Difficult Math Question #49 - Percentages

[800guy]

If 75% of a class answered the 1st question on a certain test correctly, 55% answered the 2nd question on the test correctly and 20% answered neither of the questions correctly, what percent answered both correctly?
10%
20%
30%
50%
65%

[rajs.kumar]

Answer is D.

Q1 + Q2 + 20 - (Q1nQ2) = 100

=> Q1nQ2 = 50

[800guy]

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..

[BTGmoderatorRO]

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

[Scott@TargetTestPrep]

If 75% of a class answered the 1st question on a certain test correctly, 55% answered the 2nd question on the test correctly and 20% answered neither of the questions correctly, what percent answered both correctly?
10%
20%
30%
50%
65%

We can use the formula:

Total = First question + Second question - Both + Neither

100 = 75 + 55 - Both + 20

100 = 150 - Both

Both = 50

Answer: D