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Re: If a and b are positive integers, what is the remainder when [#permalink]
20 Jul 2013, 08:35

4

This post received KUDOS

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.

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.

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

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