The Income of a Broker Remains Unchanged though the Rate of Commission GMAT Problem Solving

Question: The income of a broker remains unchanged, though the rate of commission is increased from 4% to 5%. The percentage of the slump in business is:

1. 8%
2. 1%
3. 20%
4. 80%
5. 5%

“The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%" - 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 Club tests questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude for reasoning and mathematics. The GMAT Quantitative Test's Club Test 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.

Answer: C
Solution and Explanation:
Approach Solution 1:

It is a given that the income of the broker remains unchanged even though the rate of commission is changed from 4% to 5%. It has asked to find out the slump in the business.

Let S1 be initial sales and S2 be sales after an increase in commission percentage. We need to find (S1−S2) / S1

Given S1 ∗ 4% = S2 ∗5% => S2 / S1 = 4 / 5. subtract both sides of the equation from 1 to get

Or, 1−S2 / S1= 1 − 4/5

(S1−S2) / S1 = ⅕ =>20%

Option C is the correct answer.

Correct Answer: C

Approach Solution 2:

It is given that the income of the broker remains unchanged even though the rate of commission is changed from 4% to 5%. It has asked to find out the slump in the business.
Here,
Let the value of business be 100
and, the percentage of slump of business is x
So, according to question,
100 * 4/100 = (100-x) * 5/100
4 = (100-x)/20
80 = 100 -x
100 -x = 80
- x = 80-100
-x = -20
x= 20

20% is the percentage of slumping business. Option C is the correct answer.

Correct Answer: C

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