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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## 500 PS section2 #20 ##### This topic has 2 expert replies and 3 member replies ## 500 PS section2 #20 Hi, I thought the answer is B) but the answer on Wiki says D).... Can you explain?? The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If x of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present? (A) y/R (B) y/R-x (C) xy/R-x (D) xy/R(R-x) (E) y/R(R-x) Master | Next Rank: 500 Posts Joined 26 Mar 2007 Posted: 174 messages Upvotes: 1 Pick values or solve algebraically: R=12 Y=120 X=2 Previously each of the students had to pay Y/R = 120/12 =$10

After X=2 dropped out, each of the remaining students had to pay Y/(R-X) = 120/10 = $12 And the additional number of dollars that each had to pay was Y/(R-X) - Y/R = 12 - 10 =$2

The only answer that gives 2 is option D

Also if u solve the underlined equation you would get option D

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I have tried my best to simplify this one for you...Hope this helps...

Total students - R

Cost of Gift - y dollars

Therefore each student has to pay y/R in order to buy their teacher a gift

Now "x" students back out. The shortfall in contribution = y/R * x = yx/R

Now this addtional amount of (yx/R) has to be contributed by the remainder of the students i.e. (R-x students)

So the addtional amount to be contributed by the remaining students = (yx/R) / (R-x)

= (yx) / (R) (R-x)

Hence Choice D

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R------>Y
R-X------> ?
? R = Y (R-X)
?=$$\frac{Y(R-X)}{R}$$ (this is the amount paid)
(Y)-$$\frac{Y(R-X)}{R}$$ (will be amount and not paid)
=$$\frac{RY\ -\ \left[Y\left(R-X\right)\right]}{R}$$
Additional number of dollars each of the remaining students must contribute = amount not paid / (R-X)
=$$\frac{RY\ -\ \left[Y\left(R-X\right)\right]}{R}$$ / (R-X)
=$$\frac{XY}{R\left(R-X\right)}$$ . Therefore, option D is the answer

### GMAT/MBA Expert

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Hello dunkin77.

At the begining each student should pay y/R dollars.

When x students failed contributing their share, the rest of the students (R-x) had to pay their part, it is, x*(y/R) dollars.

Now, each one of the remaining students had to pay $$\frac{x\cdot\left(\frac{y}{R}\right)}{R-x}$$ dollars more. It is the same as $$\frac{x\cdot y}{R\left(R-x\right)}.$$

So, the correct answer is D.

I'm available if you'd like any follow up.

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### GMAT/MBA Expert

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Hi All,

While this question is wordy, and will require some note-taking, it can be solved by TESTing VALUES.

Let's TEST...
R = 5 students
Y = 50 dollars
X = 3 fail to pay

So the 'story' is that 5 students agree to pay an equal amount for a $50 present (that's$10 per student). We're told that 3 of them fail to pay (3 students x $10/each =$30 unpaid). Thus, the remaining 2 students have to pay an extra $30/2 =$15 each for the present.

Thus, we're looking for an answer that equals 15 when R=5, Y=50 and X=3

While the answer choices look complex, there are some patterns involved: several of the calculations repeat (for example, R-X appears in 4 of the answers, so you do NOT need to calculate it 4 separate times). Since Y = 50, any answer with Y alone in the numerator can be skipped over (there is no integer that will make 50/integer = 15). That leaves two answers to TEST and just a bit of arithmetic.

GMAT assassins aren't born, they're made
Rich

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