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

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Joined: 02 Dec 2012
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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, 08:51
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Difficulty:

15% (low)

Question Stats:

82% (01:42) correct 18% (02:18) wrong based on 1390 sessions

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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%
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Joined: 02 Sep 2009
Posts: 51072
Re: Mary's income is 60 percent more than Tim's income, and Tim'  [#permalink]

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12 Dec 2012, 08:58
3
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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%

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, 22:02
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, 22:19
1
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, 22:25
1
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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Re: Mary's income is 60 percent more than Tim's income, and Tim'  [#permalink]

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02 Jul 2013, 23:47
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, 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

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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21 Apr 2014, 23:10

Refer chart below:

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

mary.jpg [ 14.21 KiB | Viewed 24026 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, 22:56
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, 10:43
1
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, 17:25
1
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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Re: Mary's income is 60 percent more than Tim's income, and Tim'  [#permalink]

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11 May 2016, 06:32
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, 05:47
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%. _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Manager Status: On a 600-long battle Joined: 21 Apr 2016 Posts: 138 Location: Hungary Concentration: Accounting, Leadership Schools: Erasmus '19 GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23 Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink] ### Show Tags 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: x/100 * (J) = M x/100 * (J) = 1.6T x/100 * (J) = 1.6 * (0.6J) x/100 = 0.96 x = 96% _________________ "When the going gets tough, the tough gets going!" |Welcoming tips/suggestions/advices (you name it) to help me achieve a 600| Manager Joined: 03 Jan 2017 Posts: 152 Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink] ### Show Tags 25 Mar 2017, 10:59 this one was tricky for me: answer is M/J M=1,6*T T=0,6*J let's find J income: J=10/6*T T=10/16*M, J=(10*10)/(16*6)=25/24 1/(25/24)=24/25=96% Answer is C Manager Joined: 06 Dec 2016 Posts: 249 Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink] ### Show Tags 25 Mar 2017, 20:14 You could even do this approach: M = 1.6T => equation 1 T = 0.6J => equation 2 Plug T = 0.6J into equation 1 M = 1.6(0.6J) M = 0.96 J Answer: C Intern Joined: 30 Mar 2016 Posts: 40 Mary's income is 60 percent more than Tim's income, and Tim' [#permalink] ### Show Tags 28 Apr 2017, 23:34 1 This is what I have been taught by Karishma: What comes after "THAN" is essentially important because it is the BASE. Back to the question. M is 60% more than T => T = BASE of M T is 40% less than J => J = BASE of T So, the FINAL BASE = J. If you want to pick a smart number and do not know which one out of M, T, and J. It's easiest to pick a smart number for the FINAL BASE = J. So, Pick J =100, and the rest would be done according to Bunuel did. Director Joined: 04 Dec 2015 Posts: 726 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) Mary's income is 60 percent more than Tim's income, and Tim' [#permalink] ### Show Tags 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.... _________________ Kindly press "+1 Kudos" to appreciate CEO Joined: 11 Sep 2015 Posts: 3228 Location: Canada Re: Mary's income is 60 percent more than Tim's income, and Tim' [#permalink] ### Show Tags 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

So, Mary's income is 96% of Juan's income

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

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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%

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Re: Mary's income is 60 percent more than Tim's income, and Tim' &nbs [#permalink] 21 Feb 2018, 19:31

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