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If bot a and b are nonzero integers, what is the value of ab

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If bot a and b are nonzero integers, what is the value of ab [#permalink]

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New post 15 Oct 2012, 07:40
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If bot a and b are nonzero integers, what is the value of a*b ?

(1) a^2=b^2
(2) \(\sqrt{b}=2\)

[Reveal] Spoiler:
1) \(a^2\) \(-\) \(b^2\) \(=\) \(0\) ---> \((a - b)\) \((a + b)\) \(=\) \(0\) ----> \(a = b\)and \(a= -b\) insuff

2) \(b = 2\) ---> basically \(\sqrt{b}\) \(=\) \(4\) or squaring both sides we have \(b = 4\) same insuff


1) + 2)\(b = 4\) and from one \(a = b\)-----> \(4*4\) \(=\)\(16\) we have\(a * b\) suff

But the OA is different :?:
[Reveal] Spoiler: OA

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Last edited by Bunuel on 15 Oct 2012, 07:51, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If bot a and b are nonzero integers, what is the value of ab [#permalink]

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New post 15 Oct 2012, 07:47
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The answer is E. When you sum up statements 1 and 2, you only considered the case when a=b. You forget to consider the case a=-b. This would mean that a = 4 & a = -4; the the answer cannot be determined.
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Re: If bot a and b are nonzero integers, what is the value of ab [#permalink]

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New post 15 Oct 2012, 07:49
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If bot a and b are nonzero integers, what is the value of a*b ?

(1) a^2=b^2 --> \(|a|=|b|\). If \(a=b=1\), then \(ab=1\) but if \(a=b=2\), then \(ab=4\). Not sufficient.

(2) \(\sqrt{b}=2\) --> \(b=4\). Nothing about \(a\). Not sufficient.

(1)+(2) Since from (2) \(b=4\), then from (1) \(a^2=16\), thus \(a=4\) or \(a=-4\) --> \(ab=4*4=16\) or \(ab=(-4)*4=-16\). Not sufficient.

Answer: E.

Hope it's clear.
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Re: If bot a and b are nonzero integers, what is the value of ab [#permalink]

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New post 15 Oct 2012, 08:08
Bunuel wrote:
If bot a and b are nonzero integers, what is the value of a*b ?

(1) a^2=b^2 --> \(|a|=|b|\). If \(a=b=1\), then \(ab=1\) but if \(a=b=2\), then \(ab=4\). Not sufficient.

(2) \(\sqrt{b}=2\) --> \(b=4\). Nothing about \(a\). Not sufficient.

(1)+(2) Since from (2) \(b=4\), then from (1) \(a^2=16\), thus \(a=4\) or \(a=-4\) --> \(ab=4*4=16\) or \(ab=(-4)*4=-16\). Not sufficient.

Answer: E.

Hope it's clear.


not consider that b = 4 a= b 4*4= 16 AND a = -b 4*-4 = -16

Thanks Mod :)
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Re: If bot a and b are nonzero integers, what is the value of ab   [#permalink] 15 Oct 2012, 08:08
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