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Percentage of income

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by Patrick_GMATFix » Thu Feb 13, 2014 10:57 am
One approach is to plug-in values. Since the Q asks for Mary's as a % of Juan's income, it would be easiest to make J=100 and go from there. Tim's is 40% less than Juan, so T=60. Mary's is 60% more than Tim so M=60+36=96. M=96 and J=100, so Mary's is 96% of Tim's

Another approach is algebraic. The full solution below is taken from the GMATFix App.

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by Brent@GMATPrepNow » Thu Feb 13, 2014 10:59 am
GmatGreen 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

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by [email protected] » Thu Feb 13, 2014 11:52 am
Hi GmatGreen,

Both Brent and Patrick have provided an explanation that focuses on TESTing Values; I'm a big fan of this approach and I highly recommend it. As an alternative, here's the algebra approach:

We'll need to translate the "math phrases" into actual equations.

"Mary's income is 60% more than Tim's income"

M = 1.6T

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

T = .6J

"What percent of Juan's income is Mary's income?"

We already have a value for M (above); now we need to take the second equation and solve for J...

T = .6J
T = 3J/5
5T/3 = J

We're asked for the value of M/J....

M = 1.6T
J = 1.666T

1.6T/1.666T = 1.6/1.666 = a little less than 1

The only answer that's close is answer C

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by Scott@TargetTestPrep » Mon Jun 29, 2015 7:06 am
GmatGreen 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%
Solution:

To solve this problem we define variables for the incomes of Mary, Tim, and Juan, and then set up some equations.

T = Tim's income

M = Mary's income

J = Juan's income

We are given that Mary's income is 60% more than Tim's. Thus, we can say:

M = 1.6T

We are also given that Tim's income is 40% less than Juan's income. So we can say:

T = 0.6J

We are asked to determine the percent of Juan's income that Mary's income is. For this we can set up the expression:

M/J x 100%

To complete this problem we must express Juan's income and Mary's income in terms of a common variable. That common variable is T. Thus, we have:

M = 1.6T

J = T/0.6

So finally we can substitute T/0.6 for J and 1.6T for M

M/J x 100%

(1.6T)/(T/0.6) x 100%

(1.6T) x (0.6/T) x 100%

The T's cancel and we have:

1.6 x 0.6 x 100%

0.96 x 100% = 96%

Answer:C

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by GMATGuruNY » Mon Jun 29, 2015 7:19 am
GmatGreen 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%
Alternate approach:

Ratios can be MULTIPLIED TOGETHER:
M/J = M/T * T/J.
In the equation above, the values in red CANCEL OUT.

Mary's income is 60 percent more than Tim's income.
Thus:
M/T = 160/100 = 8/5.

Tim's income is 40 percent less than Juan's income.
Thus:
T/J = 60/100.

Since M/J = M/T * T/J, we get:
M/J = 8/5 * 60/100 = 8/1 * 12/100 = 96/100 = 96%.

The correct answer is C.
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by Matt@VeritasPrep » Mon Jun 29, 2015 3:28 pm
Algebra works too:

M = T + .6T = 1.6T
T = J - .4J = .6J

So M = 1.6T = 1.6(*6J) = .96J

and we're done!
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