Is a^7b^2c^3 0? (1) bc 0

Question

Is a^7∗b^2∗c^3 > 0?

(1) bc < 0
(2) ac > 0

M11-26

Bunuel · Accepted Answer

Is  a^7*b^2*c^3 \gt 0 ? 
 
Inequality  a^7*b^2*c^3 \gt 0  to be true two conditions must be met:

(i)  a  and  c  must be either both positive or both negative: in this case  a^7*c^3  will be positive;
 
(ii)  b  must not be zero: if  b = 0 , then the entire expression ( a^7*b^2*c^3 ), irrespective  a  and  c , will be 0, not more than 0.

(1)  bc \lt 0 . Hence,  b 
e 0 . Don't know about  a  and  c . Not sufficient.
 
(2)  ac \gt 0 . Hence,  a  and  c  are either both positive or both negative. Don't know about  b : if  b=0 , then the expression will be equal 0. Not sufficient.
 
(1)+(2) Sufficient.

Answer: C

VineelSurya · Answer

a^{7} * b^{2} *
 c^{3} >0

From the question, we can conclude that bis always a 
Statement 1 says bc>0

With this we can't say much because, for any sign, the whole equation depends on "a" as well. 
Insufficient.

Statement 2 says that ac>0

Means either a & c has to be positive or negative.

In any way,  a^{7} * c^{3}  will be greater that zero and also  b^{2}  is always positive.
Sufficient.

So the answer has to be Option B

I wonder why it is C. Can someone explain?

Posted from my mobile device

vv65 · Answer

With Statement 2 alone, 
If b=0 then a^7 * b^2 * c^3 = 0, even if ac>0

Statement 1 tells us that b cannot be 0.

So we need both statements

Posted from my mobile device

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Is a^7b^2c^3 > 0? (1) bc < 0 (2) ac > 0

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