If x is divided by 7, the remainder is 5. What is the

[VJesus12]

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?

A. 1
B. 2
C. 4
D. 6
E. 8

The OA is the option D.

How can I find the remainder? I know that option E is not possible. But, how can I get which one is the correct answer?

Experts, I will wait for your answer. <i class="em em-frowning"></i>

[Brent@GMATPrepNow]

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?

A. 1
B. 2
C. 4
D. 6
E. 8

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.

If x is divided by 7, the remainder is 5
So, some possible values of x are: 5, 5+7, 5+(2)(7), 5+(3)(7), . . . etc
The easiest number to work with is the smallest, 5.

So, let's see what happens when x = 5

What is the remainder if 4x is divided by 7?
4x = 4(5) = 20
20 divided by 7 equals 2 with remainder 6

Answer: D

Cheers,
Brent

[Scott@TargetTestPrep]

If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?

A. 1
B. 2
C. 4
D. 6
E. 8

Since when x is divided by 7, the remainder is 5, we can create the following equations in which the quotient = Q:

x/7 = Q + 5/7

x = 7Q + 5

Since we need to determine the remainder when 4x is divided by 7, we can multiply both sides of the equation x = 7Q + 5 by 4 and we have:

4x = 28Q + 20

Finally, we can divide 28Q + 20 by 7:

(28Q + 20)/7

28Q/7 + 20/7

Since 7 divides into 28Q, we are only concerned with the remainder of the division of 20 by 7, which is 6.

Alternate solution:

We are given that when x is divided by 7, the remainder is 5. We can see that a possible number for x is 12. Therefore, we need to determine the remainder when 4x, or in this case, 48, is divided by 7. Since 48/7 = 6, R 6, the remainder is 6.

Answer: D