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

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Math Expert
Joined: 02 Sep 2009
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There were P people in a room when a meeting started. Q people left th  [#permalink]

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16 Oct 2017, 00:41
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Difficulty:

25% (medium)

Question Stats:

87% (01:56) correct 13% (02:36) wrong based on 43 sessions

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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]

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16 Oct 2017, 03:32
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]

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17 Oct 2017, 10:48
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

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Re: There were P people in a room when a meeting started. Q people left th  [#permalink]

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22 Oct 2017, 14:25
-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]

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22 Oct 2017, 21:52
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]

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22 Oct 2017, 22:12
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 &nbs [#permalink] 22 Oct 2017, 22:12
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