Overlapping DS

[yellowho]

In Monroe School, 30 members of the faculty coach boysÂ’or girlsÂ’
sports or both. If 18 of these members of the faculty do not coach
boysÂ’sports, how many of these members of the faculty coach
both boysÂ’and girlsÂ’sports?

(1) The 30 members of the faculty who coach boysÂ’or girlsÂ’
sports or both represent 60% of the total faculty
members.

(2) 10 of these members of the faculty do not coach girlsÂ’
sports.


Why is D not correct?

[Anurag@Gurome]

In Monroe School, 30 members of the faculty coach boysÂ’ or girlsÂ’ sports or both. If 18 of these members of the faculty do not coach boysÂ’ sports, how many of these members of the faculty coach both boys Â’and girls Â’sports?

(1) The 30 members of the faculty who coach boysÂ’or girlsÂ’ sports or both represent 60% of the total faculty members.
(2) 10 of these members of the faculty do not coach girlsÂ’ sports.

Note that "total faculty members" and "30 members of the faculty" are not same. Statement 1 says, the 30 members of the faculty who coach boys' Â’or girls'Â’ sports or both represent 60% of the total faculty members. Hence, number of total faculty members = 30/(60%) = 50

But the questions is asking about "how many of these members of the faculty coach both boys Â’and girls' Â’sports", i.e. how many out of the 30 faculty members. But statement 1 provides no information about that. Hence NOT sufficient.

Now say, number of faculty teaching only boys' sports = B, number of faculty teaching only girls' sports = G, number of faculty teaching both = BG

Hence, (B + G + BG) = 30
From question stem, G = 18
From statement 2, B = 10

Hence, BG = 30 - 18 - 10 = 2

Thus, statement 2 is SUFFICIENT.

The correct answer is B.

[yellowho]

you're right.....stupid mistake.