M7MBA wrote: ↑Wed Jun 24, 2020 6:35 am
When \(x\) is divided by 10, the quotient is \(y\) with a remainder of 4. If \(x\) and \(y\) are both positive integers, what is the remainder when \(x\) is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
[spoiler]OA=E[/spoiler]
Source: Manhattan GMAT
APPROACH #1: Test a possible value of x
When it comes to remainders, we have a nice property 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.
So, from the given information, the possible values of x are: 4, 14, 24, 34, 44, 54,....
If you divide any of these possible x-values by 5, you'll always get a remainder of 4.
Answer: E
APPROACH #2: Use algebra
There's a nice rule that says, "
If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
From the given information we can write: x = 10y + 4
We can rewrite this as: x = (
5)(2x) + 4
We know that (
5)(2x) is a multiple of
5, which means (
5)(2x)
+ 4 is
4 MORE THAN a multiple of
5
So, when we divide (
5)(2x) + 4 by
5, the remainder will be
4
Answer: E
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