Q is a set of four distinct prime numbers. If the sum . . .

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

Q is a set of four distinct prime numbers. If the sum . . .

by M7MBA » Sat Jan 13, 2018 11:17 am

Q is a set of four distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?

A. 2
B. 3
C. 4
D. 5
E. 7

The OA is the option B.

Why is B the correct option? Can't it be the option A? Experts, I would appreciate your help here. Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sat Jan 13, 2018 11:17 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 13, 2018 11:22 am

M7MBA wrote:Q is a set of four distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?

A. 2
B. 3
C. 4
D. 5
E. 7

We need to minimize the four distinct prime numbers.

We're told that the SUM of the four numbers is EVEN.
This means ALL FOUR prime numbers must be odd

ASIDE: We know this because there is only one even prime number (2). Since the four numbers are distinct, there can be, AT MOST, one 2. However, if there were one 2 (and three other odd primes), the sum of the four numbers would be ODD). So, we can conclude that the number 2 is NOT in the set of values.

So, the SMALLEST set of values is: {3, 5, 7, 11}

The number x is a member of Q, then what is the least value that x can be?
Answer: 3 (B)

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Aug 05, 2019 4:17 pm

M7MBA wrote:Q is a set of four distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?

A. 2
B. 3
C. 4
D. 5
E. 7

Since the sum of the integers is even, we must have 4 odd prime numbers. Thus, the least value of x is 3.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]