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# If a and b are positive integers, what is the remainder when

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Joined: 26 Jun 2012
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Kudos [?]: 43 [4] , given: 1

If a and b are positive integers, what is the remainder when [#permalink]  20 Jul 2013, 08:26
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27% (02:23) correct 73% (01:52) wrong based on 321 sessions
If a and b are positive integers, what is the remainder when ab is divided by 40?

(1) b is 60% greater than a.

(2) Each of $$a^2b$$ and $$ab^2$$ is divisible by 40.

Can post OE if needed.
[Reveal] Spoiler: OA

Last edited by kingflo on 22 Jul 2013, 05:13, edited 1 time in total.
Math Expert
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Kudos [?]: 42559 [4] , given: 6038

Re: If a and b are positive integers, what is the remainder when [#permalink]  20 Jul 2013, 08:35
4
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Expert's post
If a and b are positive integers, what is the remainder when ab is divided by 40?

(1) b is 60% greater than a --> $$b=1.6a$$--> $$b=\frac{8}{5}a$$ --> $$\frac{b}{a}=\frac{8}{5}$$ --> b is a multiple of 8 (8x) and a is a multiple of 5 (5x) --> ab=5x*8x=40x^2. The remainder when $$ab=40x^2$$ is divided by 40 is 0. Sufficient.

(2) Each of a^2 *b and a*b^2 is divisible by 40. If a=2 and b=10, then ab=20 and the the remainder is also 20 but if a=b=40, then ab=40^2 and the remainder si 0. Not sufficient.

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Intern
Joined: 26 Jun 2012
Posts: 24
Location: Germany
GMAT 1: 570 Q31 V39
GMAT 2: 710 Q43 V44
Followers: 0

Kudos [?]: 43 [0], given: 1

Re: If a and b are positive integers, what is the remainder when [#permalink]  20 Jul 2013, 08:39
Could we also pick numbers for (1)?

(1) b = 1,6a
--> pick smart numbers: b=10 , a=16 --> 10*16 / 40 = 4 + R0 --> Sufficient

Right?
Math Expert
Joined: 02 Sep 2009
Posts: 27526
Followers: 4327

Kudos [?]: 42559 [1] , given: 6038

Re: If a and b are positive integers, what is the remainder when [#permalink]  20 Jul 2013, 08:47
1
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Expert's post
kingflo wrote:
Could we also pick numbers for (1)?

(1) b = 1,6a
--> pick smart numbers: b=10 , a=16 --> 10*16 / 40 = 4 + R0 --> Sufficient

Right?

This won't work in all cases. If the question were "what is the remainder when ab is divided by 80?", then with your numbers you'd still get that the remainder is 0, and the statement is sufficient. But this would be wrong: if b=5 and a=5, then ab=40 and the remainder is 40 not 0.

Hope it's clear.
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Kudos [?]: 55 [0], given: 0

Re: If a and b are positive integers, what is the remainder when [#permalink]  01 Aug 2014, 00:25
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Re: If a and b are positive integers, what is the remainder when   [#permalink] 01 Aug 2014, 00:25
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