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maya2008: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Apr 29, 2008 8:10 pm

percents

by maya2008 » Mon May 05, 2008 9:44 am

I'm not so good at percents..it always confuses me
Here is a question from OG11TH Q115

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?

the answers are: A 124% B 120% C 96% D 80% E 64%

I was trying to substitute 100 as the whole. Anyone have an easier approach?

Thanks...

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Source: Beat The GMAT — Problem Solving | Mon May 05, 2008 9:44 am

ajguerre: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Tue Apr 22, 2008 11:54 am; Thanked: 1 times

by ajguerre » Mon May 05, 2008 11:43 am

The answer is D 96%.

In essence, Mary's income is 60% more than Tim's income translates into:

M = T + 3/5T = 8/5T

Tim's income is 40% less than Juan's income is:

T = J - 2/5J = 3/5J

The questions asks what percent is Tim's income relative to Juan's income (read carefully: it is not asking for Juan's in term of Tims'). So based on this you need to find M/J

First express the second equation in terms of T as follows:

J = 5/3T

Then,

M/J = (8/5) / (5/3) (note that the T's cancel each other)

M/J = 24/25

Now if you want to express in terms of 100's just multiply the fraction by 4

M/J = 24*4 / 25*4 = 96 / 100 = 96%

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amitansu: Master | Next Rank: 500 Posts; Posts: 294; Joined: Tue Feb 26, 2008 9:05 pm; Thanked: 13 times; Followed by:1 members

by amitansu » Tue May 06, 2008 12:58 am

You can very well substitute 100 as a whole :

Start with Juan's income as 100.
Tim's =100-60=40
Mary's = 60+60 X 60/100= 96, which is 96% 0f 100 i.e Juan's income

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640