GMAT Math

Among the 150 people attending GMAT preparation course, if 90 attend Verbal classes, 80 attend Quant classes, and 35 are on a special challenging program and do not attend either the Verbal or Quant classes, how many people attend only Quant classes? (A) 25 (B) 35 (C) 40 (D) 45 (E) 50 87. Answer (A)

A consumer preference survey revealed that out of the 200 surveyed people 80 liked tea and 70 liked both tea and coffee. If 100 of the surveyed people liked neither tea nor coffee, how many of the surveyed people liked coffee but not tea? (A) 10 (B) 20 (C) 40 (D) 50 (E) 60 63. Answer ( B )
plz explain with formulae etc

See, for the first question,

We know 35 people are neither attending QA nor VA, so we are dealing with only 115 attendees....

Use the formula

(A U B)= A + B - [A (intersection) B]

=> 135 = 90 + 80 - x

=> x=65

=> only verbal is 90 - 65 = 25 <= Ans.

150 - 35(students attending neither) = 115 (students attending either Verbal or Quant)

students attending either Verbal or Quant = Students attending verbal + Students attending quant - Students attending both verbal and quant

115 = 90 + 80 - x
115 = 170 - x
Solving for x,
x=55

So the students attending Quant only = student attending Quant - Student attending both = 80-55 = 25

Solution to the second problem:
200 (total) - 100(people who like neither) = 100 (people who like either coffee or tea)

people who like either coffee or tea = people who like tea + people who like coffee - people who like both tea and coffee

100 = 80 + x - 70
Solving for x,
x = 90 (people who like coffee)

Now for people who only like coffee = people who like coffee - people who like both tea and coffee
= 90 - 70 = 20