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))
OA D
Source: Princeton Review
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The R students in a class agree to contribute equally to buy
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BTGmoderatorDC
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Let y=$10 and R=10 students, with the result that the original share per student = ($10)/(10 students) = $1.BTGmoderatorDC 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))
Let x=9, implying that the number of students decreases by 9 to 1.
New share per student = ($10)/(1 student) = $10.
Increase in share per student = 10-1 = $9.
The correct answer must yield $9 when y=10, R=10 and x=9.
Only D works:
xy/(R(R-x)) = (9*10)/(10(10-9)) = 90/10 = 9.
The correct answer is D.
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The original amount of money paid is y/RBTGmoderatorDC 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))
OA D
Source: Princeton Review
The new amount of money paid is y/(R - x)
The difference is:
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)]
Answer: D
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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.
Final Answer: D
GMAT assassins aren't born, they're made
Rich
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
