NIMCET 2027 Puzzle Previous Year Questions (PYQs) – Page 2 of 12
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A, B, C, D, E, F and G are seven girls having different amount of money from among Rs. 10, 20, 40,60, 80, 120 and 200 with them. They had 3 chocolates, 2 toffees, and 2 lollipops together, each one
having one of these seven items.
- B and F do not have chocolates and they have Rs. 200 and Rs. 80 respectively.
- C has Rs. 60 with her and G has an amount which is neither Rs. 40 nor Rs. 120.
- A has Rs. 10 and does not have a toffee.
- The girl having Rs. 40 with her is the only one other than A to have the same type of item.
- E and the girl having Rs. 20 with her have the same kind of item.
Which of the following combination is definitely correct?
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Solution
| Girl | Amount (Rs.) | Item |
|---|---|---|
| A | 10 | Lollipop |
| B | 200 | Toffee |
| C | 60 | Chocolate |
| D | 40 | Lollipop |
| E | 120 | Chocolate |
| F | 80 | Toffee |
| G | 20 | Chocolate |
Final Answer: G has Rs. 20
Four students A, B, C and D distributed 30 marbles
among themselves. No two students got equal
number of marbles. No student got more than 10
marbles. No student got less than 5 marbles. A and C
got odd number of marbles. B and D got even
number of marbles. A got more marbles than B, C
got more marbles than D, B got more marbles than
D.
What is the number of marbles with A?
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Solution
Given: Total marbles = 30, each student gets between 5 and 10 marbles, all different.
A and C got odd marbles. B and D got even marbles.
A > B, C > D, and B > D.
Step 1: Possible distinct sets (5 to 10) with sum 30:
{5, 6, 9, 10}, {5, 7, 8, 10}, {6, 7, 8, 9}
Step 2: Check parity and conditions:
In {6, 7, 8, 9}:
Evens: 6, 8 → B > D ⇒ B = 8, D = 6
Odds: 7, 9 → A > B ⇒ A = 9, C = 7
Verify:
A > B ⇒ 9 > 8 ✔
C > D ⇒ 7 > 6 ✔
B > D ⇒ 8 > 6 ✔
Final Distribution:
A = 9, B = 8, C = 7, D = 6
A, B, C, D, E, F and G are seven girls having different amount of money from among Rs. 10, 20, 40,60, 80, 120 and 200 with them. They had 3 chocolates, 2 toffees, and 2 lollipops together, each one
having one of these seven items.
- B and F do not have chocolates and they have Rs. 200 and Rs. 80 respectively.
- C has Rs. 60 with her and G has an amount which is neither Rs. 40 nor Rs. 120.
- A has Rs. 10 and does not have a toffee.
- The girl having Rs. 40 with her is the only one other than A to have the same type of item.
- E and the girl having Rs. 20 with her have the same kind of item.
Which girl has Rs. 40 with her?
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Solution
| Girl | Amount (Rs.) | Item |
|---|---|---|
| A | 10 | Lollipop |
| B | 200 | Toffee |
| C | 60 | Chocolate |
| D | 40 | Lollipop |
| E | 120 | Chocolate |
| F | 80 | Toffee |
| G | 20 | Chocolate |
Final Answer: G has Rs. 20
Four students A, B, C and D distributed 30 marbles
among themselves. No two students got equal
number of marbles. No student got more than 10
marbles. No student got less than 5 marbles. A and C
got odd number of marbles. B and D got even
number of marbles. A got more marbles than B, C
got more marbles than D, B got more marbles than
D.
Mean of number of marbles with B, C, D is:
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Solution
Given: Total marbles = 30, each student gets between 5 and 10 marbles, all different.
A and C got odd marbles. B and D got even marbles.
A > B, C > D, and B > D.
