ziyuenlau wrote:If a, b, and c are consecutive odd positive integers and a<b<c, which of the following must be true?
I. at least one of the three numbers is prime
II. ab>c
III. a + b + c = 3b
A. III only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
While it is possible under timed condtions to prove that a huge integer is NOT prime -- if the integer is even, if the integer is a multiple of 3, etc. -- it is NOT possible under timed conditions to prove that a huge integer IS prime.
Thus, if a GMAT problem asks whether a huge integer is prime, the answer must be NO.
I: at least one of the three numbers is prime
Here, it is possible that a, b and c are HUGE.
Since the problem asks whether these potentially huge numbers are all prime, the answer must be NO.
Since Statement I does not have to be true, eliminate any answer choice that includes Statement I.
Eliminate B, C and E.
II: ab > c
If a=1, b=3, and c=5, then ab < c.
Since Statement II does not have to be true, eliminate any remaining answer choice that includes Statement II.
Eliminate D.
The correct answer is
A.
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