CAT 2001 — DILR Question 37
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.
Four friends Ashok, Bashir, Chirag and Deepak are out shopping. Ashok has less money than three times the amount that Bashir has. Chirag has more money than Bashir. Deepak has an amount equal to the difference of amounts with Bashir and Chirag. Ashok has three times the money with Deepak. They each have to buy at least one shirt, or one shawl, or one sweater, or one jacket that are priced Rs. 200, Rs. 400, Rs. 600, and Rs. 1,000 a piece, respectively. Chirag borrows Rs. 300 from Ashok and buys a jacket. Bashir buys a sweater after borrowing Rs. 100 from Ashok and is left with no money. Ashok buys three shirts. What is the costliest item the Deepak could buy with his own money?
Answer & solution
- A
A shirt
A shawl
- C
A sweater
- D
A jacket
Let Ashok, Bashir, Chirag and Deepak have amounts Rs. A, Rs. B, Rs. C and Rs. D respectively. From the data given in the question, we have following equations.
A < 3B ... (i)
C > B ... (ii)
D = C − B ... (iii)
A = 3D ... (iv)
Chirag borrows Rs. 300 from Ashok and buys a jacket worth Rs. 1000.
∴ C ≥ 700 ... (v)
Bashir buys a sweater after borrowing Rs. 100 from Ashok and left with no money.
∴ B = 500 ... (vi)
Ashok buys 3 shirts (costing Rs. 600 in total) with Rs. A − 300 − 100
∴ A ≥ 1000
From (i) and (vi), we get,
A < 1500
∴ 1000 ≤ A < 1500 ... (vii)
From equation (iv) and (vii), we get,
333 < D < 500
∴ Deepak could buy a shawl worth Rs. 400.
Hence, option (b).