If m is an even integer, then which of the following is...

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Thu Apr 05, 2018 8:50 am

If m is an even integer, then which of the following is the sum of the next two even integers greater than 4m + 1?

A. 8m + 2
B. 8m + 4
C. 8m + 6
D. 8m + 8
E. 8m + 10

The OA is C.

I tried to solve this PS question but I can't get the correct answer. Can anyone help me with it? Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Apr 05, 2018 8:50 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Fri Apr 06, 2018 1:59 am

Hello swerve.

This is the best way I could solve it.

We don't need to know the value of m. We just have to note that 4m+1 is an odd number.

Therefore, the next two even integers greater than 4m+1 are 4m+2 and 4m+4.

Therefore, the sum is $$\left(4m+2\right)+\left(4m+4\right)=8m+6.$$ Therefore, the correct answer is the option C.

I really hope this helps you.

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Sionainn@PrincetonReview: GMAT Instructor; Posts: 41; Joined: Mon Mar 12, 2018 9:54 amFollowed by: 1 member

by Sionainn@PrincetonReview » Fri Apr 06, 2018 4:51 am

An alternative to the algebraic solution is to plug in. Pick an even integer. Let's say m = 2, then 4m + 1 = 9. Then the next two even integers are 10 and 12. The sum of 10 and 12 = 22. So that's the answer when m = 2. So go to the answer choices and replace m with 2 and see which choice gives an answer of 22. Only C works.

A. 8m + 2
B. 8m + 4
C. 8m + 6
D. 8m + 8
E. 8m + 10

Take care,

Sionainn Marcoux
BA - Stanford University, MPP - Harvard University
Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Apr 10, 2018 10:25 am

swerve wrote:If m is an even integer, then which of the following is the sum of the next two even integers greater than 4m + 1?

A. 8m + 2
B. 8m + 4
C. 8m + 6
D. 8m + 8
E. 8m + 10

We first note that (4m + 1) is an odd integer because 4m is even and 1 is odd and (even + odd) = odd. Thus, the next even integer greater than (4m + 1) is (4m +2), and the next even integer greater than (4m + 2) is (4m + 4). The sum of those two integers is (4m + 2) + (4m + 4) = 8m + 6.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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