Mary's income is 60% more Than Tim's income and Tim's income

Question

Mary's income is 60% more Than Tim's income and Tim's income is 40% less than Juan's income.What % of Juan's income is Mary's income.

A. 124%
B.120%
C. 96%
D. 80%
E. 64%

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Let Tim's income is t
Juan's income is j

Mary Tim Juan
1.6t t .6j=t => j=t/.6

x/100*j=1.6t

x=1.6*100*.6=96%

Which is wrong

fluke · Answer

Even I got 96%

J = 100
T = 100*0.6 = 60
M = 60*1.6 = 96

If Mary's income is x percent of J
M = J*x/100

x = M*100/J = 96*100/100 = 96

Ans: "C"

Bunuel · Answer

Solution is right, it's OA provided which is wrong.

OA edited.

KarishmaB · Answer

Word of advice: In % questions, try not to take Tim's income as t and Juan's income as j.
Take one of them as 100 instead. 
Since Mary's income is linked to Tim and Tim's in linked to Juan, take Juan's income as 100.
Then Tim's is 60. Then Mary's income is 96 i.e. 96% of Juan's.

naveenhv · Answer

+1 to Karishma. Its always easy if we plug in 100 for problems involving percentages.

mbafall2011 · Answer

karishma,
I usually follow your approach -which is assigning numbers to the percentages.

So in my case: Mary - 160
Tim = 100

Juan = 166.66

Therefore mary =x% 166.67

160/167 ~ x% = 95.8% but the last division takes more time!

I could have started with mary = 100 and tim = 60. Is there a trick to which person gets assigned 100?

fluke · Answer

I believe you are doing something wrong in your calculation or you would have gotten the exact value 96%.

While there are no set rules as to whose value should be chosen as 100, it is generally preferred to take "100" as a value of the person with reference to whom the final question is posed.

Here the question is: What % of   juan's   income is Mary's income.

What percent of JUAN's income; how many dollars does Mary earn with reference to every $100 Juan earns; so it is best to take Juan's income as 100 so that the value for Mary's income would be her percentage as well.

if Mary's income is 120. Mary's income will be 120% of Juan's income.
If Mary's income is 68. Mary's income will be 68% of Juan's income.

You won't have to do any extra calculation to find percentage that way.

mbafall2011 · Answer

Fluke,
I see your point

Juan = 100
Tim is 40% less = 60
mary is 160% of Tim which is 96 .

therefore 96/100

mbafall2011 · Answer

I went back and looked at my calculation:

I read the first 2 sentences and assigned values. Hence i omitted the final part where the answer is in terms of Juan's income. I assigned 100 to Tim.
Another perfect example where reading the qn completely and then assigning variables helps to save time!

KarishmaB · Answer

Yes, there is. Assign 100 to the person who is the base (which means the person to whom everyone else links up) e.g.

Mary's income is 60% more Than Tim's income 
- Mary's income is linked to Tim's. So, I might assign 100 to Tim if there is no Juan.

and Tim's income is 40% less than juan's income.
- Now Tim's income is further linked to Juan. Juan's income is the base against which others are compared.

So I assign 100 to Juan. Calculations will not be tough in this case. Else they could get a little tricky.

scbguy · Answer

Marts income is 60 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income

A) 124%
b) 120 %
c) 96 %
d) 80 %
e) 64 %

I solved it like this

Keep tims income as 100 hence marys income is 160 and juans is 140 so effectively it will be 160/140x 100 which is approximate 96%

But that's wrong the answer is c

fluke · Answer

Tim=100
Mary's income is 60 percent more than tims income;
Mary's Income = T+0.6T = 1.6T = 1.6*100=160

Tims income is 40 percent less than juans income .
100 is 40% less than Juan's Income
100=J-0.4J
100=0.6J
J = 100/0.6=1000/6

What percentage of juans income is marts income
(160/(1000/6))*100 = (160*6*100)/1000 = 96%

Please look @
 https://gmatclub.com/forum/mary-s-income-109262.html?hilit=juan

KarishmaB · Answer

The error in your solution is that Tim's income is 40% less than Juan's. Juan's income is not 40% more than Tim's. These are 2 different things. Say I scored a 90 in an exam and you scored a 100. My score is 10%  less than yours    Notice that your score, 100, is the base on which we are comparing. On the other hand, your score is 11.11%  more than mine . Now my score is the base on which we are comparing

The trick is to assign 100 for easy calculations but to assign it to the 'right' person. Assign 100 to the person who is the base (which means the person to whom everyone else links up) e.g.

Mary's income is 60% more Than Tim's income
- Mary's income is linked to Tim's. So, I might assign 100 to Tim if there is no Juan.

and Tim's income is 40% less than juan's income.
- Now Tim's income is further linked to Juan. Juan's income is the base against which others are compared.

So I assign 100 to Juan. Calculations will not be tough in this case. Else they could get a little tricky.

Juan - 100
Tim - 60
Mary - 96
So Mary's income is 96% of Juan's income (which is 100).

lawschoolsearcher · Answer

I used to have my jaw-dropping with these types of questions... but after reading Manhattan GMAT.. this seems really easy... and I sound like an advertisment now...

My Solution:

Convert the given to algebraic equations:
m = T + 0.6 T = 1.6T
T = J - 0.4J = 0.6J

Simplify M in terms of J:
M = 1.6(0.6J)
M = 0.96J

Therefore, Marta's income is 96% of Juan's. =)

Spidy001 · Answer

M = (160/100)T
T = (60/100)J

=> M = (96/100)J

Answer C.

gmatprep2011 · Answer

Consider Juan Income as 100. So Tim's is 60. M is 1.6*60 = 96
So J/M = 96/100*100 = 96%

Bunuel · Answer

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. OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/mary-s-incom ... 43995.html

Mary's income is 60% more Than Tim's income and Tim's income

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Mary's income is 60% more Than Tim's income and Tim's income

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