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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] New post 20 Jul 2013, 08:26
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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, 05:13, edited 1 time in total.
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Re: If a and b are positive integers, what is the remainder when [#permalink] New post 20 Jul 2013, 08:35
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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.

Answer: A.
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Re: If a and b are positive integers, what is the remainder when [#permalink] New post 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?
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Re: If a and b are positive integers, what is the remainder when [#permalink] New post 20 Jul 2013, 08:47
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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] New post 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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