Bunuel wrote:
Competition Mode Question
If a and b are both factors of 50, which of the following must be true?
(A) ab≥ 2
(B) a + b≤ 50
(C) ab is a factor of 100.
(D) ab is a factor of 2500.
(E) ab is even.
Since a is a factor of 50 and b is also a factor of 50, then ab is a factor of 50 x 50 = 2500.
To eliminate the other choices,consider the factors of 50: 1, 2, 5, 10, 25, and 50.
Choice A is incorrect because if a = 1 and b = 1, then ab = 1, and A is not true.
Choice B is incorrect because if a = 50 and b = 10, then a + b = 60 and B is not true.
Choice C is incorrect because if a = 25 and b = 10, then ab = 250, which is not a factor of 100.
Choice D is true because every product of two factors of 50 is also a factor of 50 x 50 = 2500.
Choice E is incorrect because if a = 1 and b = 5, then ab = 5, which is odd, so E is not true.
Answer: D
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