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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.

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.

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01 Aug 2014, 00:25

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08 Sep 2015, 08:12

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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, 17:37

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.

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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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, 01:50

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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, 09:20

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.

Answer: A.

In (2), how can I figure out that I should pick 2 and 10 please shed me some light

gmatclubot

Re: If a and b are positive integers, what is the remainder when
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27 Nov 2016, 09:20

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