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

RELATED VIDEO

Def:

if rem(a/n) = f and rem(b/n) = g, so the remainder of ((a*b)/n) is

f*g, and if f*g is greater than n, the remainder is f*g - n

Now, the problem is:

x = 10*y + 4

If we divide x/5 we have:

remainder(x/f) ) = remainder ((10*y +4)/5)

= rem[(10*y)/5] + remainder (4/5)

= rem [10/5] + 4

= 0 + 4 = 4

Answer is 4.

When x is divided by 10, the quotient is y with a remainder of 4

Theory: Dividend = Divisor*Quotient + Remainder

x -> Dividend
10 -> Divisor
y -> Quotient (Assume)
4 -> Remainders
=> x = 10*y + y = 10y + 4

what is the remainder when x is divided by 5

x = 10y + 4
Remainder of x by 5 = Remainder of 10y + 4 by 5 = Remainder of 10y by 5 + Remainder of 4 by 5 = 0 + 4 = 4

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Remainders