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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It was a typo. Edited. Thank you.
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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.

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 %

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?