If a = 1 and (a - b)/c = 1, Which of the Following is NOT a Possible GMAT Problem Solving

Question: If a = 1 and (a - b)/c = 1 Which of the Following is NOT a Possible Value of b?

1. -2
2. -1
3. 0
4. 1
5. 2

Correct Answer: D

Solution and Explanation
Approach Solution 1:

Lets try to implement the cross multiply process to solve this question-
you CAN cross-multiply because division by zero is undefined,
hence c≠0

\(\frac{a-b}{c}=1 \)

As it is given that the value of a = 1, this can be further evaluated through the following way-

\(\frac{1-b}{c}=1 \)

On solving the equation which is presented above we will get,
1 - b = c
But, as said above in the first sentence that c ≠ 0
1 - b ≠ 0
b ≠ -1
therefore b = 1 is not possible.
Answer is D, Which is 1

Approach Solution 2:

Lets try a different approach
It is given that a = 1, we have:

\(\frac{1-b}{c}=1 \)

this can be further evaluated through the following way-
so,
1 - b = c
But one must remember that

\(\frac{1-b}{c}=1 \)

The value of c cannot be zero
since dividing by zero creates an undefined result
Now
Let’s test the answer choices we have

1.  -2

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

2.  -1

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

100.  0

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

500.  1

Since c = 1 - 1 = 0,
b cannot be 1.
Answer is D, Which is 1

Approach Solution 3:

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≠ 0 and that's why we can cross-multiply.
a−b/c= 1--> as a= 1--> 1−b/c= 1--> 1−b= c, but since c≠ 0, then 1-b≠ 0--> b≠ 1. 

“If a = 1 and (a - b)/c = 1 Which of the Following is NOT a Possible”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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