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Re: The R students in a class agree to contribute equally to buy their [#permalink]
The question exploits those who can be in a rush of time and do not read the Q properly.
The question is asking how much more did the students contribute if only R-x were left to contribute and not what they actually contributed.
Choice B is set as a trap answer which is y/R-x :)

Coming back to the question:- how much more did the students have to pay
y/(R-x)- y/R
if we simplify this we get choice D, which is the correct answer.
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Re: The R students in a class agree to contribute equally to buy their [#permalink]
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Bunuel wrote:
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))


Quote:
R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars

Contribution of each student is \(\frac{y}{R}\)
Quote:
If x of the students later fail to contribute their share,

Contribution of each student becomes \(\frac{y}{(R-x)}\)
Quote:
additional number of dollars that each of the remaining students must contribute in order to pay for the present

=> \(\frac{y}{(R-x)}\) \(-\) \(\frac{y}{R}\)

=> \(\frac{(yR - yR + yx )}{R(R - x )}\)

=> \(\frac{( yx )}{R(R - x )}\)

Hence answer will be (D)
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Re: The R students in a class agree to contribute equally to buy their [#permalink]
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Expert Reply
Bunuel wrote:
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))

Solution:

The cost per student if all R students contribute is y/R dollars. If x students do not contribute, then there are (R - x) students remaining who will contribute. Thus, the cost per student if x students fail to contribute while the remaining students contribute is y/(R - x) dollars. Therefore, each of the remaining students has to contribute

y/(R - x) - y/R = yR/[R(R - x)] - y(R - x)/[R(R - x)] = (yR - yR + yx)/[R(R - x)] = yx/[R(R - x)]

more dollars.

Answer: D
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Re: The R students in a class agree to contribute equally to buy their [#permalink]
Total cost is Y,
Cost per person is Y/R
No of people that did not pay (or amount that should be additional) = X * Y/R

above amount should be shared between R-X people hence >>>>>>> (X*Y/R) / (R-X) = XY/R(R-X)
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Re: The R students in a class agree to contribute equally to buy their [#permalink]
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