Which of the following CANNOT be a value of 1/(x - 1)?

Question

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

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

Chethan92 · Accepted Answer

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.

NandishSS · Answer

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

NandishSS · Answer

Bunuel  Can you check the OA?

We are getting as B...

Bunuel · Answer

_________________________
B is the OA. Edited. Thank you.

Hero8888 · Answer

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

.

BrentGMATPrepNow · Answer

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

BrentGMATPrepNow · Answer

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

ScottTargetTestPrep · Answer

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

Abhishek009 · Answer

\frac{Numerator}{Denominator} = 0 , possible only when the Numerator itself is 0 , since if the denominator is 0 the result will be undefined, hence Answer must be (B)

achloes · Answer

The only way a fraction can equal 0 is if its numerator is 0.

Therefore, since the numerator in the given expression is not 0, the fraction cannot equal 0, no matter its denominator.

egmat · Answer

Here's the key approach:

The question asks which value  \frac{1}{x-1}   cannot  equal. So, we need to test each answer choice by setting up the equation  \frac{1}{x-1} = 	ext{ }  and solving for  x . If we can find a valid  x , that value is possible. If we hit a contradiction or an invalid  x , that value is impossible.

Let's test a couple of choices to see the pattern:

Choice A: Can  \frac{1}{x-1} = -1 ?

Setting up:  \frac{1}{x-1} = -1

Multiply both sides by  (x-1) :  1 = -1(x-1)

Simplify:  1 = -x + 1

Solve:  0 = -x , so  x = 0

Check: When  x = 0 , we get  \frac{1}{0-1} = \frac{1}{-1} = -1  ✓

So  -1   is possible .

Choice D: Can  \frac{1}{x-1} = 1 ?

Setting up:  \frac{1}{x-1} = 1

Multiply both sides by  (x-1) :  1 = x - 1

Solve:  x = 2

Check: When  x = 2 , we get  \frac{1}{2-1} = 1  ✓

So  1   is possible .

Now here's the critical insight you need to see:

Choice B: Can  \frac{1}{x-1} = 0 ?

Think about what it takes for a fraction to equal zero. The only way a fraction equals zero is if the  numerator  is zero (while the denominator is non-zero).

But look at our expression  \frac{1}{x-1}  — the numerator is always  1 , which is  never zero .

Let's verify algebraically:

Setting up:  \frac{1}{x-1} = 0

Multiply both sides by  (x-1) :  1 = 0(x-1)

Simplify:  1 = 0

This is a  mathematical contradiction ! There's no value of  x  that can make this true.

Answer: B

The expression  \frac{1}{x-1}  can never equal  0  because that would require the numerator to be zero, which is impossible when the numerator is the constant  1 .

You can verify that choices C and E are also possible by testing them the same way.

Want to master this concept completely?

The full solution on Neuron shows you how to test  all five choices  systematically, reveals the broader pattern for identifying impossible values of rational expressions, and teaches you time-saving techniques for spotting the answer quickly. You can check out the  detailed step-by-step solution on Neuron by e-GMAT  to understand how this concept applies to similar GMAT problems. You can also practice with comprehensive solutions for  many other official questions on Neuron  with detailed analytics to track your progress.

Hope this helps! Let me know if you have questions.

SameeranKarpe · Answer

The only way a number can be 0 is if the numerator is 0, hence B

Which of the following CANNOT be a value of 1/(x - 1)?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following CANNOT be a value of 1/(x - 1)?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards