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Director  Joined: 21 Jul 2006
Posts: 978
If a = 1 and (a - b)/c = 1 which of the following is NOT a possible va  [#permalink]

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Difficulty:   15% (low)

Question Stats: 78% (01:13) correct 22% (01:31) wrong based on 379 sessions

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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

Originally posted by tarek99 on 11 Dec 2007, 03:22.
Last edited by Bunuel on 08 Oct 2018, 03:43, edited 3 times in total.
Renamed the topic and edited the question.
Director  Joined: 03 Sep 2006
Posts: 602
Re: If a = 1 and (a - b)/c = 1 which of the following is NOT a possible va  [#permalink]

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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.
Director  Joined: 12 Jul 2007
Posts: 641
Re: If a = 1 and (a - b)/c = 1 which of the following is NOT a possible va  [#permalink]

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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.

Manager  Joined: 07 Sep 2010
Posts: 246
Re: If a = 1 and (a - b)/c = 1 which of the following is NOT a possible va  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 60555
Re: If a = 1 and (a - b)/c = 1 which of the following is NOT a possible va  [#permalink]

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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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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1399
Location: India
Re: If a=1 and (a-b)/c = 1 which of the following is NOT a  [#permalink]

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If a=1, then (a-b)/c = (1-b)/c which is given to be = 1

Obviously b cannot be equal to 1, because then (1-b) will become 0, which is not possible.

Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806
Re: If a=1 and (a-b)/c = 1 which of the following is NOT a  [#permalink]

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zisis 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

If a = 1, we have:

(1 - b)/c = 1

1 - b = c

We must also remember that since (1 - b)/c = 1, and since dividing by zero creates an undefined result, c cannot be zero.

A) -2

Since c = 1 - (-2) = 3, b could be -2.

B) -1

Since c = 1 - (-1) = 2, b could be -1.

C) 0

Since c = 1 - 0 = 1, b could be 0.

D) 1

Since c = 1 - 1 = 0, b cannot be 1.

Alternate Solution:

If a = 1, we have:

(1 - b)/c = 1

1 - b = c

The original equation had c in the denominator, so we know that c cannot equal 0. The value of b that makes c = 0 is b = 1. Thus, b cannot equal 1.

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_________________ Re: If a = 1 and (a - b)/c = 1 which of the following is NOT a possible va   [#permalink] 04 Dec 2019, 00:27
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