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

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Director
Joined: 07 Jun 2004
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If a is an integer and a=|b|/b is a=1 [#permalink]

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18 Feb 2012, 05:04
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If a is an integer and a=|b|/b is a=1

(1) b> 0
(2) a>-1
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
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18 Feb 2012, 05:16
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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.

Hope it's clear.
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Re: If a is an integer and a=|b|/b is a=1 [#permalink]

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18 Feb 2012, 05:21
B

thanks i thought non zero / 0 was undefined and 0 / 0 = 0

but if the former is undefined too then the question is missing the b <> 0 clause

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

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18 Feb 2012, 05:27
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rxs0005 wrote:
B

thanks i thought non zero / 0 was undefined and 0 / 0 = 0

but if the former is undefined too then the question is missing the b <> 0 clause

thanks

Yes, division by zero is undefined, so 0/0 is undefined too.
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25 Feb 2012, 12:10
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.

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
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Joined: 02 Sep 2009
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25 Feb 2012, 12:20
saxenaashi wrote:
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.

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.
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25 Feb 2012, 12:34
Bunuel wrote:
saxenaashi wrote:
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.

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
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25 Feb 2012, 12:47
saxenaashi wrote:
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.
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Re: If a is an integer and a=|b|/b is a=1 [#permalink]

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26 Feb 2012, 06:12
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rxs0005 wrote:
If a is an integer and a=|b|/b is a=1

(1) b> 0
(2) a>-1

a = IbI/b = (+/-)*b/b = (+/-)*1 ........(i)

If b > 0, then IbI/b >0 ==> a = 1
hence (1) is sufficient

if a > -1 , then a = 1 from eq (i). hence (2) is also sufficient
Hence D
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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.

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
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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.

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

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22 Sep 2017, 00:14
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1) b>0. Sufficient.
(2) a>-1. Since aa can take only 2 values -1 and 1 and this statement tells that aa is not -1 then a=1a=1. Sufficient.

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

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27 Nov 2017, 00:08
manhasnoname wrote:
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?

Hi

Just as you said, a will be defined only when b is non-zero. So b cannot be zero here, we can safely assume that.
Re: If a is an integer and a=|b|/b is a=1   [#permalink] 27 Nov 2017, 00:08
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