When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?
A. 2
B. 3
C. 4
D. 5
E. 6
OA B
Source: Magoosh
When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- 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
When it comes to remainders, we have a nice rule that says:BTGmoderatorDC wrote: ↑Fri Jun 11, 2021 7:58 pmWhen positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?
A. 2
B. 3
C. 4
D. 5
E. 6
OA B
Source: Magoosh
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 5, the remainder is 2
The possible values of k are: 2, 7, 12, 17, 22, 27, 32, 37, 42, . . .
When k is divided by 6, the remainder is 5.
The possible values of k are: 5, 11, 17, 23, 29, 35, 41. . . .
Since 17 is the only number (less than 40) that both lists share, it must be the case that k = 17
What is the remainder when k is divided by 7?
17 divided by 7 = 2 with remainder 3
Answer: B