The R students in a class agree to contribute equally to buy their

Question

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))

(A) y/R
(B) y/(R-x)
(C) xy/(R-x)
(D) xy/(R(R-x))
(E) y/(R(R-x))

Skywalker18 · Accepted Answer

Initially,
contribution per student = y/R

Later,since x students failed to contribute their share
Contribution per student = y/(R-x)

Additional dollar amount per student = y/(R-x) - y/R
 =y 
 =y 
 
 Answer D

EMPOWERgmatRichC · Answer

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.

Final Answer:  D

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

ajdse22 · Answer

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.

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.

Abhishek009 · Answer

Contribution of each student is  \frac{y}{R} 
 
Contribution of each student becomes  \frac{y}{(R-x)} 
 
=>  \frac{y}{(R-x)}   -   \frac{y}{R}

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

=>  \frac{( yx )}{R(R - x )} 
 
Hence answer will be (D)

ScottTargetTestPrep · Answer

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

more dollars.

Answer: D

Ashok.Battula · Answer

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)

bumpbot · Answer

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