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

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The R students in a class agree to contribute equally to buy their  [#permalink]

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New post 18 Nov 2015, 00:31
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Question Stats:

69% (01:25) correct 31% (01:08) wrong based on 86 sessions

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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))

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Re: The R students in a class agree to contribute equally to buy their  [#permalink]

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New post 18 Nov 2015, 00:39
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[(1/(R-x) - (1/R)]
=y[x/R(R-x)]

Answer D
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Re: The R students in a class agree to contribute equally to buy their  [#permalink]

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New post 29 Nov 2015, 12:04
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:

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Re: The R students in a class agree to contribute equally to buy their  [#permalink]

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New post 18 Jun 2016, 21:12
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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New post 19 Jun 2016, 07:12
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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