When integer b is divided by 13, the remainder is 6. Which o

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by BTGmoderatorAT » Wed Jan 24, 2018 5:58 pm

When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

A) 13b/52
B) b/26
C) b/17
D) b/12
E) b/6

OA: B

Is there a strategic approach to this question? Can any experts assist?

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Source: Beat The GMAT — Problem Solving | Wed Jan 24, 2018 5:58 pm

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by [email protected] » Wed Jan 24, 2018 7:08 pm

Hi ardz24,

We're told that B is an integer and when B is divided by 13, the remainder is 6. We're asked which of the following CANNOT be an integer. This is a great 'concept question', meaning that if you recognize the concepts involved, then you won't need to do much (if any) math to get the correct answer.

Since dividing B by 13 always gives us a remainder of 6, this means that B CANNOT be a multiple of 13. By extension, B cannot be a multiple of 26 or 39 or 52 or any other multiple of 13. Since B cannot be a multiple of 26, then dividing B by 26 would always leave a remainder - meaning that B/26 will NEVER be an integer.

Final Answer: B

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Rich

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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 » Mon Jan 29, 2018 9:47 am

ardz24 wrote:When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

A) 13b/52
B) b/26
C) b/17
D) b/12
E) b/6

If, when b is divided by 13, the remainder is 6, then that means b = 13q + 6 for some integer q. Let's analyze each answer choice to see whether the given expression can produce an integer.

A) 13b/52

We need to see if 13(13q + 6)/52 = (13q + 6)/4 could equal an integer for some integer value of q. We can choose q = 2. If q = 2, then 13q + 6 = 32, which is is divisible by 4; hence 13(32)/52 is an integer.

B) b/26

Could (13q + 6)/26 result in an integer for some integer value of q? Notice that 26 is exactly 2 times 13. So, for any integer value of q, 13q will either be divisible by 26 (if q is even) or produce a remainder of 13 (if q is odd). Adding 6 to 13q, the expression will either produce a remainder of 6 or 19, but will never produce a remainder of zero. Therefore, (13q + 6)/26 = b/26 can never equal an integer.

Answer: B

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