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Mary's income is 60 percent more than Tim's income, and Tim'
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12 Dec 2012, 08:51

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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?

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12 Dec 2012, 08:58

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Walkabout 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%

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).

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02 Jul 2013, 22:19

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hfbamafan 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 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

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.

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02 Jul 2013, 22:25

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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)
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13 Apr 2014, 13:21

Mary's income is 60 percent more than Tim's income: M = 1.6T Tim's income is 40 percent less than Juan's income: T = 0.6J To compare them, we will need to rationalise the ratio of the 3 individuals M : T : J

M : T : J => 1 : 1.6(1) : 0.6(1.6) = 1 : 1.6 : 0.96

Mary's income is 60 percent more than Tim's income, and Tim'
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07 Dec 2014, 22:56

Bunuel wrote:

Walkabout 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%

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.

Hi Bunuel! Really hoping you can help me understand something. I can not for the life of me make this equation work by setting Tim 100. I read your other comment regarding this, but I saw you wrote: Mary's income = "100/0.6". May I ask why you divided 0.6 rather than multiplied?

My quant is very weak so sorry if the answer is obvious.

EDIT: I just ran into another question and made a similar mistake. Therefore I think my question needs to be when should I use "amount*0.%" vs "amount/1.%"?

E.g why did you (and others here) go with "100/0.6" and not "100*0.60" since it says Tim's income is 60% of Juan's;

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31 Jan 2016, 10:43

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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

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10 May 2016, 17:25

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Attached is a visual that should help.

Attachments

Screen Shot 2016-05-10 at 5.53.13 PM.png [ 59.67 KiB | Viewed 16636 times ]

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One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).

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11 May 2016, 06:32

Walkabout 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
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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11 Jun 2016, 05:47

Walkabout 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 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%.
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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22 Jan 2017, 07:12

Walkabout 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 solved it this way:

Mary = M = 1.6T Tim = T = 0.6J Juan = J

I translated the sentence "What percent of Juan's income is Mary's income" into:

Mary's income is 60 percent more than Tim's income, and Tim'
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17 May 2017, 13:13

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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30 Aug 2017, 13:39

Top Contributor

Walkabout 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

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21 Feb 2018, 19:31

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%