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

Question

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%

Bunuel · Accepted Answer

Juan's income = 100 (assume);
Tim's income = 60 (40 percent less than Juan's income);
Mary's income = 96 (60 percent more than Tim's income).

Thus, Mary's income (96) is 96% of Juan's income (100).

Answer: C.

hfbamafan · Answer

I am working on trying to nail down these questions.

Is there a way to solve this problem by assuming that Mary's income is 160, which is 60% more than Juan's?

Or does that just cause problems.

Thanks,
Hunter

Bunuel · Answer

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%.\

ibtrippinyo · Answer

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)

hfbamafan · Answer

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.

PareshGmat · Answer

Answer = (C) 96%

Refer chart below:

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

colorblind · Answer

Given:
M = 1.6 T = 8/5T;  
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 =  J =  J = 0.96J

mcelroytutoring · Answer

Attached is a visual that should help.

JeffTargetTestPrep · Answer

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%.

sashiim20 · Answer

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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BrentGMATPrepNow · Answer

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

EMPOWERgmatRichC · Answer

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  C

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

MITIMITIM · Answer

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

ArnauG · Answer

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.

plpurva · Answer

Assuming that the number is 100
Mary= 160% of Tim's income
Tim = 60% of Juan's income

Substituting Tim's income:
Mary= (160/100 * 60/100 )Juan's income
Mary= 96% Juan's income

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=yUbc551_N0c Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

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