BTGmoderatorDC wrote:Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?
(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.
OA B
Source: Princeton Review
Let the number of 30 cent stamps, 35 cent stamps and 40 cent stamps be x, y and z, respectively.
Thus, we have
30x + 35y + 40z = 420
6x + 7y + 8z = 84
We have to determine where at least one of x, y and z is greater than 5.
Let's take each statement one by one.
(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
=> y = z
Thus, from 6x + 7y + 8z = 84, we have
6x + 7z + 8z = 84
6x + 15z = 84
2x + 5z = 28
Case 1: Say z = y = 2,
=> x = 9 > 5. The answer is Yes.
Case 1: Say z = y = 4,
=> x = 4 < 5. The answer is No.
No unique answer. Insufficient.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.
=> x = z and y ≤ z
Thus, from 6x + 7y + 8z = 84, we have
6z + 7y + 8z = 84
14z + 7y = 84
Case 1: Say x = z = 4
=> y = 4 < 5. The answer is No.
Case 2: Say x = z = 2
=> y = 8 > 5. But this is not a valid case since we know that y ≤ z; however, since for this case, y = 8 > z = 2.
Thus, we can conclude that x, y, and z, each is not greater than 5. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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