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GRE Practice Question-If b= 0 and a/b >0
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29 Apr 2015, 12:53

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Question Stats:

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

A. a > b

B. b > 0

C. ab > 0

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Joined: **10 Apr 2015 **

Posts: **6218**

Given Kudos: **136 **

Re: GRE Practice Question-If b= 0 and a/b >0
[#permalink]
27 Mar 2019, 12:55

1

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

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

Re: GRE Practice Question-If b= 0 and a/b >0
[#permalink]
04 Jul 2019, 11:45

1

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

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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Joined: **10 Apr 2015 **

Posts: **6218**

Given Kudos: **136 **

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

I've edited my solution accordingly.

Cheers,

Brent

Re: GRE Practice Question-If b= 0 and a/b >0
[#permalink]
04 Jul 2019, 12:14

1

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

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. \(\frac{x^2}{y^2}=1\)

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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Joined: **10 Apr 2015 **

Posts: **6218**

Given Kudos: **136 **

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.

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

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 \(> 0\)

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 \(> 0\)

Re: GRE Practice Question-If b= 0 and a/b >0
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14 Aug 2024, 20:44

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).

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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.

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

14 Aug 2024, 20:44
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