mgasset wrote:When a number x is divided by 5 it leaves a reminder of 3 and when divided by 7 it leaves a remainder of 4. If another number y leaves a reminder of 3 when divided by 5 and a reminder of 4 when divided by 7 and x is bigger than y. Which of the following must be a factor of x-y?
a) 10
b) 15
c) 20
d) 25
e) 35

We can also solve the question by plugging in numbers. Along that line, how do we find numbers that satisfy the given conditions? There's a nice rule that goes like this:

If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

When a number x is divided by 5 it leaves a reminder of 3
So, the possible values of x include 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53,...

When x is divided by 7 it leaves a remainder of 4.
So, the possible values of x include 4, 11, 18, 25, 32, 39, 46, 53,...

So, we can see that x could equal 18 or 53, or some other values, which we need not concern ourselves with.

Since y has the same attributes as x, y could also equal 18 or 53, or some other values (which we need not concern ourselves with).

Given all of this, one possible value of x-y could be 35, since 53-18 = 35.
Since answer choices A, B, C and D are not factors of 35, we can eliminate them.
This leaves us with E, the correct answer.

Cheers,
Brent