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If it were a realistic GMAT question it would mention that b does not equal to zero (because b is in denominator and division by zero is undefined). So, the proper question should read:

If b does not equal tot zero and a=|b|/b is a=1

Now, if \(b>0\) then \(a=\frac{|b|}{b}=\frac{b}{b}=1\) and if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). So, the question basically asks whether we have the first case.

(1) b>0. Sufficient. (2) a>-1. Since \(a\) can take only 2 values -1 and 1 and this statement tells that \(a\) is not -1 then \(a=1\). Sufficient.

If it were a realistic GMAT question it would mention that b does not equal to zero (because b is in denominator and division by zero is undefined). So, the proper question should read:

If b does not equal tot zero and a=|b|/b is a=1

Now, if \(b>0\) then \(a=\frac{|b|}{b}=\frac{b}{b}=1\) and if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). So, the question basically asks whether we have the first case.

(1) b>0. Sufficient. (2) a>-1. Since \(a\) can take only 2 values -1 and 1 and this statement tells that \(a\) is not -1 then \(a=1\). Sufficient.

Answer: D.

Hope it's clear.

Bunuel, For this statement. if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). If b < 0, |b| = -b. Would not you consider b = -b so that result of division is 1 [ -b / -b ].

I understand that this does not change the answer anyways but just wanted to know.

If it were a realistic GMAT question it would mention that b does not equal to zero (because b is in denominator and division by zero is undefined). So, the proper question should read:

If b does not equal tot zero and a=|b|/b is a=1

Now, if \(b>0\) then \(a=\frac{|b|}{b}=\frac{b}{b}=1\) and if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). So, the question basically asks whether we have the first case.

(1) b>0. Sufficient. (2) a>-1. Since \(a\) can take only 2 values -1 and 1 and this statement tells that \(a\) is not -1 then \(a=1\). Sufficient.

Answer: D.

Hope it's clear.

Bunuel, For this statement. if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). If b < 0, |b| = -b. Would not you consider b = -b so that result of division is 1[ -b / -b ].

I understand that this does not change the answer anyways but just wanted to know.

Regards

First of all: if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). You can not say "let's consider that b=-b", since you have what you have: \(\frac{-b}{b}\) which equals to -1 only.

Next, if \(b=-b\) then \(2b=0\) and \(b=0\), which is not possible, since \(b\) is in the denominator.

If it were a realistic GMAT question it would mention that b does not equal to zero (because b is in denominator and division by zero is undefined). So, the proper question should read:

If b does not equal tot zero and a=|b|/b is a=1

Now, if \(b>0\) then \(a=\frac{|b|}{b}=\frac{b}{b}=1\) and if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). So, the question basically asks whether we have the first case.

(1) b>0. Sufficient. (2) a>-1. Since \(a\) can take only 2 values -1 and 1 and this statement tells that \(a\) is not -1 then \(a=1\). Sufficient.

Answer: D.

Hope it's clear.

Bunuel, For this statement. if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). If b < 0, |b| = -b. Would not you consider b = -b so that result of division is 1[ -b / -b ].

I understand that this does not change the answer anyways but just wanted to know.

Regards

First of all: if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). You can not say "let's consider that b=-b", since you have what you have: \(\frac{-b}{b}\) which equals to -1 only.

Next, if \(b=-b\) then \(2b=0\) and \(b=0\), which is not possible, since \(b\) is in the denominator.

Hope it's clear.

I guess I framed my question incorrectly. Let me try again.

When we consider b < 0, would not the denominator be negative as well. |b| is -b for b < 0. Consider b = -2. So a = |b| / b ---> -2 / -2 = 1

I guess I framed my question incorrectly. Let me try again.

When we consider b < 0, would not the denominator be negative as well. |b| is -b for b < 0. Consider b = -2. So a = |b| / b ---> -2 / -2 = 1

Again, irrespective of the question: \(\frac{-b}{b}=-1\) ONLY: \(\frac{-b}{b}=-(\frac{b}{b})=-1\).

Next, as for you reasoning: if \(b<0\), so when \(b\) is negative then \(-b=-negative=positive\), so denominator will be negative as it's \(b\), but nominator \({-b}\) will be positive. So, if \(b=-2<0\): \(\frac{|-2|}{-2}=\frac{2}{-2}=-1\).

Remember |b| is an absolute value of b and it's always nonegative.
_________________

Re: If a is an integer and a=|b|/b is a=1 [#permalink]

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02 Oct 2013, 03:58

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Re: If a is an integer and a=|b|/b is a=1 [#permalink]

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16 Jun 2015, 19:51

Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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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Re: If a is an integer and a=|b|/b is a=1 [#permalink]

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03 Jul 2015, 10:41

Bunuel wrote:

If a is an integer and a=|b|/b is a=1

If it were a realistic GMAT question it would mention that b does not equal to zero (because b is in denominator and division by zero is undefined). So, the proper question should read:

If b does not equal tot zero and a=|b|/b is a=1

Now, if \(b>0\) then \(a=\frac{|b|}{b}=\frac{b}{b}=1\) and if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). So, the question basically asks whether we have the first case.

(1) b>0. Sufficient. (2) a>-1. Since \(a\) can take only 2 values -1 and 1 and this statement tells that \(a\) is not -1 then \(a=1\). Sufficient.

Answer: D.

Hope it's clear.

Bunuel: The question states a is an integer. Hence b cannot be zero or else the equation wont hold. Therefore a has to be 1 from usage of either statement

Re: If a is an integer and a=|b|/b is a=1 [#permalink]

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22 Jul 2015, 15:44

Bunuel wrote:

If a is an integer and a=|b|/b is a=1

If it were a realistic GMAT question it would mention that b does not equal to zero (because b is in denominator and division by zero is undefined). So, the proper question should read:

If b does not equal tot zero and a=|b|/b is a=1

Now, if \(b>0\) then \(a=\frac{|b|}{b}=\frac{b}{b}=1\) and if \(b<0\) then \(a=\frac{|b|}{b}=\frac{-b}{b}=-1\). So, the question basically asks whether we have the first case.

(1) b>0. Sufficient. (2) a>-1. Since \(a\) can take only 2 values -1 and 1 and this statement tells that \(a\) is not -1 then \(a=1\). Sufficient.

Answer: D.

Hope it's clear.

Thanks for the clarification. I considered the 0-case and realized A as the answer. I was pretty surprised at the OA

Re: If a is an integer and a=|b|/b is a=1 [#permalink]

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27 Aug 2016, 05:30

Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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: If a is an integer and a=|b|/b is a=1 [#permalink]

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27 Oct 2016, 15:13

It is not very clear to me that why b can't be 0. Question stem just has an expression a = |b|/b. a will be defined only when b is non-zero. How can we assume b is non-zero?

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