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

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

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New post 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?

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

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New post 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).

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

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New post 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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New post 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.

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

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New post 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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New post 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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New post 21 Apr 2014, 23:10
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Answer = (C) 96%

Refer chart below:

\(\frac{96}{100} * 100 = 96\)
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Mary's income is 60 percent more than Tim's income, and Tim'  [#permalink]

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New post 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;

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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New post 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

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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New post 10 May 2016, 17:25
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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 23376 times ]

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

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

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

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

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

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

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New post 28 Apr 2017, 23:34
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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.
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Mary's income is 60 percent more than Tim's income, and Tim'  [#permalink]

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New post 17 May 2017, 13:13
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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%

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'  [#permalink]

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New post Updated on: 04 May 2020, 14:39
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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%


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
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Originally posted by BrentGMATPrepNow on 30 Aug 2017, 13:39.
Last edited by BrentGMATPrepNow on 04 May 2020, 14:39, edited 1 time in total.
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Re: Mary's income is 60 percent more than Tim's income, and Tim'  [#permalink]

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New post 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%

The only answer that's close is answer

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

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