanges occur: At the end of this hour, who has received the most messages directly from other scientists
within the group? (Consider only messages sent within the described hour and only
between the five scientists mentioned).
- Dr. Anand sends a message to Dr. Beena and Dr. Chirag.
- Dr. Beena replies only to Dr. Anand.
- Dr. Anand sends a reminder message to who did not reply.
- Dr. Chirag sends a message to Dr. Dinesh and Dr. Elango.
- While replying to Dr. Chirag, Dr. Dinesh accidentally sends a "Reply All"
- Dr. Elango, having received Dr. Chirag's message, sends a message to Dr. Beena.
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Solution
Dr. Chirag received the most.
Quick count of messages received:
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B: from A (initial) + from E = 2
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C: from A (initial) + from A (reminder) + from D (reply-all) = 3
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D: from C = 1
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E: from C + from D (reply-all) = 2
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A: from B = 1
Highest is 3 → Dr. Chirag.
Mr. and Mrs. Birla and Mr. and Mrs. Tata competed in a Chess tournament. Of the three games played:
1.In only the first game were the two players married to each other.
2.The men won two games and the women won one game.
3.The Birlas won more game than the Tatas.
4.Anyone who lost a game did not play a subsequent game.
Who did not lose a game?
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Solution
the person who keeps playing must keep winning.
Combining all conditions, the only consistent possibility is Mrs. Tata.
NIMCET 2027
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