Mike, Tom, and Walt are Working as Sales Agents for an Insurance Company.

Question: Mike, Tom, and Walt are working as sales agents for an insurance company. Previous month relationship between their commissions was \(\frac{MT}{6}=W\), where M, T, and W are the commissions received by Mike, Tom, and Walt respectively. If this month, Mike's commission is 60% more than previous month and Tom's commission is 50% less than previous month, then how much should Walt's commission change compared to the previous month to ensure that the relationship between their commissions remains the same?

A.  Decrease by 12.5%
B. Decrease by 20%
C. Decrease by 22.5%
D. Increase by 12.5%
E. Increase by 15%

“Mike, Tom, and Walt are working as sales agents for an insurance company. ” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer

Approach 1

From the given data in the question:

Previous Month \(\frac{MT}{6}=W\)

Therefore, This month = 1.6 M * 0.5 T = 0.8 MT

So, MT is decreased by 20%

So, W should also be decreased by the same percentage for the relationship to remain the same.

Correct option: B

Approach 2:

For the previous month, we are given that \(\frac{MT}{6}=W\)

Rearranging this equation, we will get: MT = 6W

For this month,

Let the commission of Mike, Tom and Walt be M’, T’ and W’.

As per the info provided in the question, M’ = 1.6M and T’ = 0.5T

Now put this new info into the rearranged equation, we will get:

1.6M * 0.5T = 6W’

After simplifying this equation, we will get:

\(\frac{16}{10}M*\frac{5}{10}T->\frac{4}{5}MT=6W^1\)

Now, we have to make this new equation equal to \(\frac{MT}{6}=W\)

As \(\frac{4}{5}MT=6W^1\)

So, \(MT=6*\frac{5}{4}W^1\)

As we can see that \(\frac{5}{4}W^1=W\) and that can be only done by making \(W^1=\frac{4}{5}W\)

Hence, this means W’ is 80% of W or W’ is 20% decrease on W.

Correct option: B

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