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%
Difficult Math Question #49 - Percentages
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 87
- Joined: Fri Jun 09, 2006 2:47 am
- Thanked: 2 times
-
- Master | Next Rank: 500 Posts
- Posts: 354
- Joined: Tue Jun 27, 2006 9:20 pm
- Thanked: 11 times
- Followed by:5 members
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..
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..
-
- Moderator
- Posts: 772
- Joined: Wed Aug 30, 2017 6:29 pm
- Followed by:6 members
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
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can use the formula:
Total = First question + Second question - Both + Neither
100 = 75 + 55 - Both + 20
100 = 150 - Both
Both = 50
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews