Carcass wrote:
If ab is divisible by c, which of the following cannot be true?
A. a is divisible by c.
B. a is not divisible by c.
C. c is a prime number.
D. ab + c is odd and c is odd.
E. ab + c is odd and c is even.
Official Explanation If ab is divisible by c, then a might be divisible by c (e.g., if a = 8, b = 3, and c = 2).
Choice (A) is possible and thus incorrect.
Additionally, this numeric example demonstrates that
choice (C) is possible and thus incorrect, since 2 is a prime number.
If ab is divisible by c, then a might also not be divisible by c (for example, if a = 3, b = 4, and c = 6).
Choice (B) is possible and thus incorrect.
In
choice (D), if c is odd and ab + c is odd, then ab must be even. An even divided by an odd can result in an integer (e.g., if ab = 12 and c = 3).
Choice (D) is possible and thus incorrect.
Finally, in
choice (E), if c is even and ab + c is odd, then ab must be odd. An odd divided by an even will never result in an integer; that is, if ab is odd and c is even, ab will never be divisible by c.
Choice (E) is impossible and therefore is the correct answer.
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