Step 1: Possible distinct sets (5 to 10) with sum 30:
{5, 6, 9, 10}, {5, 7, 8, 10}, {6, 7, 8, 9}
Step 2: Check parity and conditions:
In {6, 7, 8, 9}:
Evens: 6, 8 → B > D ⇒ B = 8, D = 6
Odds: 7, 9 → A > B ⇒ A = 9, C = 7
Verify:
A > B ⇒ 9 > 8 ✔
C > D ⇒ 7 > 6 ✔
B > D ⇒ 8 > 6 ✔
Final Distribution:
A = 9, B = 8, C = 7, D = 6
mean(B,C,D)=$\dfrac{8+7+6}{3}$=7
Nine individuals - Z, Y, X, W, V, U, T, S and R - are
the only candidates, who can serve on three
committees — K1, K2 and K3, and each candidate
should serve on exactly one of the committees.
Committee K1 should consist of exactly one member
more than committee K2. It is possible that there are
no members in committee K3. Among Z, Y and X
none can serve on committee K1. Among W, V and
U none can serve on committee K2. Among T, S and R none can serve on committee K3.
In case committee K2 is served by T and Z only, how
many of the nine individuals should serve on
committee K3?
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Solution
Nine individuals - Z, Y, X, W, V, U, T, S and R - are
the only candidates, who can serve on three
committees — K1, K2 and K3, and each candidate
should serve on exactly one of the committees.
Committee K1 should consist of exactly one member
more than committee K2. It is possible that there are
no members in committee K3. Among Z, Y and X
none can serve on committee K1. Among W, V and
U none can serve on committee K2. Among T, S and R none can serve on committee K3.
Of the nine individuals, the largest number that can
serve together on committee K3 is:
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Solution
A circular field with inner radius of 10 meters and outer radius of 20 meters is divided into 5
successive stages for ploughing, The ploughing at each stage, with starting points P1, P2, P3, P4 and
P5, was allotted to one of the five farmers F1, F2, F3, F4 and F5, not necessarily in that order.
- F was allotted the stage starting at point P4.
- The stage from P5 to P3 was not the first Stage.
- F4 was allotted the work of the fourth stage.
- Finishing point of stage 3 was P1 and the work was not allotted to F1.
- F3 was allotted the work of stage 3 was P1 and the work was not allotted to F1.
Which of the following is the finish point for farmer F2?
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Solution
A circular field with inner radius of 10 meters and outer radius of 20 meters is divided into 5
successive stages for ploughing, The ploughing at each stage, with starting points P1, P2, P3, P4 and
P5, was allotted to one of the five farmers F1, F2, F3, F4 and F5, not necessarily in that order.
- F was allotted the stage starting at point P4.
- The stage from P5 to P3 was not the first Stage.
- F4 was allotted the work of the fourth stage.
- Finishing point of stage 3 was P1 and the work was not allotted to F1.
- F3 was allotted the work of stage 3 was P1 and the work was not allotted to F1.
Which stage was ploughed by F5?
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Solution
A circular field with inner radius of 10 meters and outer radius of 20 meters is divided into 5
successive stages for ploughing, The ploughing at each stage, with starting points P1, P2, P3, P4 and
P5, was allotted to one of the five farmers F1, F2, F3, F4 and F5, not necessarily in that order.
- F was allotted the stage starting at point P4.
- The stage from P5 to P3 was not the first Stage.
- F4 was allotted the work of the fourth stage.
- Finishing point of stage 3 was P1 and the work was not allotted to F1.
- F3 was allotted the work of stage 3 was P1 and the work was not allotted to F1.
What are the starting and ending points of the field ploughed by F4?
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Solution
A circular field with inner radius of 10 meters and outer radius of 20 meters is divided into 5
successive stages for ploughing, The ploughing at each stage, with starting points P1, P2, P3, P4 and
P5, was allotted to one of the five farmers F1, F2, F3, F4 and F5, not necessarily in that order.
- F was allotted the stage starting at point P4.
- The stage from P5 to P3 was not the first Stage.
- F4 was allotted the work of the fourth stage.
- Finishing point of stage 3 was P1 and the work was not allotted to F1.
- F3 was allotted the work of stage 3 was P1 and the work was not allotted to F1.
What is the starting point for stage?
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Solution
NIMCET 2027
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and More.
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NIMCET 2027
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and More.
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