Official Solution:

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%


Previous month \(\frac{MT}{6}=W\);

This month \(1.6M*0.5T=0.8MT\). So, \(MT\) is decreased by 20% so \(W\) should also decrease by the same percent for the relationship to remain the same.


Answer: B
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Sorry, i don't understand how do you get W=MT*6.
the questions states W=MT/6

It was a typo. Edited. Thank you.
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Hi

Shouldnt we have an increase of 20% in Ws commission?
Assuming numbers say M=3, T=4 so as per old rates W=2
Now, M=4.8, T=2 so W=1.6
We have to bring the commissions back to old levels so W from 1.6 has to go back to 2 relative to 2 as mentioned in the question. So 0.4/2 which is an increase of 20%?

Hi Bunuel,

I reached the part where \(\frac{0.8MT}{6}\)= W, however the next step I did was \(\frac{MT}{6}\) = \(\frac{W}{0.8}\) This implies that there's an increase in the value of W.

Please correct me. Thanks.

MT is decreased by 20% so W should also decrease by the same percent for the relationship to remain the same. Try plugging some values for better understanding.
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6W in RHS of original equation is there to confuse test takers.

The concept here is simple: If LHS decreases by 20 % of original value for LHS=RHS , the RHS should also decrease by 20 %

Why does 6 not have any effect on the relationship when it changes?

I'm still missing something.

If we plug in numbers for M & T, lets go with 10 & 10...

(10*10)/6 = 16.67 for W

The total output of all three there would be 10+10+16.67, or 36.67 in the first month.

Then M increases by 60% to 16
T decreased by 50% to 5

Therefore M&T total is 21 and we need 15.67 out of W to get us to the same total of 36.67.

So I get an answer of W needs to decrease from 16.67 to 15.67, or 1/16.67 or about 6%.

What's wrong with my logic here?

Nevermind. Read question wrong

Thought it was asking what W had to decrease to get same sales as prior month, not keep ratio the same.

I think this is a high-quality question and I agree with explanation.

1. For the previous month, we are given that \(\frac{MT}{6}=W\). Rearranging this equation to \(MT=6W\)
2. For this month, let the commissions of Mike, Tom and Walt be \(M'\), \(T'\) and \(W'\). As per the info. provided in the question stem \(M'=1.6M\) and \(T'=0.5T\)
3. Plugging this new information in the rearranged equation we get \(1.6M*0.5T=6W'\). Simplifying this equation we get \(\frac{16}{10}M*\frac{5}{10}T -> \frac{4}{5}MT = 6W'\)
4. We are asked to make this new equation (\(\frac{4}{5}MT = 6W'\)) equal to \(\frac{MT}{6}=W\). Let's work that out
\(\frac{4}{5}MT = 6W'\) -> \(MT = 6 * \frac{5}{4}W'\) (I just rearranged the equation)
As we can see, we need to make \(5/4W'=W\) and that can only be done by making \(W'=\frac{4}{5}W\)

\(W'=\frac{4}{5}W\) means that \(W'\) is 80% of \(W\) or \(W'\) is a 20% decrease on \(W\)

Ans. B
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Given relationship between commissions -> MT/6=W

Changes in commisions
M -> 1.6M
T -> 0.5T

W or MT/6-> (1.6M * 0.5T)/6
MT/6-> 0.8MT/6 (20% decrease)

MartyTargetTestPrep chetan2u Bunuel BrentGMATPrepNow

Could anyone please explain the official solution given by Bunuel?

Does part MT/6=W have any role in the problem?

Hi

What MT/6=W tells us is that W is directly proportional to product of M and T.

So, if M1=1.6M and T1=0.5T, then W1=M1T1=1.6M*0.5T=0.8MT=0.8W

Thus, W1 is 20% less than W.
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chetan2u
I thought the products M and T should be divided by 6 to get the desired result or value of W.

Could you please clarify why denominator 6 is ignored?

Thanks in advance!

Yes, you have to divide the product by 6, but that will be the case in both initial W and later W_1 and will get cancelled out.

Old W=MT/6 so \(W_1=\frac{M_1T_1}{6}=\frac{1.6M*0.5T}{6}=1.6*0.5*\frac{MT}{6}=0.8W\)
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chetan2u, you are great! Your explanation helps all groups of learners: weak, moderately good, and expert.