Mike, Tom, and Walt are working as sales agents for an insurance compa

Simplifying the condition:

mt = 6w

6 is a constant; for the sake of the required calculation, it can be ignored.

mt = w ............... (1)

60% increase in m, 50% decrease in t

\(\frac{160}{100} m * \frac{50}{100} t = w\)

\(mt = \frac{100}{80} w\) .................. (2)

By comparing (1) & (2), increase in\(w = \frac{100}{80} - 1 = \frac{20}{80}\)

Required decrease = 20%

Answer = B

Mike, Tom, and Walt are working as sales agents for an insurance company, and the commissions they receive can be expressed by the following formula: MT=W/6 . If Mike sells 60% more this month and Tom decreases his sales by 50%, how should Walt's performance change to ensure that the above relationship is true ?

I believe this is the same question that has already been answered. But here's my take:

MT = W/6 => 6MT = W (1)

1.6M * 0.5T = Wx/6
0.8MT = Wx/6
4.8MT = Wx (2)

Comparing (1) and (2):

(1) 6MT = W
(2) 4.8MT = Wx

Since 4.8 is 4/5 of 6, x would need to be 4/5 for the equation to hold. Therefore, W needs to decrease by 20%, or answer choice B, for the equation to remain intact.

Please tell me the official answer

It is given that: MT = W/6....eq(1)

Now, M 's sales increased by 60 percent, whereas that of T decreased by 50 %.

Thus, Mnew= 1.6M, and Tnew = 0.5T. So, now lets assume that we increase or decrease W by X%. As the equation is still valid, we can represent it as:

1.6M * 0.5T = [ W (1 + X/100) ] / 6 ....where X is the percent increase or decrease

We can further simplify this as,
0.8MT = [W (1 + X/100) ] / 6 ]
From eq 1, however, W = 6MT
So,
0.8MT = [W (1 + X/100) ] / 6 ] => 0.8MT = [6MT (1+ X/100)] / 6
Further simplifying,

0.8MT/6MT * 6 = (1 + X/100) => (1 + X/100) = 0.8 => X/100 = -0.2 => X = -20 => Answer Choice B

Thus, we need to reduce W by 20% in order to maintain the equation. I have listed all the steps to clarify, otherwise the problem could be solved much faster.

Lost
shouldnt any change in MT be 6 times that of W?

\(MT/6=W\)

\(0.8MT=6W\)

(8/5)(1/2)*(MT/6)=x*W <-> x=(4/5)

->20% decrease

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.