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

##### This topic has expert replies
Moderator
Posts: 6591
Joined: 07 Sep 2017
Followed by:20 members

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

by BTGmoderatorDC » Thu Mar 31, 2022 1:26 am

00:00

A

B

C

D

E

## Global Stats

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

### GMAT/MBA Expert

GMAT Instructor
Posts: 16084
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

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

by [email protected] » Thu Mar 31, 2022 5:32 am
BTGmoderatorDC wrote:
Thu Mar 31, 2022 1:26 am
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
When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

When positive integer k is divided by 35, the remainder is 14.
So, some possible values of k are: 14, 49, 84, 119, . . . etc

Let's test some values.
If k = 14, then we can ELIMINATE A, C and E, since they are not divisors of 14, and the questions says "Which of the following MUST be a divisor of k?
We're left with answer choices B and D

Let's test another value.
If k = 49, then we can ELIMINATE D, since 14 is not a divisor of 49.

By the process of elimination, we're left with B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

Legendary Member
Posts: 1100
Joined: 10 May 2014
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

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

by GMATinsight » Sat Apr 02, 2022 5:09 am
BTGmoderatorDC wrote:
Thu Mar 31, 2022 1:26 am
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
Two important inferences for questions like this:
1) Divisor is always greater than the remainder
2) Dividend - remainder (i.e. k-14) must be divisible by divisor (i.e. 35)

i.e. k-14 could be 0 or 35 or 70 etc.
i.e. k could be 14 or 49 or 84 etc.

the HCF of {14, 49, 84} = 7

i.e. 7 MUST be a divisor of k