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Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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12 Dec 2012, 09:51

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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?

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).

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.

Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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02 Jul 2013, 23:25

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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)
_________________

Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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13 Apr 2014, 14:21

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' [#permalink]

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07 Dec 2014, 23:56

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;

Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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31 Jan 2016, 11:43

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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

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

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

Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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22 Jan 2017, 08:12

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' [#permalink]

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17 May 2017, 14:13

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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Mary's income is 60 percent more than Tim's income, and Tim'
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17 May 2017, 14:13

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