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gmatprep test 2 - ps question 11

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gmatprep test 2 - ps question 11

by gmatjoe » Sat Feb 16, 2008 7:33 am
Hi there, anybody know how to do this one? Not so sure where my method goes wrong:

Q: Pate, Kate and Mark charged a total of 162hrs in a certain project.
If Pat charged twice as much time in the project as Kate and 1/3 as much time as Mark, how many hrs did Mark charge to the project more than Kate?

a) 18
b) 36
c) 72
d) 90
e) 108

My attempt is as follows:
1) P+K+M=162, Question is M-K=?
2) P=2*K -> K=(1/2)*P
3) P=(1/3)*M -> M=3*P
4) substitute 2) & 3) in 1) gives unfortunately wrong answer... correct answer is (d)

Thanks in advance.
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by mleviko » Sat Feb 16, 2008 8:40 am
The question gives you two different equations as well as two factors:

Let's say kate charged x hours and Mark y hours.

The first equation tells us that pat + kate + mark charged 162 hours together, and that pat charged twice as much as kate, so the equation is:
2x + x + y = 162


the second equation tells us that Mark charged three times as much as Pat, or:
3 * 2x = y

substitue 6x with y in the first equation to get:
2x + x + 6x = 162
x = 18

so Kate charged 18 hours, Mark charged six times as much, or 108.
108 - 18 = 90 , [D] is the answer.
Smashed the GMAT: 760
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by gmatjoe » Sat Feb 16, 2008 8:50 am
well done! thanks, i realize how close i was, next time around I should stop confusing myself when translating the problem into equations as the math itself is simple. when pressured, the translation part can be horrible for me.
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by getso » Tue Dec 22, 2009 11:27 pm
Hello guys,

I'm reopening this thread.

My approach is lets take time taken by Pat=X
Therefore kate=X/2 and Mark=3X

X+X/2+3x=162.

and X=27

So I get the 36 as answer.

I'm not able to understand what is wrong in my approach.

Could anybody help me here.

Thanks,
Shobha
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by papgust » Tue Dec 22, 2009 11:35 pm
getso wrote: X+X/2+3x=162.

and X=27

So I get the 36 as answer.
Your method is right but your calculation is wrong.

x + x/2 + 3x = 162

2*x + x + 2*3x = 2*162

9x = 324

x = 36

So, Mark is charged 3*36 = 108
Kate is charged 36/2 = 18

Mark - Kate = 108 - 18 = 90 (D)
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by linkinpark » Tue Dec 22, 2009 11:44 pm
x + x/2 + 3x = 162

i.e. 4x + x/2 = 162
==> 9x/2 = 162
9x = 324 i.e. x = 36

x = p's time which is twice of K so k = 18 and M = 3x so 3*36=108
and M-K= 108-18 = 90.

HTH
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by getso » Wed Dec 23, 2009 12:00 am
Ya that was a calculation mistake....

@papagust: Thanks for pointing it out.

Regards,
Shobha
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by LalaB » Thu Mar 15, 2012 9:40 am
p/a=2/1
p/m=1/3


p:a:m
2:1:-
2:-:6

p:a:m
2:1:6

2x+x+6x=162
x=18

(6-1)*18=90
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