At a store where apples cost 50 cents each and bananas cost 31 cents

Question

At a store where apples cost 50 cents each and bananas cost 31 cents each, Van bought only some apples whereas Anya bought only some bananas. How many apples did Van buy?

(1) If, instead of apples, Van had bought bananas in the same number in which he bought the apples, he would have spent $1.33 less.

(2) Van spent $1.33 more than Anya spent.

Source:  Marty Murray Coaching

BhavyaYadav · Answer

Solution:

Let the number of apples bought is x.

1. The number of bananas is equal to the number of apples = x
So the total cost of bananas = x*.31
Total cost of apples = x*.5
Acc. to question:
x*.31 = x*.5 - 1.33
=> .5x - .31x = 1.33
=> x = 7
Thus, the number of apples = number of bananas = 7
 Sufficient

2. Amount spent by Van > Amount spent by Anya 
 Provides no relation or information about the number 
 Not Sufficient

Hence ans. A

Shubhardwaj31 · Answer

for option B,

we know that

0.5 X - 0.31 Y = 1.33

By putting in random values for X & Y starting from 1 (since fruits can't be negative), we can find out the value of X and Y, while it will take time but a definite value is possible which is the main objective of these questions

Hence, correct value shall be C

MartyMurray  your thoughts?

MartyMurray · Answer

Take another look.

No definite value is locked in by statement (2).

Rather, since the difference between the cost of 7 apples and the cost of 7 bananas is 1.33, all statement (2) indicates is that X and Y are in the following relationship:

0.50(X - 7) = 0.31(Y - 7)

For instance, both of the following work.

X = 38 Y = 57 -> 0.5(38) = 0.31(57) + 1.33 = 19

X = 69 Y = 107 -> 0.5(69) = 0.31(107) + 1.33 = 34.5

Basically, since we are not provided with information on what Anya spent, there's no way to determine mathematically what Van spent using the information provided by statement (2).

On the other hand statement (1) is sufficient for the following reason.

Each banana costs 50 - 31 = 19 cents less than each apple.

So, since, as statement 1 says, "If, instead of apples, Van had bought bananas in the same number in which he bought the apples, he would have spent $1.33 less," we can use that information to calculate how many bananas would have been substituted for apples by dividing 1.33 by 0.19 to get 7.

In other words, if he can save 19 cents per banana swapped for each apple, he must have bought the number of apples such that there would be the right number of swaps to add up to $1.33.

Correct answer:   A

At a store where apples cost 50 cents each and bananas cost 31 cents

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