CAT 2001 — DILR Question 36
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.
I have a total of Rs. 1,000. Item A costs Rs. 110, item B costs Rs. 90, item C costs Rs. 70, item D costs Rs. 40 and item E costs Rs. 45. For every item D that I purchase, I must also buy two of item B. For every item A, I must buy one of item C. For every item E, I must also buy two of item D and one of item B. For every item purchased I earn 1000 points and for every rupee not spent I earn a penalty of 1500 points. My objective is to maximise to points I earn. What is the number of items that I must purchase to maximise my points?
Answer & solution
- A
13
14
- C
15
- D
16
To maximise the points, I should spent the entire amount and should get as many items as possible.
∴ I can maximize my points by purchasing 13C’s and 1B as there is no condition on the purchase of C and B.
∴ Total cost = 13 × 70 + 90 = 910 + 90 =1000
âµ The entire amount has been spent, there is no penalty.
∴ Number of points earned = 14 × 1000 = 14000
Hence, option (b).