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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   35% (medium)

Question Stats: 71% (01:22) correct 29% (01:29) wrong based on 158 sessions

### HideShow timer Statistics 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%

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Math Expert V
Joined: 02 Sep 2009
Posts: 56371

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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.

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Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38 GPA: 3.75

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Bunuel wrote:
Pick numbers. Assume $$M = 5$$, $$T = 4$$, and $$W =MT * 6 = 120$$.

Sorry, i don't understand how do you get W=MT*6.
the questions states W=MT/6
Math Expert V
Joined: 02 Sep 2009
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oss198 wrote:
Bunuel wrote:
Pick numbers. Assume $$M = 5$$, $$T = 4$$, and $$W =MT * 6 = 120$$.

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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Manager  B
Joined: 27 Aug 2014
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Bunuel wrote:
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.

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%?
Intern  Joined: 16 Mar 2016
Posts: 6

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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.

Math Expert V
Joined: 02 Sep 2009
Posts: 56371

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pwnuts wrote:
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.

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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Intern  Joined: 26 May 2014
Posts: 39
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

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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 %
Manager  B
Joined: 02 Feb 2016
Posts: 88
GMAT 1: 690 Q43 V41 ### Show Tags

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Why does 6 not have any effect on the relationship when it changes?
Intern  Joined: 24 Feb 2018
Posts: 4

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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?
Intern  Joined: 24 Feb 2018
Posts: 4

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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. Re: M06-36   [#permalink] 25 Feb 2018, 11:45
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# M06-36

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