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# If b is positive, is ab positive?

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Math Expert
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If b is positive, is ab positive? [#permalink]

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11 Aug 2017, 03:43
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72% (00:46) correct 28% (00:29) wrong based on 112 sessions

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If b is positive, is ab positive?

(1) $$a^2b>0$$

(2) $$a^2+b=13$$
[Reveal] Spoiler: OA

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Re: If b is positive, is ab positive? [#permalink]

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11 Aug 2017, 04:14
2
KUDOS
For ab>0 => a and b must be of the same sign.
So by giving us b>0 the question is really asking us if a>0 or not.

So the question can be transformed into -->
If b>0 then Is a>0 .

Lets begin.

Statement 1-->
a^2 * b > 0

This just tells us that a≠0
a can be positive or negative a^2*b will always be positive.

Hence not sufficient.

Statment 2->
Lets use two examples =>
(0,13)
(1,12)

Hence not sufficient.

Combining the two statements =>

(x,y) => (-1,12) or (1,12) are two easy test cases to take.

Hence not sufficient.

Hence E.

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Re: If b is positive, is ab positive? [#permalink]

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11 Aug 2017, 04:27
I would go for E as well.
1) A^2b > 0 A can be any value and so can B (positive)

2) A^2+B =13
A^2 can be 12
B can be 1
or A^2 (-1^2) can 1
B can be 12

both 1 and 2 - No difference.

I hope its correct

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Re: If b is positive, is ab positive? [#permalink]

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11 Aug 2017, 05:42
If b is positive, is ab positive?

1. $$a^2b>0$$

Since we are given b is positive,
if a is either positive or negative, the expression $$a^2b>0$$ holds true.
Case 1: a=-3, b=2 Here, ab is negative
Case 2: a=3, b=2 Here, ab is positive(Insufficient)

2. $$a^2+b=13$$

Since we are given b is positive,
if a is either positive or negative, the expression $$a^2+b=13$$ holds true.
Case 1: a=-3, b=5 Here, ab is negative
Case 2: a=3, b=5 Here, ab is positive(Insufficient)

Even combining both the statements, we will be left with two options
in the first one - both a and b are positive
in the second one - a is negative and b is positive. (Insufficient)(Option E)
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Re: If b is positive, is ab positive? [#permalink]

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11 Aug 2017, 08:32
given b>0
1) (a^2).b>0 from this b>0 then a can be positive as well as negative, so sign of axb can't be determined. A,D ruled out
2) (a^2)+b=13 , b>0 and b <13 a can have Positive and Negative values, also if b>13 , then a is not defined hence sign of axb can't be determined. B ruled out.

Combining both ,
a^2+b = 13 and (a^2) x b > 0 cant solve the problem with the sign from above 2 statements, a can be negative as well as positive since its square will always be positive and therefore C ruled out

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Re: If b is positive, is ab positive? [#permalink]

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11 Aug 2017, 10:18
+1 E

a^2*b>0
a can be both positive and negative

a^2 + b = 13
a can be both positive and negative

Even combining both we do not get if a is positive or negative
Hence E
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Re: If b is positive, is ab positive? [#permalink]

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11 Aug 2017, 11:52
St:1 says nothing but what is given in question. B is positive. A can be -ve as well as +ve.Insufficient
St:2 says that a2 will be positive .Again A can be -ve as well as +ve.Insufficient

Combining does not help either. Therefore E.

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Re: If b is positive, is ab positive? [#permalink]

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07 Sep 2017, 04:10
Silly Mistake, I did -> assumed that a is positive in place b - marked option D that is incorrect
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Re: If b is positive, is ab positive?   [#permalink] 07 Sep 2017, 04:10
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