For Which of the Following does f(a)−f(b) = f(a−b) for all Values of a and b GMAT Problem Solving

bySayantani Barman Experta en el extranjero

Question: For which of the following does f(a) − f(b) = f(a − b) for all values of a and b?

A) f(x) = x^2
B) f(x) = x/2
C) f(x) = x+5
D) f(x) = 2x−1
E) f(x) = |x|

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

You must use the information supplied in the question to solve this GMAT problem. These concerns cover numerous mathematical disciplines. This question concerns algebra. Because of how the options are presented, it is difficult to select the optimal option. Candidates must comprehend the correct approach to obtaining the required response. Only one of the five supplied alternatives is correct.

The simplest solution is to enter the value and check to see if it equals or not.
with choice 1. f(a) equals a2 and f(b) equals b2

hence, L.H.S. = a2 - b2.
Furthermore, RHS = (a-b)2 ==> a2 + b2 - 2ab
LHS is therefore not equivalent to RHS

with choice 2. f(a) = a/2 and b = f(b)
L.H.S = a/2 - b/2 ==> 1/2 (a-b)
R.H.S = (a-b)/2
L.H.S = R.H.S is the right response, therefore.

B is the correct answer.

Approach Solution 2:

let a=3 & b=2

Which of the subsequent functions does f(3) - f(2) equal f(1), then?
Answer option A: 9 - 4 = 5
f(3) = 9
f(2) = 4 f(1) = 1
Eliminate

Answer option B: 3/2 - 1 = ½
f(3) = 3/2
f(2) = 1
f(1) = 1/2.
Keep

Answer option C: f(3) = 8,
f(2) = 7,
f(1) = 6,
8 - 7 = 1.
Eliminate

Answer option D: 5 - 3 = 2
f(3) = 5
f(2) = 3
f(1) = 1.
Eliminate

Answer option E: 3 - 2 = 1
f(3) = 3
f(2) = 2
f(1) = 1.
Keep

So, let's pick another illustration. Let a=2 & b=3
E is the correct response because f(2) = 2, f(3) = 3, and f(1) = 1 2 - 3 = 1.
Eliminate

There is just one viable response which is B.

Approach Solution 3:

You must use the information supplied in the question to solve this GMAT problem. These concerns cover numerous mathematical disciplines. This question concerns algebra. Because of how the options are presented, it is difficult to select the optimal option. Candidates must comprehend the correct approach for obtaining the required response. Only one of the five supplied alternatives is correct.

1.LHS --> a - b --> (a-b) --> (f(x) = x2 RHS
RHS! = LHS — Reject

2.LHS -> (a/2) - (b/2)
RHS -> (a-b)/2
f(x) = x/2
RHS = LHS

B is the correct answer.

“For which of the following does f(a)−f(b)=f(a−b) for all values of a" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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