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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