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

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Manager
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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?

(A) 124%
(B) 120%
(C) 96%
(D) 80%
(E) 64%
[Reveal] Spoiler: OA
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Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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12 Dec 2012, 09:58
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Expert's post
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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Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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02 Jul 2013, 23:02
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
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Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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02 Jul 2013, 23:19
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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.

(160)/(500/3)*100 = 480/500*100 =96%.\
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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)
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Manager
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Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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03 Jul 2013, 00:47
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.
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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

Here we got the answer required: M:J = 1 : 0.96
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Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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22 Apr 2014, 00:10

Refer chart below:

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

mary.jpg [ 14.21 KiB | Viewed 9007 times ]

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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:
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).

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;

And for this (similar) question (the-price-of-lunch-for-15-people-was-207-including-a-68537.html)

To get ride of the 15% around, why is 207=1.15x correct and not "207*.85"?

Hope my question makes sense and makes in advance for your/anyone who can help.
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Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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31 Jan 2016, 11:43
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
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Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink]

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10 May 2016, 18:25
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Attached is a visual that should help.
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Screen Shot 2016-05-10 at 5.53.13 PM.png [ 59.67 KiB | Viewed 1627 times ]

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

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11 May 2016, 07:32
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%

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

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11 Jun 2016, 06:47
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%

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%. _________________ Jeffrey Miller Jeffrey Miller Head of GMAT Instruction Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink] 11 Jun 2016, 06:47 Similar topics Replies Last post Similar Topics: 1 Quentin's income is 60% less than Rex's income, and Sam's income is 25 2 28 Mar 2016, 02:25 10 Mary’s annual income is$15,000 and John’s annual income is 10 04 Mar 2013, 07:50
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