CAT 1991 — QA Question 15
Use the following information:
Prakash has to decide whether or not to test a batch of 1000 widgets before sending them to the buyer. In case he decides to test, he has two options: (a) Use test I ; (b) Use test II. Test I cost Rs. 2 per widget. However, the test is not perfect. It sends 20% of the bad ones to the buyer as good. Test II costs Rs. 3 per widget. It brings out all the bad ones. A defective widget identified before sending can be corrected at a cost of Rs. 25 per widget. All defective widgets are identified at the buyer’s end and penalty of Rs. 50 per defective widget has to be paid by Prakash.
Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal then said to Mushtaq. “If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the same number of cards, I will have thrice as many cards as you will have “. Of the given choices, which could represent the number of cards with Iqbal?
Answer & solution
- A
9
31
- C
12
- D
35
Let Mushtaq has M cards while Iqbal has got I cards with him.
Let number of cards exchanged be x.
Case 1: I + x = 4(M – x) ... (i)
Case 2: I – x = 3(M + x) ... (ii)
From (i) and (ii)
I = 31x
Since I + M has to be less than or equal to 52, the only possible value for I could be 31.
Hence, option (b).