Is ab negative? (1) ab^8

Question

Is ab negative?

(1)  ab^8 < 0

(2)  a + b^8 = 12

gvij2017 · Answer

Statement 1
a*b^8 < 0
implies that a is negative but doesn't tell us about b so insufficient.

Statement 2
a+b^8= 12
Nothing is clear form this statement. 
Insufficient.

St.1 + st. 2
Still not clear.

Answer is E

Please appraise my answer.

NonPlus · Answer

IMO A.

1. a*(b^8) < 0. b^8 will be positive. Hence, 'a' will be -ve. Sufficient
2. In this case, 'a' can be -ve or +ve depending upon magnitude of b^8. Insufficient

nehakhetan88 · Answer

In statement 1, we know for sure that b is positive because of the even power of b. And for the whole thing to be less than 0. A has to be negative. Therefore, sufficient
Hence, option A is correct choice

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bunny12345 · Answer

nehakhetan88  and  NonPlus 
Answer is E.

Statement 1  is not sufficient because "a" is negative we know, but coming back to question at hand that whether ab<0 lets consider this.
a is -ve but when b is +ve, we get ab<0
but when a is -ve and b is also -ve, then ab>0
So, Just because b^8 is +ve we cant comment on the nature of b. b can either be +ve or -ve.

Statement  2 is also not sufficient.
a + b^8 = 12. In this, we will have break points when b is 1 or 2 or -2 etc.
When b is 1, a is +ve but when b is -2, a is -ve. So even in this case we are not clear. Hence insufficient.

Taking Statement 1 and 2 together .

In this we rule out all the cases where a is +ve. Just take a -ve since thats what we got from statement 1.
Now, a can be -ve when b is 3, -3, 2, -10 etc.
Hence even after taking both the statements we cant tell whether ab is <0.

Hope it clears your queries.

dharde9 · Answer

Statement 1 : ab^8<0 Here b^8 irrespective of b being negative or positive will be positive. Hence, we can conclude a is negative. But we don't know anything about b. If b is positive then ab is negative; but if b is negative ab will be positive. Not sufficient Statement 2 : a+b^8 = 12 Again b^8 will be positive and a can be negative or positive, suppose b is positive and a is negative but less than b Then outcome will be positive. Also a can be positive and a+b^8 will sum up to 12. Not sufficient Also Stmt 1 & 2 together doesn't reflect whether b is negative or positive as b^8 will always be positive. Answer : E Please hit Kudos if this post in anyway helps you

Is ab negative? (1) ab^8 < 0 (2) a + b^8 = 12

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