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Official Guide PS #123

by mcadorette » Wed Apr 02, 2014 5:40 pm
I wanted to see if somebody could tell me a different way to solve this problem. I thought I could do it without using an Algebra equation but maybe I am wrong. I spent a lot of time on this problem and thought I was doing the right thing by assigning Tim's income at $100 and finding out the other incomes but obviously my answer was not one of the choices. Looking for alternate explanations to this problem.
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by mcadorette » Wed Apr 02, 2014 5:42 pm
Here is the problem sorry I didnt post it before

Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

A) 124%
B) 120%
C) 96%
D) 80%
E) 64%
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by Brent@GMATPrepNow » Wed Apr 02, 2014 5:45 pm
mcadorette wrote: Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

A) 124%
B) 120%
C) 96%
D) 80%
E) 64%
I suggest that we choose some nice values that meet the given conditions.

Tim's income is 40 percent LESS THAN Juan's income.
Let Juan's income = $100
40% of $100 = $40
This means Tim's income = $100 - $40 = $60

Mary's income is 60 percent MORE THAN Tim's income
60% of $60 = $36
So Mary's income = $60+ $36 = $96

What percent of Juan's income is Mary's income?
Juan's income = $100
Mary's income = $96

So, Mary's income is [spoiler]96%[/spoiler] of Juan's income
Answer: C

Cheers,
Brent
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by Brent@GMATPrepNow » Wed Apr 02, 2014 5:48 pm
mcadorette wrote: Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

A) 124%
B) 120%
C) 96%
D) 80%
E) 64%
ASIDE: A lot of people incorrectly conclude that, if Tim's income is 40% less than Juan's, then Juan's income must be 40% more than Tim's. This incorrect conclusion can get students into trouble.

Consider this scenario:
Tim's income = $60
Juan's income = $100
As you can see, Tim's income is 40% less than Juan's income. However, Juan's income is not 40% more than Tim's. In fact, Juan's income is 66 2/3% more than Tim's.


Cheers,
Brent
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by mcadorette » Wed Apr 02, 2014 6:12 pm
Thanks for the help Brent the wording is what got me. I have to realize that it is 40 percent less than and not of. When I look at the question again as well I should realize it uses the words is and of and 96 is 96% of Juan's income. I hope I can fix this problem in the future. Thanks again for the quick response.
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by Abhishek009 » Thu Apr 03, 2014 6:51 am
mcadorette wrote:Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

A) 124%
B) 120%
C) 96%
D) 80%
E) 64%
Let Juan's income is $ 100
Tim's income is 40 percent less than Juan's income
Tim's income is 60
Mary's income is 60 percent more than Tim's income
Mary's Income is 160 * 60 / 100 =>96



So the ratio of the income of the three people are as follows-

Mary : Tim : Juan = 96 : 60 : 100 => 24 : 15 : 25
What percent of Juan's income is Mary's income?
Mary's Income / Juan's Income => 24/25 * 100 => 96%
Abhishek
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