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# Initially, the men and women in a room were in the ratio of 5:7. Six

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Math Expert
Joined: 02 Sep 2009
Posts: 46191
Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 04:09
00:00

Difficulty:

35% (medium)

Question Stats:

64% (01:19) correct 36% (01:16) wrong based on 185 sessions

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Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many women are currently in the room?

A. 12
B. 14
C. 15
D. 24
E. 36

Kudos for a correct solution.

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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 04:44
Going by options,
Currently there are 14 men. (2 men were added)
Therefore earlier there were 12 Men.

Ratio of Men: Women = 4:5
If Men = 12, Women = 15.

So out of original 15 women, 3 have left.
So Women remaining = 12
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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 04:48
Still wondering, why does that piece of info exist :
Then, the number of women doubled. ??
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Joined: 26 Dec 2011
Posts: 116
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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 05:32
1
Bunuel wrote:
Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled.
Now there are 14 men in the room. How many women are currently in the room?

A. 12
B. 14
C. 15
D. 24
E. 36

Kudos for a correct solution.

Solution -
Initially, 4X men and 5X women in the room ------> 4X:5X
After 2M entered and 3W left the room, new ratio-->(4X+2):(5X-3)

4X+2 = 14 ---> X=3.
After 3 women left the room -> 5X-3 = 5*3 - 3 = 12 women in the room.

After that, the number of women doubled = 12*2 = 24.
ANS D
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Math Expert
Joined: 02 Aug 2009
Posts: 5893
Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 06:07
NickHalden wrote:
Still wondering, why does that piece of info exist :
Then, the number of women doubled. ??

hi NickHalden,
the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..

let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number=5*3-3=12, then doubled=24..
ans D
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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 06:59
Number of men, initially: $$4x$$
$$4x + 2 =14$$
$$x=3$$

Number of women, initially: $$5x$$
$$5(3)-3 = 12$$
$$12 * 2 = 24$$

D. 24

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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 10:01
Let x be common multiplier

Initially, Total no of men in room = 4x and Total No of women in room = 5x

4x + 2 = 14
or,x= 3

So, currently no of women in the room = 5(3) - 3
= 12

Ans A
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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 11:20
guys sorry new to the forum, could anyone help me out in this question?

"X will get 10 more apples for $5 if its price decreases by 20%. How many apples will x get for$5 at the new price?"
A)40
B)50
C)15
D)10
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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 11:29
Bhuvaneshfly wrote:
guys sorry new to the forum, could anyone help me out in this question?

"X will get 10 more apples for $5 if its price decreases by 20%. How many apples will x get for$5 at the new price?"
A)40
B)50
C)15
D)10

For your question, assume that the original price per apple is A $/apple. In 5$ you can thus get = 5/A apples
When you decrease the price by 20%, per apple price becomes 0.8A. IN 5$now you can get = 5/0.8A apples As per the question, 5/0.8A - 5/A = 10, giving A = 0.125 or 1/8$/apple

The new price becomes = 0.8*0.125 = 0.1

Thus, number of apples = 5/0.1 = 50, B is the answer.
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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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03 Jul 2015, 11:56
Bunuel wrote:
Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled.
Now there are 14 men in the room. How many women are currently in the room?

A. 12
B. 14
C. 15
D. 24
E. 36

Kudos for a correct solution.

Men / women = 4 / 5

i.e. Initially the Number of People was a Multiple of 9 i.e. $$9x$$

2 men entered and 3 women left i.e. in total 1 person less in the room so the total number of people in the room must be of the form $$9x-1$$ before doubling the Number of Women

If Men = 14

A. 12 i.e. Total people in room before doubling the women = 14+(12/2) = 20 which is NOT of the form $$9x-1$$ i.e. NOT a Possible Answer
B. 14 i.e. Total people in room before doubling the women = 14+(14/2) = 21 which is NOT of the form $$9x-1$$ i.e. NOT a Possible Answer
C. 15 i.e. Total people in room before doubling the women = 14+(15/2) = 21.5 NOT of the form $$9x-1$$ i.e. NOT a Possible Answer
D. 24 i.e. Total people in room before doubling the women = 14+(24/2) = 26 which is of the form $$9x-1$$ i.e. a Possible Answer
E. 36 i.e. Total people in room before doubling the women = 14+(36/2) = 32 which is NOT of the form $$9x-1$$ i.e. NOT a Possible Answer

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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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04 Jul 2015, 11:28
D is correct
4X men and 5X women in the room ------> 4X:5X
After 2M entered and 3W left the room, new ratio-->(4X+2):(5X-3)

4X+2 = 14 ---> X=3.
After 3 women left the room -> 5X-3 = 5*3 - 3 = 12 women in the room.

After that, the number of women doubled = 12*2 = 24.
Math Expert
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Posts: 46191
Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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06 Jul 2015, 06:40
Bunuel wrote:
Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many women are currently in the room?

A. 12
B. 14
C. 15
D. 24
E. 36

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Use the Unknown Multiplier to solve this problem. Initially, there are 4x men in the room and 5x women. Then, follow the series of entrances and exits one-by-one to establish the number of men and women who are currently in the room, in terms of x.

Men: 4x + 2 = 14 --> x = 3.

The unknown multiplier is 3. Plug 3 in for x:
Women: 2(5x - 3) = ?
2[5(3) - 3] =2(12) = 24

Attachment:

2015-07-06_1737.png [ 7.07 KiB | Viewed 3521 times ]

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Re: Initially, the men and women in a room were in the ratio of 5:7. Six [#permalink]

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13 May 2017, 09:20
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Re: Initially, the men and women in a room were in the ratio of 5:7. Six   [#permalink] 13 May 2017, 09:20
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