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# If a*b = −8, what is the value of a + b? (1) a − b = 6 (2) a^2*b = 32

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Joined: 02 Sep 2009
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If a*b = −8, what is the value of a + b? (1) a − b = 6 (2) a^2*b = 32  [#permalink]

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Updated on: 26 Nov 2019, 08:33
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55% (hard)

Question Stats:

60% (02:05) correct 40% (01:39) wrong based on 56 sessions

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If $$a*b = −8$$, what is the value of $$a + b$$?

(1) $$a − b = 6$$

(2) $$a*b^2 = 32$$

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Originally posted by Bunuel on 25 Nov 2019, 01:13.
Last edited by chetan2u on 26 Nov 2019, 08:33, edited 1 time in total.
Edited statement (2)
Math Expert
Joined: 02 Aug 2009
Posts: 8257
Re: If a*b = −8, what is the value of a + b? (1) a − b = 6 (2) a^2*b = 32  [#permalink]

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25 Nov 2019, 20:24
If $$a*b = −8$$, what is the value of $$a + b$$?

(1) $$a − b = 6$$
This will clearly give us two values....a=b+6
So $$a*b=b(b+6)=-8.......b^2+6b+8=0...(b+4)(b+2)=0$$
Two cases
b=-4, a=2...a+b=-4+2=-2
b=-2, a=4...a+b=4-2=2
Insuff

(2) $$a^2*b = 32.......a*(a*b)=32.....a*(-8)=32.....a=-4$$
So b = 2 and a+b=-4+2=-2
Suff

B

However the values of b differs in both statements. It should have been $$a*b^2=32$$
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Re: If a*b = −8, what is the value of a + b? (1) a − b = 6 (2) a^2*b = 32  [#permalink]

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26 Nov 2019, 08:31
Bunuel wrote:
If $$a*b = −8$$, what is the value of $$a + b$$?

(1) $$a − b = 6$$

(2) $$a^2*b = 32$$

(1) $$a − b = 6$$ insufic

$$a − b = 6…a=6+b…b(6+b)=-8…b^2+6b+8=0…(b+4)(b+2)=0$$
$$(b,a)=(-4,2);(-2,4)…(a+b)=(-2;2)$$

(2) $$a^2*b = 32$$ sufic

$$a^2*b = 32…a(ab)=32…a=32/(-8)=-4…b=2…a+b=-2$$

Ans (B)

*note: if a^2b=32 then a^2>0 and b>0; but (1) b=-4,-2… so there is something wrong with (2).
Re: If a*b = −8, what is the value of a + b? (1) a − b = 6 (2) a^2*b = 32   [#permalink] 26 Nov 2019, 08:31
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