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

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Moderator
Joined: 01 Sep 2010
Posts: 3355

Kudos [?]: 9043 [0], given: 1152

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

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15 Oct 2012, 07:40
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Difficulty:

35% (medium)

Question Stats:

77% (00:29) correct 23% (00:46) wrong based on 26 sessions

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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.

Kudos [?]: 9043 [0], given: 1152

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

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15 Oct 2012, 07:47
1
KUDOS
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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Kudos [?]: 20 [1], given: 233

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Joined: 02 Sep 2009
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Kudos [?]: 128627 [1], given: 12180

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

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15 Oct 2012, 07:49
1
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Expert's post
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.

Hope it's clear.
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Kudos [?]: 128627 [1], given: 12180

Moderator
Joined: 01 Sep 2010
Posts: 3355

Kudos [?]: 9043 [0], given: 1152

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

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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.

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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Kudos [?]: 9043 [0], given: 1152

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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