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

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Intern
Joined: 26 Jun 2012
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Location: Germany
GMAT 1: 570 Q31 V39
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If a and b are positive integers, what is the remainder when ab is [#permalink]

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20 Jul 2013, 09:26
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Nov 2017, 02:07, edited 2 times in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 44421
Re: If a and b are positive integers, what is the remainder when ab is [#permalink]

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20 Jul 2013, 09:35
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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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Re: If a and b are positive integers, what is the remainder when ab is [#permalink]

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20 Jul 2013, 09:39
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?
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Re: If a and b are positive integers, what is the remainder when ab is [#permalink]

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20 Jul 2013, 09:47
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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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Re: If a and b are positive integers, what is the remainder when ab is [#permalink]

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08 Sep 2015, 18:37
Hi Bunuel,
i got this question wrong,but can you poiunt out th eflaw in my reasoning here,
what i did was i calculated that b= 8* a /5 and then ab = (8 * a^2 )/5. now if i divide this new ab by 40 i am left with a^2/25. after this i plugged numbers for a and got different remainders i.e if a^2 = 1, 4, 9, 16 etc , i will have different remainders therefore S1 is insufficient.
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Re: If a and b are positive integers, what is the remainder when ab is [#permalink]

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08 Sep 2015, 21:37
Jerry1982 wrote:
Hi Bunuel,
i got this question wrong,but can you poiunt out th eflaw in my reasoning here,
what i did was i calculated that b= 8* a /5 and then ab = (8 * a^2 )/5. now if i divide this new ab by 40 i am left with a^2/25. after this i plugged numbers for a and got different remainders i.e if a^2 = 1, 4, 9, 16 etc , i will have different remainders therefore S1 is insufficient.

From b= 8* a /5 (b/a = 8/5) it follows that a must be a multiple of 5, so you should plug only multiples of 5 there.
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Re: If a and b are positive integers, what is the remainder when ab is [#permalink]

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10 Sep 2015, 11:43
3
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Bunuel wrote:
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.

Isn't it possible to actually pick numbers here for (1) ?
We know both 'a' and 'b' have to be positive integers, and b is always 1.6 times of a.
So, all integer combinations which satisfy the condition - b=1.6a can help us.

a --> b = 1.6 a
5 --> 8
10 --> 16
15 --> 24
and likewise, and in all cases remainder will be 0. Right ?
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Re: If a and b are positive integers, what is the remainder when ab is [#permalink]

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18 Nov 2017, 02:08
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Re: If a and b are positive integers, what is the remainder when ab is   [#permalink] 18 Nov 2017, 02:08
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