CAT 1998 — QA Question 25
Direction: Answer the question based on the following information.
A, B, C and D collected one-rupee coins following the given pattern.
- Together they collected 100 coins.
- Each one of them collected even number of coins.
- Each one of them collected at least 10 coins.
- No two of them collected the same number of coins.
My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates he wishes. But then he must have biscuits twice the number of chocolates and should have apples more than biscuits and chocolates together. Each chocolate cost Re 1. The cost of apple is twice the chocolate and four biscuits are worth one apple. Then which of the following can be the amount that I spent on that evening on my son if number of chocolates, biscuits and apples brought were all integers?
Answer & solution
Rs. 34
- B
Rs. 33
- C
Rs. 8
- D
None of these
Let the number of chocolates be c.
Number of apples has to be more than 3c, lets say 3c + k, k is a positive integer.
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Total spend = 8c + 2k
for c = 4, k = 2
Total spend = 34
Hence (a) is the answer.
The cost of each chocolate is Re 1. So the cost of apple should be Rs. 2 and that of one biscuit should be Re 0.5. Thus, if he eats x chocolates, he has to eat 2x biscuits. Hence, the total value of chocolates will be Rs. x and that of biscuits will be (0.5)(2x) = Rs. x. Hence, we see that the value of chocolates is to the value of biscuits will always be 1 : 1. As per our assumption he will have to eat more than (x + 2x) = 3x apples and hence the total value of the apples will be more than (2)(3x) = 6x. In other words, the ratio of value chocolates to apples or biscuits to apples will be more than 1 : 6. In other words, if the value of chocolates and biscuits is Re 1 each, then the value of apples has to be more than Rs. 6, or the combined value will be more than Rs. 8. This means that the
value of apples will always constitute more than or of the entire bill. It can further be observed that the total value of chocolates and biscuits together will always be an even integer and so will be the value of apples. This means that the combined value of all three of them has to be even and not odd. So Rs. 33 cannot be the answer. Also Rs. 8 cannot be the answer as, if we take the value of chocolates and biscuits to be minimum, i.e. Re 1 each, then the value of apples can be a minimum of Rs. 8. Hence, the total value will always be Rs. 10 or higher. The only option possible is Rs. 34. To verify this let us find two even numbers (one of them higher than of 34) which adds 34.
We can find many such numbers e.g. 32 + 2, 30 + 4, 28 + 6 and 26 + 8. All of these could be a possible combination.