When positive integer k is divided by 35, the remainder is

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Apr 15, 2019 10:47 pm

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When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

OA B

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Mon Apr 15, 2019 10:47 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Apr 15, 2019 11:40 pm

BTGmoderatorDC wrote:When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

OA B

Source: Veritas Prep

Say when the positive integer k is divided by 35, the quotient is q and the remainder is 14. Then, we have

k = 35q + 14
k = 7(5k + 2)

We see that k must be a multiple of 7 or divisible by 7.

The correct answer: B

Hope this helps!

-Jay
The correct answer: [spoiler][/spoiler]

Hope this helps!

-Jay
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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue Apr 16, 2019 10:43 am

$K = 35Q+14$

When $Q = 1$

$K = 49 \cdots $ it is divisible by $7$

When $Q = 2$

$K = 84 \cdots$ it is divisible by $7$ and $21$

When $Q = 3$

$K = 109$.

it is divisible by $7 \cdots $

Therefore, __B__ is the correct answer.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Apr 17, 2019 5:45 pm

BTGmoderatorDC wrote:When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

OA B

Source: Veritas Prep

We can create the following equation:

k = 35Q + 14

We see that 35Q + 14 is divisible by 7.

Answer: B

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Founder and CEO
[email protected]

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