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# Is a/b>0?

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Math Expert
Joined: 02 Aug 2009
Posts: 7984

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11 Nov 2017, 10:19
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Difficulty:

35% (medium)

Question Stats:

68% (01:13) correct 32% (01:21) wrong based on 215 sessions

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Is $$\frac{a}{b}>0$$, where $$b\ne{0}$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

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11 Nov 2017, 10:45
1
chetan2u wrote:
Is $$\frac{a}{b}>0$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

Statement 1: implies $$b=-a$$, So $$\frac{a}{b} = \frac{a}{-a} = -1$$

So we have a NO for our question stem. Sufficient

Statement 2: mod will always be greater than or equal to $$0$$. hence $$a$$ and $$b$$ can have any sign

for eg. $$a=-2$$, $$b=1$$, $$\frac{a}{b}<0$$ but $$|\frac{a}{b}|>0$$

and if $$a=b=1$$, then $$\frac{a}{b}>0$$ and $$|\frac{a}{b}|>0$$. So Insufficient

Option A
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15 Nov 2017, 01:02
chetan2u wrote:
Is $$\frac{a}{b}>0$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

For yes/no DS questions, the correct answer is definitely yes or definitely NO .

Statement 1 is a define No while statement 2 is a definite yes. so the correct answer should be D
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15 Nov 2017, 01:05
IMO A
Stmt 1 tells a and b have opposite signs. So a/b<0. Sufficient

Stmt 2 tells a/b>0 or a/b<0

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15 Nov 2017, 02:15
Aussy2000 wrote:
chetan2u wrote:
Is $$\frac{a}{b}>0$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

For yes/no DS questions, the correct answer is definitely yes or definitely NO .

Statement 1 is a define No while statement 2 is a definite yes. so the correct answer should be D

Hi Aussy2000

Can you explain how Statement 2 proves that $$\frac{a}{b}>0$$ ?
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15 Nov 2017, 11:22
Aussy2000 wrote:
chetan2u wrote:
Is $$\frac{a}{b}>0$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

For yes/no DS questions, the correct answer is definitely yes or definitely NO .

Statement 1 is a define No while statement 2 is a definite yes. so the correct answer should be D

Hi Aussy

Statement 2 is actually NOT a definite yes. Its given that |a/b| > 0 or modulus of a/b is positive. For any non-zero number, its modulus will be positive only.

We can have say a=b=2, and so a/b = 2/2 =1 and |a/b| = 1. Here a/b > 0 and |a/b| is also > 0

But we can also have say a=-2 and b=2 and so a/b = -2/2 = -1 but |a/b| = 1. So here a/b < 0 but |a/b| >0

So we can't say whether a/b will be positive or negative on the basis of second statement.

Also in GMAT, whenever the answer is D, both statements give the same answer. So its NOT possible to get No from statement 1 and Yes from statement 2. If I ever come across such a case in my practice (different answers from the two statements) I know I am going off somewhere and I recheck.
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17 Nov 2017, 08:51
1
chetan2u wrote:
Is $$\frac{a}{b}>0$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

Hi chetan2u

Can you explain why option A is incorrect and why C is correct choice here?
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Posts: 7984

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17 Nov 2017, 08:56
niks18 wrote:
chetan2u wrote:
Is $$\frac{a}{b}>0$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

Hi chetan2u

Can you explain why option A is incorrect and why C is correct choice here?

hi..
Typo.. ans is A .. Thanks
Kudos for pointing out
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17 Nov 2017, 08:59
chetan2u wrote:
niks18 wrote:
chetan2u wrote:
Is $$\frac{a}{b}>0$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

Hi chetan2u

Can you explain why option A is incorrect and why C is correct choice here?

hi..
Typo.. ans is A .. Thanks
Kudos for pointing out

Thanks chetan2u for clarifying. I have been scratching my head for past half an hour to arrive at C
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17 Nov 2017, 09:24
chetan2u wrote:
niks18 wrote:
chetan2u wrote:
Is $$\frac{a}{b}>0$$?

(1) $$a+b = 0$$
(2) $$|\frac{a}{b}|>0$$

Hi chetan2u

Can you explain why option A is incorrect and why C is correct choice here?

hi..
Typo.. ans is A .. Thanks
Kudos for pointing out

Hi chetan2u,

May be not worth asking, still...

From statement A, A+B=0, we could have A=B=0, So 0/0 ---Undefined ..... We don't know its +ve or -ve. Can we definitely arrive at a conclusion?
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17 Nov 2017, 10:53
Hi chetan2u,

May be not worth asking, still...

From statement A, A+B=0, we could have A=B=0, So 0/0 ---Undefined ..... We don't know its +ve or -ve. Can we definitely arrive at a conclusion?[/quote]

Hi

Chetan will be best to answer this, but in my opinion, even if its not specified, we can ignore such things where we know its undefined. so eg - if its given that x/y > 2, we have to assume y not equal to 0, because otherwise the question stem becomes not defined. Similarly here I think we can safely assume that A and B will not be 0, because then A/B will become undefined.
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05 Jan 2018, 21:04
Hi,

I had a question regarding the original statement. I was wondering if we can multiply b with 0 and can get the final equation as if a>0?

Thank You!
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Joined: 02 Aug 2009
Posts: 7984

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05 Jan 2018, 21:27
csaluja wrote:
Hi,

I had a question regarding the original statement. I was wondering if we can multiply b with 0 and can get the final equation as if a>0?

Thank You!

Hi..
No you cannot cross Multiply till you know that B is Positive..
If b is positive, a/b>0 will mean a>0..
If b is NEGATIVE, first multiply both sides by NEGATIVE to make statements POSITIVE.
Here a/b>0 will become a/b<0 if be is NEGATIVE and ao a<0..
Hope it helps you.

ManishKM1, sorry I missed out on your post..
It's ofcourse always better to mention that B is not equal to zero.
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Re: Is a/b>0?   [#permalink] 05 Jan 2018, 21:27
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