CAT 2001 — DILR Question 33
Answer the following question based on the information given below.
A group of three or four has to be selected from seven persons. Among are two women: Fiza and Kavita, and five men: Ram, Shyam, David, Peter and Rahim. Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to be in the group only if David is also there. David, if selected, would not like Peter in the group. Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group.
On her walk through the park, Hansa collected 50 coloured leaves, all either maple or oak. She sorted them by category when she got home, and found the following:
A. The number of red oak leaves with spots is even and positive.
B. The number of red oak leaves without any spot equals the number of red maple leaves without spots.
C. All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves.
D. There are no spotted maple leaves that are not red.
E. There are exactly 6 red spotted maple leaves.
F. There are exactly 22 maple leaves that are neither spotted nor red.
How many oak leaves did she collect?
Answer & solution
- A
22
17
- C
25
- D
18
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Let the number of red but not spotted oak leaves be ‘x’ and number of red spotted oak leaves be ‘y’.
From the given conditions, we get the following tabulated table.
But, 6 + x + 22 + y + x + 5y = 50
∴ 28 + 2x + 6y = 50
∴ x + 3y = 11
âµ Red spotted oak leaves has to be positive and even.
∴ y = 2
∴ x = 11 − 3 × 2 = 5
∴ Number of Oak leaves = x + y + 5y = 5 + 6 × 2 = 17
Hence, option (b).