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

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

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

Last edited by kingflo on 22 Jul 2013, 06:13, edited 1 time in total.
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Re: If a and b are positive integers, what is the remainder when [#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 [#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 [#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 [#permalink]

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01 Aug 2014, 01:25
Hello from the GMAT Club BumpBot!

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Re: If a and b are positive integers, what is the remainder when [#permalink]

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08 Sep 2015, 09:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a and b are positive integers, what is the remainder when [#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 [#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 [#permalink]

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10 Sep 2015, 11:43
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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 [#permalink]

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23 Sep 2016, 02:50
Hello from the GMAT Club BumpBot!

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Re: If a and b are positive integers, what is the remainder when [#permalink]

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27 Nov 2016, 10:20
Bunuel wrote:
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.

In (2), how can I figure out that I should pick 2 and 10
Re: If a and b are positive integers, what is the remainder when   [#permalink] 27 Nov 2016, 10:20
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