richachampion wrote:A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?
A. 33
B. 46
C. 49
D. 53
E. 86
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.
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n students can be divided into equal groups of 4 with 1 student left over
So, n divided by 4 leaves a remainder of 1.
So, the possible values of n are: 1, 5, 9,
13, 17, 21, 25, 29,
33, 37, etc.
Aside: It's unclear whether n could equal 1 here. Can we say that 1 student can be divided into equal groups of 4 with 1 student left over? Even 5 students might night be okay, since we can't really say that 5 students can be divided into equal groups of 4 with 1 student left over. Anyhoo, it doesn't really matter since those two values (1 and 5) don't come into play.
n students can be divided into equal groups of 5 with 3 students left over
So, n divided by 5 leaves a remainder of 3.
So, the possible values of n are: 3, 8,
13, 18, 23, 28,
33, 38, etc.
So, the two smallest values of n that satisfy BOTH conditions are
13 and
33.
13 +
33 =
46
Answer:
B
RELATED VIDEO
- Introduction to Remainders:
https://www.gmatprepnow.com/module/gmat ... /video/842Brent Hanneson - Creator of GMATPrepNow.com
