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# The ratio of men to women in a certain club with 150 members is m : w

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Math Expert
Joined: 02 Sep 2009
Posts: 44630
The ratio of men to women in a certain club with 150 members is m : w [#permalink]

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01 Jan 2018, 01:39
00:00

Difficulty:

35% (medium)

Question Stats:

78% (01:29) correct 22% (02:56) wrong based on 63 sessions

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The ratio of men to women in a certain club with 150 members is m : w and the ratio of officers to non-officers is o : n. There are 75 men in the club and there are 16 officers in the club. If two-fifteenths of female members are officers, how many male non-officers are in the club?

A. 6
B. 10
C. 65
D. 69
E. It cannot be determined from information given.
[Reveal] Spoiler: OA

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Re: The ratio of men to women in a certain club with 150 members is m : w [#permalink]

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01 Jan 2018, 03:04
Bunuel wrote:
The ratio of men to women in a certain club with 150 members is m : w and the ratio of officers to non-officers is o : n. There are 75 men in the club and there are 16 officers in the club. If two-fifteenths of female members are officers, how many male non-officers are in the club?

A. 6
B. 10
C. 65
D. 69
E. It cannot be determined from information given.

As one of our solutions is 'it cannot be determined' we cannot use the answers in this question.
Therefore, we'll go for a direct calculation, a Precise approach.

Let's write down what we know, going from the start of the question:
Men + Women = 150
Men = 75 --> Women = 150 - 75 = 75
Women officers = 2/15 * Women = 2/15 * 75 = 10
male officers = 16 - 10 = 6
male non-officers = 75 - 6 = 69.

Bunuel are we assuming that the club contains only men and women (and not, say, children)?
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Re: The ratio of men to women in a certain club with 150 members is m : w [#permalink]

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01 Jan 2018, 03:24
Bunuel wrote:
The ratio of men to women in a certain club with 150 members is m : w and the ratio of officers to non-officers is o : n. There are 75 men in the club and there are 16 officers in the club. If two-fifteenths of female members are officers, how many male non-officers are in the club?

A. 6
B. 10
C. 65
D. 69
E. It cannot be determined from information given.

Total members 150
Men 75
So women = 150-75 = 75

16 members are officers
2/15 of women are officers
So women officers = 75 * 2/15 = 10
So men officers = 16-10 = 6
So men who are not officers = 75-6 = 69

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Re: The ratio of men to women in a certain club with 150 members is m : w [#permalink]

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01 Jan 2018, 08:47
1
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Bunuel wrote:
The ratio of men to women in a certain club with 150 members is m : w and the ratio of officers to non-officers is o : n. There are 75 men in the club and there are 16 officers in the club. If two-fifteenths of female members are officers, how many male non-officers are in the club?

A. 6
B. 10
C. 65
D. 69
E. It cannot be determined from information given.

Breakdown and solve -

Quote:
The ratio of men to women in a certain club with 150 members is m : w.........

There are 75 men in the club.....

Men = Women = 75

Quote:
there are 16 officers in the club...

Officers = 16 & Non Officers = 134

Quote:
If two-fifteenths of female members are officers....

Female Officers = $$\frac{2}{15}*75$$ => 10
Male Officers = 6

Finally we have -

Officers = 16 ( Female Officers - 10 , Male Officers - 6) & Non Officers = 134 (Female Non Officer - 65 ; Male Non Officer = 69 )

So, Total number of male non-officers in the club is 69 , Answer is (D)
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The ratio of men to women in a certain club with 150 members is m : w [#permalink]

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01 Jan 2018, 09:51
Bunuel wrote:
The ratio of men to women in a certain club with 150 members is m : w and the ratio of officers to non-officers is o : n. There are 75 men in the club and there are 16 officers in the club. If two-fifteenths of female members are officers, how many male non-officers are in the club?

A. 6
B. 10
C. 65
D. 69
E. It cannot be determined from information given.

Total members = 150

Total Men = 75 (Given); Total Women = 150 - 75 (Total Men) = 75

Officers = 16 (Given) ; Non - officers = 150 - 16 (Officers) = 134

Female Officers = 2/15*75 = 10

Male Officers = 16 - 10 (Female Officers) = 6

Male Non Officers = Total Men - Male Officers = 75 - 6 = 69

(D)
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Re: The ratio of men to women in a certain club with 150 members is m : w [#permalink]

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01 Jan 2018, 21:29
Men -75
Women-75
Officers -16
Non officers-134
Female officers- 10
Male officers- 16- 10=6
Non officers male- 75-6=69
D

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Re: The ratio of men to women in a certain club with 150 members is m : w   [#permalink] 01 Jan 2018, 21:29
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