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

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Math Expert
Joined: 02 Sep 2009
Posts: 52430
Is ab negative? (1) ab^8 < 0 (2) a + b^8 = 12  [#permalink]

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07 May 2018, 01:51
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Difficulty:

35% (medium)

Question Stats:

73% (01:55) correct 27% (01:04) wrong based on 95 sessions

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Is ab negative?

(1) $$ab^8 < 0$$

(2) $$a + b^8 = 12$$

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Senior Manager
Joined: 08 Aug 2017
Posts: 302
Re: Is ab negative? (1) ab^8 < 0 (2) a + b^8 = 12  [#permalink]

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07 May 2018, 03:04
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.

Manager
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Re: Is ab negative? (1) ab^8 < 0 (2) a + b^8 = 12  [#permalink]

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07 May 2018, 06:31
1
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
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Joined: 13 Mar 2018
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Re: Is ab negative? (1) ab^8 < 0 (2) a + b^8 = 12  [#permalink]

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07 May 2018, 07:14
gvij2017 wrote:
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.

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

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07 May 2018, 08:41
nehakhetan88 and NonPlus

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.

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Joined: 28 Nov 2017
Posts: 7
Re: Is ab negative? (1) ab^8 < 0 (2) a + b^8 = 12  [#permalink]

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13 Jun 2018, 13:26
1
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.

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Re: Is ab negative? (1) ab^8 < 0 (2) a + b^8 = 12 &nbs [#permalink] 13 Jun 2018, 13:26
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