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# How many more men than women are in the room?

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Math Expert
Joined: 02 Sep 2009
Posts: 48077
How many more men than women are in the room?  [#permalink]

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16 May 2018, 06:47
00:00

Difficulty:

15% (low)

Question Stats:

86% (00:40) correct 14% (00:54) wrong based on 44 sessions

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How many more men than women are in the room?

(1) There is a total of 20 women and men in the room.
(2) The number of men in the room equals the square of the number of women in the room.

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Intern
Joined: 16 Aug 2015
Posts: 18
Location: India
Re: How many more men than women are in the room?  [#permalink]

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16 May 2018, 07:34
Let number of men = m and women = w

(1) m+n=20; not sufficient
(2) m = n^2; notsufficient

Together we arrive at the equation => n^2 + n =20; can be solved to give n and consequently m

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1900
Re: How many more men than women are in the room?  [#permalink]

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16 May 2018, 08:28

Solution

To find:
• How many more men are there in the room, compared to women

Analysing Statement 1
• As per the information given in Statement 1, there are total 20 people in the room, taking all men and women
o But from this statement we cannot find out the exact number of men and women

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information given in Statement 2, the number of men in the room equals the square of the number of women in the room
o If we assume number of women to be x, then number of men will be $$x^2$$
o But from this statement we cannot find out the difference between the number of men and number of women

Hence, statement 1 is not sufficient to answer

Combining Both Statements
• Combining the information from both the statements, we can say
o $$x^2$$ + x = 20
Or, (x + 5) (x – 4) = 0
As x cannot be negative, x = 4
• Therefore, we can find out the exact number of men and women, and subsequently the difference between them

Hence, the correct answer is option C.

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Re: How many more men than women are in the room?  [#permalink]

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16 May 2018, 10:21
Need both statements to solve. 1) any value of m and n can add to 20 so NS. 2) Could be any number so NS. Combined we only receive one set.
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Re: How many more men than women are in the room? &nbs [#permalink] 16 May 2018, 10:21
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