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GRE Practice Question-If b= 0 and a/b >0

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Osira

Intern

Joined: 21 Apr 2015

Posts: 9

GRE Practice Question-If b= 0 and a/b >0 [#permalink]

29 Apr 2015, 12:53

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If b ≠ 0 and $\frac{a}{b}$ >0, then which of the following must be true?

A. a > b
B. b > 0
C. ab > 0

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GreenlightTestPrep

GRE Prep Club Legend

Joined: 10 Apr 2015

Posts: 6215

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

27 Mar 2019, 12:55

Osira wrote:

If b ≠ 0 and $\frac{a}{b}$ > 0, then which of the following must be true?

A. a > b
B. b > 0
C. ab > 0

The question asks "What MUST be true?"
So, if we can find a case in which a statement is NOT true, we can eliminate it.

A. a > b
We're told that a/b > 0
So, it COULD be the case that a = 1 and b = 2 (since 1/2 > 0)
If a = 1 and b = 2, then the statement that a > b is NOT TRUE
ELIMINATE A

B. b > 0
We're told that a/b > 0
So, it COULD be the case that a = -3 and b = -2 (since -3/-2 > 0)
If a = -3 and b = -2, then the statement that b > 0 is NOT TRUE
ELIMINATE B

C. ab > 0
We're told that a/b > 0, which means EITHER a and b are both positive OR a and b are both negative
If a and b are both positive, then ab > 0
If a and b are both negative, then ab > 0
In BOTH possible cases ab > 0, which means statement C MUST be true.

Answer: C

Cheers,
Brent
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huda

Director

Joined: 22 Jun 2019

Posts: 521

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

04 Jul 2019, 11:45

GreenlightTestPrep wrote:

Osira wrote:

If b ≠ 0 and $\frac{a}{b}$ > 0, then which of the following must be true?

A. a > b
B. b > 0
C. ab > 0

The question asks "What MUST be true?"
So, if we can find a case in which a statement is NOT true, we can eliminate it.

A. a > b
We're told that a/b > 0
So, it COULD be the case that a = 1 and b = 2 (since 1/2 > 0)
If a = 1 and b = 2, then the statement that a > b is NOT TRUE
ELIMINATE A

B. b > a
We're told that a/b > 0
So, it COULD be the case that a = 3 and b = 2 (since 3/2 > 0)
If a = 3 and b = 2, then the statement that b > a is NOT TRUE
ELIMINATE B

C. ab > 0
We're told that a/b > 0, which means EITHER a and b are both positive OR a and b are both negative
If a and b are both positive, then ab > 0
If a and b are both negative, then ab > 0
In BOTH possible cases ab > 0, which means statement C MUST be true.

Answer: C

Cheers,
Brent

Actually !!!!!

B. b > 0, not b > a, that you get to solve.

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GreenlightTestPrep

GRE Prep Club Legend

Joined: 10 Apr 2015

Posts: 6215

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

04 Jul 2019, 11:53

Good catch!
I've edited my solution accordingly.

Cheers,
Brent
_________________

Brent Hanneson - founder of Greenlight Test Prep

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huda

Director

Joined: 22 Jun 2019

Posts: 521

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

04 Jul 2019, 12:14

huda wrote:

GreenlightTestPrep wrote:

Osira wrote:

If b ≠ 0 and $\frac{a}{b}$ > 0, then which of the following must be true?

A. a > b
B. b > 0
C. ab > 0

The question asks "What MUST be true?"
So, if we can find a case in which a statement is NOT true, we can eliminate it.

A. a > b
We're told that a/b > 0
So, it COULD be the case that a = 1 and b = 2 (since 1/2 > 0)
If a = 1 and b = 2, then the statement that a > b is NOT TRUE
ELIMINATE A

B. b > a
We're told that a/b > 0
So, it COULD be the case that a = 3 and b = 2 (since 3/2 > 0)
If a = 3 and b = 2, then the statement that b > a is NOT TRUE
ELIMINATE B

C. ab > 0
We're told that a/b > 0, which means EITHER a and b are both positive OR a and b are both negative
If a and b are both positive, then ab > 0
If a and b are both negative, then ab > 0
In BOTH possible cases ab > 0, which means statement C MUST be true.

Answer: C

Cheers,
Brent

Actually !!!!!

B. b > 0, not b > a, that you get to solve.

--------------------------------------

sandy wrote:

If $x^2 - y^2 = 0$ and $xy \neq 0$, which of the following MUST be true?
Indicate all such statements.

A. x = y
B. |x| = |y|
C. $\frac{x^2}{y^2}=1$

In the above example, if we are allowed to take different numbers for the value of a and b, we must take them here too. If so, then why don't we eliminate the answer choice B. here? I'm so confused.

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GreenlightTestPrep

GRE Prep Club Legend

Joined: 10 Apr 2015

Posts: 6215

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

04 Jul 2019, 12:39

For these kinds of questions, you can try different pairs of values for each statement.
_________________

Brent Hanneson - founder of Greenlight Test Prep

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huda

Director

Joined: 22 Jun 2019

Posts: 521

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

04 Jul 2019, 14:38

GreenlightTestPrep wrote:

For these kinds of questions, you can try different pairs of values for each statement.

To be better if it has an explanation
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Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 25502

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

04 Jul 2019, 23:49

Expert Reply

No need ti pick numbers. Just think fundamental rules

For $\frac{a}{b} > 0$ the two numbers, a and b, must be or both positive or both negative. So clearly the problem is NOT if a is > of be or vice-versa. This is a question to test and about signs.

So a could be or not true. However, the question is a must be true question.

A is out.

B > 0 ? could be positive or negative. Out

C is true. Is the only correct choice because $minus \times minus$ OR $plus \times plus$= always the result is $> 0$
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bellavarghese

Manager

Joined: 18 Jun 2019

Posts: 122

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

15 Jul 2019, 15:23

thanks for sharing!

bumpbot

CEO

Joined: 07 Jan 2021

Posts: 3736

Re: GRE Practice Question-If b= 0 and a/b >0 [#permalink]

14 May 2022, 04:18

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.