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There were P people in a room when a meeting started. Q people left th

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Bunuel
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There were P people in a room when a meeting started. Q people left th [#permalink] New post   16 Oct 2017, 01:41
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There were P people in a room when a meeting started. Q people left the room during the first hour, while R people entered the room during the same time. What expression gives the number of people in the room after the first hour as a percentage of the number of people in the room who have been there since the meeting started?


(A) \(\frac{(P - Q)}{(P - Q + R)}\)

(B) \(100 * \frac{(P - Q + R)}{(P - Q)}\)

(C) \(\frac{(P + R)}{(P - Q)}\)

(D) \(100 * \frac{(P - Q)}{(P - Q + R)}\)

(E) \(100 * \frac{(P + R)}{(P - Q)}\)
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Re: There were P people in a room when a meeting started. Q people left th [#permalink] New post   16 Oct 2017, 04:32
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Bunuel wrote:
There were P people in a room when a meeting started. Q people left the room during the first hour, while R people entered the room during the same time. What expression gives the number of people in the room after the first hour as a percentage of the number of people in the room who have been there since the meeting started?


(A) \(\frac{(P - Q)}{(P - Q + R)}\)

(B) \(100 * \frac{(P - Q + R)}{(P - Q)}\)

(C) \(\frac{(P + R)}{(P - Q)}\)

(D) \(100 * \frac{(P - Q)}{(P - Q + R)}\)

(E) \(100 * \frac{(P + R)}{(P - Q)}\)



Following points should be noted:-
1) Looking for % means multiplication by 100
2) Numerator is number of people after 1 hour - Q move out and R move in so numerator is P-Q+R
3) Denominator is who remain from beginning, so P-Q

Ans B
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Re: There were P people in a room when a meeting started. Q people left th [#permalink] New post   17 Oct 2017, 11:48
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Bunuel wrote:
There were P people in a room when a meeting started. Q people left the room during the first hour, while R people entered the room during the same time. What expression gives the number of people in the room after the first hour as a percentage of the number of people in the room who have been there since the meeting started?


(A) \(\frac{(P - Q)}{(P - Q + R)}\)

(B) \(100 * \frac{(P - Q + R)}{(P - Q)}\)

(C) \(\frac{(P + R)}{(P - Q)}\)

(D) \(100 * \frac{(P - Q)}{(P - Q + R)}\)

(E) \(100 * \frac{(P + R)}{(P - Q)}\)


The number of people who have been in the room since the meeting started is P - Q, and the number of people who are there after the first hour is P - Q + R; thus, we have:

(P - Q + R)/(P - Q) x 100

Answer: B
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Re: There were P people in a room when a meeting started. Q people left th [#permalink] New post   22 Oct 2017, 15:25
-P # of people in the room at the very start
-Then q leave, (P-Q)
-At the same time R people enter (P-Q+R), which is our numerator.
-Denominator is # of people in the room since the meeting began which is P-Q
-So the number is [P-Q+R][/P-Q]*100
-B
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Re: There were P people in a room when a meeting started. Q people left th [#permalink] New post   22 Oct 2017, 22:52
The most important point should be noted in this question is that we are looking for a percentage. => eliminate A, C
- The number of people who have been in the room since the meeting started = P - Q
- The number of people in the room after the first hour = P - Q + R

=> we have: 100* (P-Q+R)/ (P - Q) => Answer B
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Re: There were P people in a room when a meeting started. Q people left th [#permalink] New post   22 Oct 2017, 23:12
IMO Option B.
Number of people who were for the whole meeting. P-Q
Total number of people after the first hour= P-Q+R
the percentage= ( P-Q+R/P-Q)*100
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Re: There were P people in a room when a meeting started. Q people left th [#permalink]
22 Oct 2017, 23:12
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