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 [ 28.71 KiB | Viewed 428 times ]
This language is misleading. We have:

A church prayer and

THE prayerThe 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: \(\frac{3}{5}*50\) =

30Female, 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:

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

6Males: \(\frac{3}{5}\) of all male members (30) attended a prayer: \((\frac{3}{5}*30)=18\)

Males who DID attend =

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

12• TOTALS - who DID and DID NOT attend a prayer

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

32Total 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