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Math Expert V
Joined: 02 Sep 2009
Posts: 57155
Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 69% (00:48) correct 31% (00:35) wrong based on 203 sessions

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Which of the following CANNOT be a value of $$\frac{1}{x-1}$$?

A. -1
B. 0
C. 2/3
D. 1
E. 2

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NUS School Moderator V
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Re: Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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Equating all the options to the given equation $$\frac{1}{x-1}$$

Only 0 doesn't satisfy.

$$\frac{1}{x-1}$$ = 0.

Gives 1 = 0. Which is not possible.

B is the answer.
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Re: Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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Bunuel wrote:
Which of the following CANNOT be a value of $$\frac{1}{x-1}$$?

A. -1
B. 0
C. 2/3
D. 1
E. 2

Only B is not possible

1/0 is undefined. Hence B

To Verify you can substitute the value for x

Sub x=0 then $$\frac{1}{x-1}$$ = -1

Sub x=5/2 then $$\frac{1}{x-1}$$ = 2/3

Sub x=2 then $$\frac{1}{x-1}$$ = 1

Sub x=3 then $$\frac{1}{x-1}$$ = 2

Hence B
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Re: Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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1
Bunuel Can you check the OA?

We are getting as B...
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Re: Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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NandishSS wrote:
Bunuel Can you check the OA?

We are getting as B...

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B is the OA. Edited. Thank you.
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Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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See graphic approach to this question below. Lines will never cross the x-axis - function y will never = 0. Answer B

.
Attachments 3.png [ 4.84 KiB | Viewed 1416 times ]

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Re: Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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Top Contributor
Bunuel wrote:
Which of the following CANNOT be a value of $$\frac{1}{x-1}$$?

A. -1
B. 0
C. 2/3
D. 1
E. 2

In order for x/y to equal 0, we need x to equal 0

So, we can see that, in the fraction 1/(x - 1), the numerator does NOT equal zero.
This means that 1/(x - 1) CANNOT equal 0.

Answer: B

Cheers,
Brent
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Re: Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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Top Contributor
Bunuel wrote:
Which of the following CANNOT be a value of $$\frac{1}{x-1}$$?

A. -1
B. 0
C. 2/3
D. 1
E. 2

Alternatively, we can test each answer choice

A) -1
Is it possible for 1/(x-1) to equal -1?
Let's find out.
We'll see if we can solve the equation: 1/(x-1) = -1
Multiply both sides by (x-1) to get: 1 = -1(x-1)
Expand right side: 1 = -x + 1
Solve: x = 0
So, when x = 0, 1/(x-1) = -1
Since 1/(x-1) CAN equal -1, we can ELIMINATE A

B) 0
Is it possible for 1/(x-1) to equal 0?
Let's find out.
We'll see if we can solve the equation: 1/(x-1) = 0
Multiply both sides by (x-1) to get: 1 = 0
Hmmmm.
Looks like 1/(x-1) CANNOT equal 0

At this point, I'd select B and move on.
But, for "kicks" let's keep going

C) 2/3
Start with the equation: 1/(x-1) = 2/3
Multiply both sides by (x-1) to get: 1 = (2/3)(x-1)
Expand right side: 1 = 2x/3 - 2/3
Add 2/3 to both sides: 5/3 = 2x/3
Multiply both sides by 3 to get: 5 = 2x
Solve: x = 2.5
So, when x = 2.5, 1/(x-1) = 2/3
Since 1/(x-1) CAN equal 2/3, we can ELIMINATE C

D) 1
Start with the equation: 1/(x-1) = 1
Multiply both sides by (x-1) to get: 1 = (1)(x-1)
Expand right side: 1 = x - 1
Add 1 to both sides: 2 = x
So, when x = 2, 1/(x-1) = 1
Since 1/(x-1) CAN equal 1, we can ELIMINATE D

E) 1
Start with the equation: 1/(x-1) = 2
Multiply both sides by (x-1) to get: 1 = (2)(x-1)
Expand right side: 1 = 2x - 2
Add 2 to both sides: 3 = 2x
Solve: x = 3/2
So, when x = 3/2, 1/(x-1) = 2
Since 1/(x-1) CAN equal 2, we can ELIMINATE E

Answer: E

Cheers,
Brent
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Re: Which of the following CANNOT be a value of 1/(x - 1)?  [#permalink]

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Bunuel wrote:
Which of the following CANNOT be a value of $$\frac{1}{x-1}$$?

A. -1
B. 0
C. 2/3
D. 1
E. 2

Recall that zero divided by a nonzero quantity is zero. However, we see that the numerator of the given expression is not zero and can never be zero, therefore, its value cannot be zero.

Answer: B
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