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

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Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]
x=7q+5

4x=7*4q+20

4x=7*4q+7*2+6

4x=7(4q+2)+6

4x=7k+6 (k=4q+2)

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Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]
Bunuel wrote:
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

x=7k+5
4x=4*7k+20
hence remainder =6
Option D
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Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]
Bunuel wrote:
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.

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Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]
Bunuel wrote:
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

If x is divided by 7, the remainder is 5
i.e. x may be = 12, 19, 26, 33 etc
i.e. 4x may be = 48, 76, 104, 312 etc

i.e. Remainder (4x/7) = 6, 6, 6, 6, etc

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Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]
Top Contributor
Bunuel wrote:
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

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Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]
Top Contributor
Given that If x is divided by 7, the remainder is 5. And we need to find What is the remainder if 4x is divided by 7

If x is divided by 7, the remainder is 5

x -> Dividend
7 -> Divisor
a -> Quotient (Assume)
5 -> Remainders
=> x = 7*a + 5 = 7a + 5

What is the remainder if 4x is divided by 7

4x = 4*(7a + 5 ) = 7*4a + 20 = 7*4a + 7*2 + 6 = 7*(4a + 2) + 6

=> 4x gives 6 as remainder when divided by 7

Hope it helps!

Watch the following video to learn the Basics of Remainders

Re: If x is divided by 7, the remainder is 5. What is the remainder if 4x [#permalink]
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