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rajatvmittal
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The only factors of 25 are 1, 5, and 25.rajatvmittal wrote:If x, y, and z are all factors of 25, which of the following must be true?
The product xyz > 25
Either x = y, y = z, or x = z
x - y - z = even
The product xyz is odd
yz/x is an integer
OA - d
Thus:
x = 1, 5, or 25.
y = 1, 5, or 25.
z = 1, 5, or 25.
Approach 1: Use REASON to prove that one of the answer choices must be true.
Given the options above, x, y and z must ALL BE ODD.
The product of 3 odd integers must also be odd.
Thus, it must be true that xyz is odd.
The correct answer is D.
Approach 2: Find cases proving that four of the answer choices DON'T HAVE TO BE TRUE.
Case 1: x=25, y=5, and z=1.
B) Here, it is not true that x=y, y=z, or x=z. Eliminate B.
C) Here, x-y-z = 25-5-1 = 19, which is not even. Eliminate C.
E) Here, yz/x = (5*1)/25 = 1/5, which is not an integer. Eliminate E.
Case 2: x=1, y=1, and z=1.
A) Here, xyz = 1, which is not greater than 25. Eliminate A.
Since A, B, C and E do not have to be true, the correct answer must be D.
