Mary's income is 60 percent more than Tim's income, and Tim'

You can do this way, though the way proposed in my post is better:

Mary's income = 160.
Tim's income = 100;
Juan's income = 100/0.6 = 500/3.

(160)/(500/3)*100 = 480/500*100 =96%.\

If Tim's income is 100
and Marys income is 160
Juan's income, J, can be found by dividing Tim's income by .6
100 = .6J
J = 167

Mary's income as a percentage of Juan's is then
160/167 = .96
(you can just estimate the .96 by looking at the answer choices)
(also Mr. Bunuels method is way better)

Thanks alot.

This problem area seems to be the hardest for me to think through logically.

I need to work hard on word problems, even though I know that they are easy.

Answer = (C) 96%

Refer chart below:

\(\frac{96}{100} * 100 = 96\)

Given:
M = 1.6 T = 8/5T; [how did i get 8/5? 60% = 3/5 & 160% = 1+(3/5) = 8/5]
T = 0.6J = 3/5J;
Substitute T:
M = 8/5 * (3/5)J
M = 24/25J;
You can either calculate 24/25 (I wouldn't) or know that 24/25 is little less than 1 ~= 0.96 (the only answer choice which is little less than 1)
Hence,
M = 0.96J or 96%J

OR

M = 1.6 * 0.6*J = [(1+0.6)*(0.6)]J = [0.6 + 0.36]J = 0.96J

Attached is a visual that should help.

To solve this problem we create variables for the income 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.

For some students, an easier way to solve this is to use convenient numbers. If we "pretend" that Juan's income is J = $100, and Tim's income is 40% less than Juan's, then Tim's income is: 100 – (100)(.40) = $60. We also are told that Mary's income is 60% more than Tim's: 60 + (60)(.60) = 60 + 36 = $96.

Now we can easily determine the percent of Juan's income that Mary's income represents: (96/100) x 100% = 96%.

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 be = 100
Tim's income = 40% less than Juan's income = 60% of 100 = \(\frac{60}{100}\) x 100 = 60
Mary's income = 60% more than Tim's income = 160% of 60 = \(\frac{160}{100}\) x 60 = 96
Required percentage = Mary income/Juan's income = \(\frac{96}{100}\) = 96%
Answer C....

_________________
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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 96% of Juan's income
Answer: C

Hi All,

Brent has 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 = a little less than 100%

The only answer that's close is answer

GMAT assassins aren't born, they're made,
Rich

Bunuel

so basically "What percent of Juan's income is Mary's income?" -> when there is "of Juan" = Juan is the denominator?



Many thanks

Given:
Tim's income = x
Juan's income = 100% (or 1 times) of x

Tim's income is 40% less than Juan's income, so Tim's income can be expressed as:
Tim's income = (100% - 40%) * Juan's income = 60% * Juan's income = 0.6 * Juan's income

Mary's income is 60% more than Tim's income, so Mary's income can be expressed as:
Mary's income = (100% + 60%) * Tim's income = 160% * Tim's income = 1.6 * Tim's income

Substituting the value of Tim's income from the earlier calculation:
Mary's income = 1.6 * (0.6 * Juan's income) = 0.96 * Juan's income

Therefore, Mary's income is 96% of Juan's income, which corresponds to option (C) in the given choices.