BTGmoderatorDC wrote: ↑Fri Jun 11, 2021 7:58 pm
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 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 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
Brent Hanneson - Creator of GMATPrepNow.com
