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# If a=1 and (a-b)/c = 1, which of the following is NOT a

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SVP
Joined: 21 Jul 2006
Posts: 1508
If a=1 and (a-b)/c = 1, which of the following is NOT a [#permalink]

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11 Dec 2007, 02:22
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If a=1 and (a-b)/c = 1 which of the following is NOT a possible value of b?

A. -2
B. -1
C. 0
D. 1
E. 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Feb 2012, 23:04, edited 2 times in total.
Edited the question and added the OA
Intern
Joined: 25 Nov 2007
Posts: 38

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11 Dec 2007, 08:08
Answer is D. b cannot be 1.

1-1/c =1 is not possible
Director
Joined: 03 Sep 2006
Posts: 860
Re: PS: Weird question [#permalink]

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11 Dec 2007, 18:57
tarek99 wrote:
If a=1 and (a-b)/c = 1 which of the following is NOT a possible value of b?

A. -2
B. -1
C. 0
D. 1
E. 2

b = (1-c)

If b=1, then C=0, which will not satisfy (a-b)/c = 1. ( divisibility by 0 is not possible.)

therefore b=1 is not possible.
Intern
Joined: 04 Nov 2007
Posts: 49
Re: PS: Weird question [#permalink]

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11 Dec 2007, 21:32
Since (1-b)/c = 1, b can not be 1. If b = 1, then (1-b)/c will always be 0, violating the rule
Director
Joined: 12 Jul 2007
Posts: 856
Re: PS: Weird question [#permalink]

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12 Dec 2007, 05:53
1
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BOOKMARKED
yezz wrote:
tarek99 wrote:
If a=1 and (a-b)/c = 1, which of the following is NOT a possible value of b?

a) -2

b) -1

c) 0

d) 1

e) 2

all r possible

Equation is:

(a-b)/c = 1 where a = 1

so plug in 1 for a and look at it again

(1-b)/c = 1

now C can be anything we want, so if b = -2 we can plug it in and make it work

(1-(-2))/c = 1
3/c = 1
c = 3 and it works

HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1

(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true

B cannot be 1.

Senior Manager
Joined: 07 Sep 2010
Posts: 326
Re: PS: Weird question [#permalink]

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29 Feb 2012, 21:51
Hi.
Can anyone let me know what is wrong in my approach -

(a-b)/c = 1

a-b = c(by cross multiplying)
Now as a= 1
1-b = c
implies, 1-c=b
Now c can take any value, and b can have any of the values provided in the answer choices. Please let me know where I am going wrong. Why it is not possible to cross multiply in the first instance. this is how I approached in my exam.

Thanks
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Math Expert
Joined: 02 Sep 2009
Posts: 43831
Re: PS: Weird question [#permalink]

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29 Feb 2012, 23:10
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1
This post was
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imhimanshu wrote:
Hi.
Can anyone let me know what is wrong in my approach -

(a-b)/c = 1

a-b = c(by cross multiplying)
Now as a= 1
1-b = c
implies, 1-c=b
Now c can take any value, and b can have any of the values provided in the answer choices. Please let me know where I am going wrong. Why it is not possible to cross multiply in the first instance. this is how I approached in my exam.

Thanks

If a=1 and (a-b)/c = 1 which of the following is NOT a possible value of b?
A. -2
B. -1
C. 0
D. 1
E. 2

First of all remember that division by zero is undefined, hence $$c\neq{0}$$ and that's why you CAN cross-multiply.

$$\frac{a-b}{c}=1$$ --> as $$a=1$$ --> $$\frac{1-b}{c}=1$$ --> $$1-b=c$$, but since $$c\neq{0}$$, then $$1-b\neq{0}$$ --> $$b\neq{1}$$.

Hope it's clear.
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Joined: 07 Sep 2010
Posts: 326
Re: If a=1 and (a-b)/c = 1, which of the following is NOT a [#permalink]

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29 Feb 2012, 23:48
Thanks Bunuel, makes sense. !:-)
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Re: If a=1 and (a-b)/c = 1, which of the following is NOT a [#permalink]

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10 Nov 2017, 23:30
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Re: If a=1 and (a-b)/c = 1, which of the following is NOT a   [#permalink] 10 Nov 2017, 23:30
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# If a=1 and (a-b)/c = 1, which of the following is NOT a

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