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At a church prayer, (3/5)th of the members were males and (3/5)th of t

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At a church prayer, (3/5)th of the members were males and (3/5)th of t  [#permalink]

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New post 25 Sep 2018, 05:09
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Question Stats:

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At a church prayer, (3/5)th of the members were males and (3/5)th of the male members attended the prayer. If (7/10)th of the female members attended the prayer, what fraction of the members at the prayer who did not attend the prayer are males?

(A) 1/4

(B) 3/7

(C) 2/3

(D) 9/10

(E) 6/19

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At a church prayer, (3/5)th of the members were males and (3/5)th of t  [#permalink]

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New post 25 Sep 2018, 20:46
Bunuel wrote:
At a church prayer, (3/5)th of the members were males and (3/5)th of the male members attended the prayer. If (7/10)th of the female members attended the prayer, what fraction of the members at the prayer who did not attend the prayer are males?

(A) 1/4

(B) 3/7

(C) 2/3

(D) 9/10

(E) 6/19

Attachment:
prayermatrix.jpg
prayermatrix.jpg [ 28.71 KiB | Viewed 635 times ]

This language is misleading. We have:
A church prayer and THE prayer
The first is a large category. The second is a small category and a subset of the first.
The categories are not similar. Time to rewrite:

Men and women are members of and in a CHURCH (= "A church prayer")
Some men and women ATTEND a PRAYER in a separate room (= "THE prayer")
We are interested in the group who goes to the separate room.

A double matrix is quick. Assign values.
The numbers in the matrix in the diagram were entered in the sequence below.

Use LCM of 5 and 10. Let total church members = 50

• Number of male vs. number of female CHURCH members (who may or may not attend a prayer)

Male, \(\frac{3}{5}\) of all members: \(\frac{3}{5}*50\) = 30

Female, must be \(\frac{2}{5}\) of all: \(\frac{2}{5}*50\) = 20

• Number of men and women in the church who DID and DID NOT attend a prayer

Females: \(\frac{7}{10}\) of all female members (20) DID attend a prayer: \((\frac{7}{10}*20)=14\)
Females who DID attend: 14

Females who DID NOT attend: (20 - 14) = 6

Males: \(\frac{3}{5}\) of all male members (30) attended a prayer: \((\frac{3}{5}*30)=18\)
Males who DID attend =18

Males who DID NOT attend: (30 - 18) = 12

• TOTALS - who DID and DID NOT attend a prayer

Total WHO DID attend a prayer = (18 + 14) = 32

Total who DID NOT attend a prayer: (50 - 32) = 18

• What fraction of the members at the prayer CHURCH, who did not attend the A prayer, are males?
Total who DID NOT attend: 18
Number of that group who were male: 12
Fraction = \(\frac{12}{18}=\frac{2}{3}\)

Answer C
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Re: At a church prayer, (3/5)th of the members were males and (3/5)th of t  [#permalink]

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New post 26 Sep 2018, 02:47
Bunuel wrote:
At a church prayer, (3/5)th of the members were males and (3/5)th of the male members attended the prayer. If (7/10)th of the female members attended the prayer, what fraction of the members at the prayer who did not attend the prayer are males?

(A) 1/4

(B) 3/7

(C) 2/3

(D) 9/10

(E) 6/19


Let the total number of members be x
male members = 3x/5
female members = 2x/5
male members who attended = 9x/25
female members who attended = 14x/50
total who did not attend the prayer = x-(9x/25 + 14x/50) = x -(32x/50) = 18x/50
males who did not attend the prayer = 3x/5 - 9x/25 = (15x-9x)25 = 6x/25
ratio = 6x/25 * 50/18x = 2/3
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Re: At a church prayer, (3/5)th of the members were males and (3/5)th of t   [#permalink] 26 Sep 2018, 02:47
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