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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7605
GMAT 1: 760 Q51 V42 GPA: 3.82
When both positive integers a and b are divided by 9, their remainders  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 59% (01:35) correct 41% (01:49) wrong based on 61 sessions

### HideShow timer Statistics [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 $$9$$?

$$A. 4$$
$$B. 3$$
$$C. 2$$
$$D. 1$$
$$E. 0$$

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: When both positive integers a and b are divided by 9, their remainders  [#permalink]

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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
D
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7605
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: When both positive integers a and b are divided by 9, their remainders  [#permalink]

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=>
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 $$1$$.

_________________ Re: When both positive integers a and b are divided by 9, their remainders   [#permalink] 26 Feb 2018, 02:35
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# When both positive integers a and b are divided by 9, their remainders  