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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
Joined: 16 Aug 2015
Posts: 6625
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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25 Feb 2018, 17:43
00:00

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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7107 Re: When both positive integers a and b are divided by 9, their remainders [#permalink] ### Show Tags 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 _________________ 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 GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6625 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When both positive integers a and b are divided by 9, their remainders [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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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