Official Guide PS #123

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mcadorette: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Fri Dec 28, 2012 8:23 pm; Location: Morgantown, WV

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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Source: Beat The GMAT — Problem Solving | Wed Apr 02, 2014 5:40 pm

mcadorette: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Fri Dec 28, 2012 8:23 pm; Location: Morgantown, WV

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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mcadorette: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Fri Dec 28, 2012 8:23 pm; Location: Morgantown, WV

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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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

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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