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A certain fruit stand sells only apples for $0.26 each, bananas for $0.24 each, and cantaloupes for $0.65 each. Can

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by BTGmoderatorDC » Wed Jan 22, 2020 4:19 pm
A certain fruit stand sells only apples for $0.26 each, bananas for $0.24 each, and cantaloupes for $0.65 each. Can Clark spend exactly $5.00 at the fruit stand buying fruit that he likes?

(1) Clark does not like bananas.
(2) Clark does not like cantaloupes.



OA A

Source: Veritas Prep
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Re: A certain fruit stand sells only apples for $0.26 each, bananas for $0.24 each, and cantaloupes for $0.65 each. Can

by Jay@ManhattanReview » Thu Jan 23, 2020 12:41 am
BTGmoderatorDC wrote: ↑
Wed Jan 22, 2020 4:19 pm
 A certain fruit stand sells only apples for $0.26 each, bananas for $0.24 each, and cantaloupes for $0.65 each. Can Clark spend exactly $5.00 at the fruit stand buying fruit that he likes?

(1) Clark does not like bananas.
(2) Clark does not like cantaloupes.

OA A

Source: Veritas Prep
The wording of this question is debatable. Here's what Veritas wants us to interpret.

Let's take each statement one by one.

(1) Clark does not like bananas.

=> Veritas wants us not to interpret is as Clark likes apples and cantaloupes.

Case 1: Clark likes only cantaloupes.

Thus, 5/0.65 must be a positive integer. We see that 5/0.65 = 500/65 = 100/13 is not an integer, the answer is NO.

Case 2: Clark likes only apples.

Thus, 5/0.26 must be a positive integer. We see that 5/0.26 = 500/26 = 250/13 is not an integer, the answer is NO.

Case 3: Clark likes both apples and cantaloupes.

Say Clark buys x apples and y cantaloupes.

Thus, 0.26x + 0.65y = 5 => 26x + 65y = 500 => 13(2x + 5y) = 500. Since 500 is not a factor of 13, 2x + 5y cannot be an integer. So, the answer is NO.

Sufficient.

(2) Clark does not like cantaloupes.

Case 1: Clark likes only apples.

We have already seen that the answer is NO.

Case 2: Clark likes only bananas.

Thus, 5/0.24 must be a positive integer. We see that 5/0.24 = 500/24 = 125/6 is not an integer, the answer is NO.

Case 3: Clark likes both apples and bananas.

Say Clark buys x apples and y bananas.

Thus, 0.26x + 0.24y = 5 => 26x + 24y = 500 => 13x + 12y = 250. One solution we have is x = y = 10. So, the answer is YES.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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