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Is ab > 0? (1) 1/a < 1 (2) b^3c^2 > 0

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Math Expert
Joined: 02 Sep 2009
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Is ab > 0? (1) 1/a < 1 (2) b^3c^2 > 0  [#permalink]

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27 Nov 2019, 01:46
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Difficulty:

45% (medium)

Question Stats:

62% (01:11) correct 38% (01:01) wrong based on 39 sessions

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Is $$ab > 0$$?

(1) $$\frac{1}{a}<1$$

(2) $$b^3c^2>0$$

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8289
Re: Is ab > 0? (1) 1/a < 1 (2) b^3c^2 > 0  [#permalink]

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27 Nov 2019, 03:34
Is $$ab > 0$$? Are a and b of SAME sign?

(1) $$\frac{1}{a}<1$$
a could be any integer except 1 and 0, so a can be positive or negative.

(2) $$b^3c^2>0$$
c^2 will always be positive, so b is positive.

Combined
b>0, but a could be anything

E
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Joined: 02 Jul 2019
Posts: 12
Re: Is ab > 0? (1) 1/a < 1 (2) b^3c^2 > 0  [#permalink]

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04 Dec 2019, 05:12
chetan2u wrote:
Is $$ab > 0$$? Are a and b of SAME sign?

(1) $$\frac{1}{a}<1$$
a could be any integer except 1 and 0, so a can be positive or negative.

(2) $$b^3c^2>0$$
c^2 will always be positive, so b is positive.

Combined
b>0, but a could be anything

E

Hello chetan2u,

if 1/a< 1 , then doesnt that mean a>1 ? When we cross multiply?

And if a>1 and b>0, then even if they are fractions, the result of ab should always be gretaer than 0?

Thank you
Math Expert
Joined: 02 Aug 2009
Posts: 8289
Re: Is ab > 0? (1) 1/a < 1 (2) b^3c^2 > 0  [#permalink]

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04 Dec 2019, 05:47
Rishbha wrote:
chetan2u wrote:
Is $$ab > 0$$? Are a and b of SAME sign?

(1) $$\frac{1}{a}<1$$
a could be any integer except 1 and 0, so a can be positive or negative.

(2) $$b^3c^2>0$$
c^2 will always be positive, so b is positive.

Combined
b>0, but a could be anything

E

Hello chetan2u,

if 1/a< 1 , then doesnt that mean a>1 ? When we cross multiply?

And if a>1 and b>0, then even if they are fractions, the result of ab should always be gretaer than 0?

Thank you

No it doesn’t mean a>1 as you do not know the sign of a.
Say a=-2, then 1/(-2)<1 does not mean 1<1*(-2).
Yes a>1 and b>0 will always give you ab>0, but you can say anything about a
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Joined: 02 Jul 2019
Posts: 12
Re: Is ab > 0? (1) 1/a < 1 (2) b^3c^2 > 0  [#permalink]

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04 Dec 2019, 07:50
chetan2u wrote:
Rishbha wrote:
chetan2u wrote:
Is $$ab > 0$$? Are a and b of SAME sign?

(1) $$\frac{1}{a}<1$$
a could be any integer except 1 and 0, so a can be positive or negative.

(2) $$b^3c^2>0$$
c^2 will always be positive, so b is positive.

Combined
b>0, but a could be anything

E

Hello chetan2u,

if 1/a< 1 , then doesnt that mean a>1 ? When we cross multiply?

And if a>1 and b>0, then even if they are fractions, the result of ab should always be gretaer than 0?

Thank you

No it doesn’t mean a>1 as you do not know the sign of a.
Say a=-2, then 1/(-2)<1 does not mean 1<1*(-2).
Yes a>1 and b>0 will always give you ab>0, but you can say anything about a

Thank you so much, I understand it now.
Re: Is ab > 0? (1) 1/a < 1 (2) b^3c^2 > 0   [#permalink] 04 Dec 2019, 07:50
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