overlapping sets

[tonebeeze]

In a certain school, out of a total of 65 students, 80 percent are currently enrolled in either a history course or a literature coursee, or both. How many of the students are currently enrolled in a history course?

1. Ten of the students are currently enrolled in both a history course and a literature course.

2. Thirty-three of the students are currently enrolled in a literature course.

[gmatmachoman]

Pick C

[maihuna]

You can make a table or venn diagram or use symbols, H, L, their completemnts H' L',

Given : H' & L' = 20% of 65 = 13
HUL = 80% of 65 = 52 = H + L - HXL , assuming X as intersec
=> H = 52 - L + HXL

So we need L, and HXL both

C

[Anurag@Gurome]

In a certain school, out of a total of 65 students, 80 percent are currently enrolled in either a history course or a literature coursee, or both. How many of the students are currently enrolled in a history course?

1. Ten of the students are currently enrolled in both a history course and a literature course.
2. Thirty-three of the students are currently enrolled in a literature course.

Say, number of students in only history course = H, number of students in only literature course = L, number of students in only both course = LH, and number of students in none of them = N.

Hence, (H + L + LH) = 80% of 65 = 52
We need to find the value of (H + LH).

Statement 1: LH = 10
Still we don't know the value of H or L.

Not sufficient

Statement 1: (L + LH) = 33
H = (52 - 33) = 19
Still we don't know the individual value of LH or L.

Not sufficient

1 & 2 Together: LH = 10 and (L + LH) = 33
Implies, L = 23
Hence, (H + LH) = 52 - 23 = 29

Sufficient

The correct answer is C.