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A room contains 160 people, 15 percent of whom are women. A group of

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rsampson
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A room contains 160 people, 15 percent of whom are women. A group of [#permalink] A room contains 160 people, 15 percent of whom are women. A group of   Updated on: 28 Sep 2020, 01:01
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A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?

A. 10
B. 20
C. 40
D. 60
E. 80

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I know the official answer explanation and it makes sense when I read it. But, I am trying to get better at seeing how to quickly setup a problem like this in order to solve it in less than 2 minutes.

.15*160 = 24, the number of women in the room.
I guess the key is to set x = group of people that left the room.
Then, .3x = the number of women in this group.
Next, the people remaining in the room is (160-x), .1 of which are women.
So, 24-.3x = .1(160-x)

Maybe what I should do is take one sentence at a time in the question stem and translate into Algebra, like I did above. Then, see how I can piece it together. Sort of like I did above.

Like I said, I am a little fuzzy about how to think about this. I would appreciate any help. Thanks!

Thanks!
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C

Originally posted by rsampson on 09 May 2012, 20:06.
Last edited by Bunuel on 28 Sep 2020, 01:01, edited 2 times in total.
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Bunuel
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Re: A room contains 160 people, 15 percent of whom are women. A group of [#permalink] A room contains 160 people, 15 percent of whom are women. A group of   10 May 2012, 02:11
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rsampson wrote:
What is your thought process when you begin to translate a problem like this into Algebra? Is it just a matter of practicing problems in order to get better at it? Here it is:

A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?

A. 10
B. 20
C. 40
D. 60
E. 80

I know the official answer explanation and it makes sense when I read it. But, I am trying to get better at seeing how to quickly setup a problem like this in order to solve it in less than 2 minutes.

.15*160 = 24, the number of women in the room.
I guess the key is to set x = group of people that left the room.
Then, .3x = the number of women in this group.
Next, the people remaining in the room is (160-x), .1 of which are women.
So, 24-.3x = .1(160-x)

Maybe what I should do is take one sentence at a time in the question stem and translate into Algebra, like I did above. Then, see how I can piece it together. Sort of like I did above.

Like I said, I am a little fuzzy about how to think about this. I would appreciate any help. Thanks!

Thanks!


You've done everything right.

A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
A. 10
B. 20
C. 40
D. 60
E. 80

Say group of x people left the room.

# of women in the room was 0.15*160=24;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(160-x);

So, 24-0.3x= 0.1(160-x) --> x=40.

Answer: C.

Hope it helps.

P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.
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rsampson
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Re: A room contains 160 people, 15 percent of whom are women. A group of [#permalink] A room contains 160 people, 15 percent of whom are women. A group of   10 May 2012, 19:55
Bunuel,

Thanks for your reply, I really appreciate it! Yes, your explanation sharpened how I should be thinking about this type of problem. Thank you!

I've heard really good things about you in this forum. Any thoughts you may have on my studies I would really appreciate. My last 3 real GMAT tests I took I scored 620, 640, and 630(q40/v36) on last one that I took. My weak area is in quant, specifically Algebra. I am currently studying the MGMAT Equalities, Inequalities, & VICs book. I've been receiving some absolutely excellent advice from other forum participants. But, any general advice you may have I would appreciate. Thank you.

Quote:
P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.


Sorry about that, you have my apologies. I will do that from now on. Thanks again!
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Manick9
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Re: A room contains 160 people, 15 percent of whom are women. A group of [#permalink] A room contains 160 people, 15 percent of whom are women. A group of   22 Dec 2017, 03:16
At first there are 0.15 * 160 = 24 women and 160 - 24 = 136 men.

24 - 0.3x = 0.1y
136 - 0.7x = 0.9y
where x is the no. of ppl who left the room and y = no. of ppl remaining in the room

solve this simultaneous eqn you will get x = 40
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A room contains 160 people, 15 percent of whom are women. A group of [#permalink] A room contains 160 people, 15 percent of whom are women. A group of   24 Dec 2018, 04:05
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rsampson wrote:
What is your thought process when you begin to translate a problem like this into Algebra? Is it just a matter of practicing problems in order to get better at it? Here it is:

A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?

A. 10
B. 20
C. 40
D. 60
E. 80

I know the official answer explanation and it makes sense when I read it. But, I am trying to get better at seeing how to quickly setup a problem like this in order to solve it in less than 2 minutes.

.15*160 = 24, the number of women in the room.
I guess the key is to set x = group of people that left the room.
Then, .3x = the number of women in this group.
Next, the people remaining in the room is (160-x), .1 of which are women.
So, 24-.3x = .1(160-x)

Maybe what I should do is take one sentence at a time in the question stem and translate into Algebra, like I did above. Then, see how I can piece it together. Sort of like I did above.

Like I said, I am a little fuzzy about how to think about this. I would appreciate any help. Thanks!

Thanks!



Think of weighted average whenever you mix two groups together or whenever you separate a group into two different groups.

In this question, a group fo 160 people split into two groups - one group that leaves (L) and one group that is remaining (R).

wL/wR = (10 - 15)/(15 - 30) = 1/3

So 1/4th of the total people left i.e. (1/4)*160 = 40 people left.
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Re: A room contains 160 people, 15 percent of whom are women. A group of [#permalink] A room contains 160 people, 15 percent of whom are women. A group of   24 Aug 2023, 04:35
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Re: A room contains 160 people, 15 percent of whom are women. A group of [#permalink]
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