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

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

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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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Re: is a =1 [#permalink]

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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.

Answer: D.

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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New post 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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New post 18 Feb 2012, 05:27
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Re: is a =1 [#permalink]

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New post 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.

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

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Re: is a =1 [#permalink]

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New post 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.

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.
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Re: is a =1 [#permalink]

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New post 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.

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

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Re: is a =1 [#permalink]

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New post 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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New post 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



The answer is "D"

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

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New post 16 Jun 2015, 19:51
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Re: If a is an integer and a=|b|/b is a=1 [#permalink]

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New post 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

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

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New post 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

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

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

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New post 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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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.

Answer: D.

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Re: If a is an integer and a=|b|/b is a=1   [#permalink] 22 Sep 2017, 00:14
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