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Interesting GMATFix Problem-44

by arora007 » Mon Oct 04, 2010 4:20 am
Working toegether, Rihanna and Jen can build 66.66% more toys in 8 hours than Patrick and Jen can build in 6 hours of working together. How many toys can Jen build alone in 1 hour?
1)In 1 hour, Rihanna can build two more toys than Patrick can
2)Rihanna can build three more toys in 4 hours than Patrick can build in 5 hours.
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by limestone » Tue Oct 05, 2010 12:49 am
Let's call:
R for the no. of toys that Rihanna can build per hour.
J: Jen
P: Patrick

Given information is:
Rihanna + Jen work for 8 hours : 8*(R+J)
Patrick and Jen work for 6 hours: 6*(P+J)

8*(R+J) = 166% * 6 * (P+J) (Note 166% = 5/3; 6*166% = 10)
8R+8J = 10P + 10J
2J =8R - 10P

1. R- P =2 or R = P+2
Plug R = P+2 into 2J =8R - 10P:
2J = 8P + 16 - 10P = 16- 2P => insuff, lack of value of P.

2. 4*R - 5*P = 3 or R = (3 + 5*P)/4
Insuff for them same reason as 1

1&2. From
R = P+2
and
R = (3 + 5*P)/4

We can calculate the value of R and P, then plug in those value into 2J =8R - 10P, we'll get J. Then suff.
Hence C.
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by mj78ind » Tue Oct 05, 2010 4:40 am
arora007 wrote:Working toegether, Rihanna and Jen can build 66.66% more toys in 8 hours than Patrick and Jen can build in 6 hours of working together. How many toys can Jen build alone in 1 hour?
1)In 1 hour, Rihanna can build two more toys than Patrick can
2)Rihanna can build three more toys in 4 hours than Patrick can build in 5 hours.
Excellent question indeed!

Say p+j make 48 toys in 6 hours, thus they make 8 toys in an hour or
p+j = 8

r+j make 5/3 toys in 8 hours 5/3*48 = 80 or 10 toys per hour
r+j = 10

We have 3 unknowns and two equations

1 - Gives us one more equation. hence sufficient
2 - same as above

Hence pick D

OA please?
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by reply2spg » Tue Oct 05, 2010 6:10 am
I didn't solve this. However, from the question we get 2 equations in which Jen is common.

If we know value of Rihanna and Pat or the relationship between Rihanna and Pat we can find out the answer for Jen.

1. We know Rihanna and Pat, we can get Jen's value
2. same as 1.

Answer must be D.
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by arora007 » Tue Oct 05, 2010 6:42 am
Guys... OA is B. have a look at the solution.


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by GMATMadeEasy » Tue Oct 05, 2010 8:18 am
Solution from mj78ind will work , only thing is condition 1 will give the same equation as gives the question stem.

Issue is , by intution if you look at choices 1 and 2, they look same, so resoing says D or E in first place. Where the trick lies in this question ?
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by limestone » Tue Oct 05, 2010 8:59 am
Yup, the answer should be B.

I wanna update my previous post.
Given information is:
Rihanna + Jen work for 8 hours : 8*(R+J)
Patrick and Jen work for 6 hours: 6*(P+J)

8*(R+J) = 166% * 6 * (P+J) (Note 166% = 5/3; 6*166% = 10)
8R+8J = 10P + 10J
2J =8R - 10P

1. R- P =2 or R = P+2
Plug R = P+2 into 2J =8R - 10P:
2J = 8P + 16 - 10P = 16- 2P => insuff, lack of value of P.

2. 4*R - 5*P = 3 or R = (3 + 5*P)/4
Insuff for them same reason as 1

1&2. From
R = P+2
and
R = (3 + 5*P)/4
I didn't realize that 2J = 8R - 10P = 2* (4R-5P)
And in (2), we got 4R-5P =3, then 2 is suff.

Pick B.
Thanks arora007 for such a good question.
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by diebeatsthegmat » Tue Oct 05, 2010 8:52 pm
arora007 wrote:Guys... OA is B. have a look at the solution.


Image
very very nice...
where did you download the source?
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