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When a certain number X is divided 63, the remainder...

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When a certain number X is divided 63, the remainder...

by BTGmoderatorLU » Sat Feb 10, 2018 7:18 am
When a certain number X is divided by 63, the remainder is 27. What is the remainder when X is divided by 7?

A. 2
B. 3
C. 4
D. 5
E. 6

The OA is E.

If, X / 63, the remainder is 27.

I can write, 63 = 9*7

Now, X / 7, what is the remainder?

I'm a little confused by this PS question. Experts, any suggestion about how o solve it? Thanks in advance.
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by Brent@GMATPrepNow » Sat Feb 10, 2018 7:30 am
LUANDATO wrote:When a certain number X is divided by 63, the remainder is 27. What is the remainder when X is divided by 7?

A. 2
B. 3
C. 4
D. 5
E. 6
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 a certain number X is divided by 63, the remainder is 27
So, some possible values of X are: 27, 27+63, 27+(2)(63), 27+(3)(63), . . . etc
The easiest number to work with is the smallest, 27.

So, let's see what happens when X = 27

What is the remainder when X is divided by 7?
27 divided by 7 equals 3 with remainder 6

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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