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When both positive integers a and b are divided by 9, their remainders

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Math Revolution GMAT Instructor
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When both positive integers a and b are divided by 9, their remainders  [#permalink]

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New post 25 Feb 2018, 17:43
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

60% (01:33) correct 40% (01:54) wrong based on 47 sessions

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[GMAT math practice question]

When both positive integers \(a\) and \(b\) are divided by \(9\), their remainders are \(7\). What is the reminder when \(a^2b\) is divided by \(9\)?

\(A. 4\)
\(B. 3\)
\(C. 2\)
\(D. 1\)
\(E. 0\)

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Re: When both positive integers a and b are divided by 9, their remainders  [#permalink]

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New post 25 Feb 2018, 18:10
MathRevolution wrote:
[GMAT math practice question]

When both positive integers \(a\) and \(b\) are divided by \(9\), their remainders are \(7\). What is the reminder when \(a^2b\) is divided by \(9\)?

\(A. 4\)
\(B. 3\)
\(C. 2\)
\(D. 1\)
\(E. 0\)



We can Multiply the Remainder ..
\(a^2*B=7^2*7=49*7\)..
49 leaves a remainder of 4 when div by 9
So 49*7 will leave same Remainder as 4*7=28..
28=3*9+1
So 1 is the answer..
D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Math Revolution GMAT Instructor
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Re: When both positive integers a and b are divided by 9, their remainders  [#permalink]

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New post 26 Feb 2018, 01:35
=>
The best way to approach remainder questions is to plug in a number. We shall plug in \(7\) for both \(a\) and \(b\) because its remainder, when divided by \(9\), is \(7\), as required by the question. Then \(a^2b=7^27=343\), and the remainder of \(343\) when it is divided by \(9\) is \(1\).

Therefore, the answer is D.

Answer : D
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Re: When both positive integers a and b are divided by 9, their remainders &nbs [#permalink] 26 Feb 2018, 01:35
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