Problem Solving

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

Official answer = A
Source = Veritas Prep

Hi ziyuenlau,

Let us test each statement one by one,.

S1: At least one of the three numbers is prime

One must know prime numbers till 100. Between 90 to 100, there are only one prime number '97.' So, there can be three consecutive odd positive integers such that none is prime: 91, 93, and 95. This statement must not be true.

S2: ab > c

Say, the three consecutive odd positive integers are 1, 3, and 5. Thus, 1*3 = 3 < c = 5. This statement must not be true.


S3: a + b + c = 3b

This statement must be true.

For any three consecutive positive integers, the middle-most integer, here b, is the mean of the three consecutive positive integers.

Thus, (a + b + c)/3 = b

=> a + b + c = 3b

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Number Properties Guide

-Jay
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