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>
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If x is divided by 7, the remainder is 5. What is the
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When it comes to remainders, we have a nice rule that says:VJesus12 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 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
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Brent
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VJesus12 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.
Answer: D
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