Difficult Math Question #49 - Percentages

Answer is D.

Q1 + Q2 + 20 - (Q1nQ2) = 100

=> Q1nQ2 = 50

OA:

This problem can be easily solved by Venn Diagrams
Lets think the total class consists of 100 students

so 75 students answered question 1
and 55 students answered question 2

Now 20 students not answered any question correctly

Therefore out of total 100 students only 80 students answered either question 1 or question 2 or both the questions...

So 75+55=130 which implies 130-80=50% are the students who answered both correctly and are counted in both the groups...that’s why the number was 50 more..

Using Venn diagrams approach to solve this.
Take the class population to be 100.
let the A represent the percentage that answered question 1 correctly
and B the percentage that answered question 2 correctly.
A=75
B=55
percentage that do not answer the neither question 1 or 2 =20

subtracting this from 100,
100-20=80
meaning that 80 students answered the question 1 or 2 correctly and some students answered both questions correctly.

so, A+B=75+55=130
therefore 130-80=50%, 50% of the students answered the 2 questions correctly and they are found in both group.
so, 50% is the answer