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What is the remainder when -12 is divided by -5?

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by Max@Math Revolution » Wed Mar 06, 2019 11:58 pm

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[GMAT math practice question]

What is the remainder when -12 is divided by -5?

A. -3
B. -2
C. 0
D. 2
E. 3
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by GMATGuruNY » Thu Mar 07, 2019 3:51 am
This problem is not relevant to the GMAT.
On the GMAT, problems involving remainders are constrained to POSITIVE INTEGERS.
From the Math Review in the OG:
If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r and 0 ≤ r < x.
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by Max@Math Revolution » Sun Mar 10, 2019 5:02 pm
=>

If we can write A = BQ + R with 0 ≤ R < |B|, then R is the remainder when A is divided by B.

-12 = (-5)*3 + 3

Thus, the remainder when -12 is divided by -5 is 3.

Therefore, the answer is E.
Answer: E
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by Scott@TargetTestPrep » Sun Mar 10, 2019 6:45 pm
Max@Math Revolution wrote:[GMAT math practice question]

What is the remainder when -12 is divided by -5?

A. -3
B. -2
C. 0
D. 2
E. 3
By definition, the remainder when m is divided by n (m and n are integers and n ≠ 0) is the positive difference between m and kn (k is an integer and kn is a multiple of n that is less than or equal to m and closest to m). For example, the remainder when 15 is divided by 4 is 3 since 12 is a multiple of 4 that is less than or equal to 15 and closest to 15, and the positive difference between 15 and 12 is 3.

Using this definition, we see that -15 is a multiple of -5 that is less than or equal to -12 and closest to -12. Since the positive difference between -12 and -15 is -12 - (-15) = 3, so the remainder when -12 is divided by -5 is 3.

Answer: E

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