Another approach is algebraic. The full solution below is taken from the GMATFix App.
-Patrick
Percentage of income
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Patrick_GMATFix
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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.
-Patrick
Another approach is algebraic. The full solution below is taken from the GMATFix App.
-Patrick
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Brent@GMATPrepNow
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I suggest that we choose some nice values that meet the given conditions.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%
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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Scott@TargetTestPrep
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Solution: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%
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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GMATGuruNY
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Alternate approach: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%
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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Algebra works too:
M = T + .6T = 1.6T
T = J - .4J = .6J
So M = 1.6T = 1.6(*6J) = .96J
and we're done!
M = T + .6T = 1.6T
T = J - .4J = .6J
So M = 1.6T = 1.6(*6J) = .96J
and we're done!
