If a and b are prime numbers, such that a > b, which of the following cannot be true?

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu Dec 03, 2020 2:51 pm

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If a and b are prime numbers, such that a > b, which of the following cannot be true?

A. a+b is prime.
B. ab is odd.
C. a(a-b) is odd.
D. a-b is prime.
E. a^b is even.

Answer: E
Source: Kaplan

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Source: Beat The GMAT — Problem Solving | Thu Dec 03, 2020 2:51 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8190; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If a and b are prime numbers, such that a > b, which of the following cannot be true?

by Scott@TargetTestPrep » Sun Dec 06, 2020 8:54 am

BTGModeratorVI wrote: ↑
Thu Dec 03, 2020 2:51 pm
If a and b are prime numbers, such that a > b, which of the following cannot be true?

A. a+b is prime.
B. ab is odd.
C. a(a-b) is odd.
D. a-b is prime.
E. a^b is even.

Answer: E

Solution:

Recall that all the prime numbers other than 2 are odd. Since a > b, a must be odd, no matter the value of b . Thus, a^b must be odd since any odd number raised to any power is odd. So, a^b can’t be even.

Answer: E

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Founder and CEO
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