Here is POTW #32:
If 75% of Mr. Milelnebarnandeshiri's class answered the first question on their Ecology test correctly,and 55% answered the second question correctly, while 20% answered neither the first nor the second question correctly, what percentage of the students answered both questions correctly?
Out of 100%, 20% for sure can not be both the students. Therefore, 80% is the net variable.
ReplyDeleteThe answer is 25% as: 20% + 30% + 50%.
If 75% answered the first question correctly and 55% answered the second question correctly, then 5% of the people answered the first question wrong because 100-(75+20) but second question correctly and 25% off the people answered the second question incorrectly because 100-(55+20) and the first question correctly. That means 50% of the people answered both the questions correctly because 50% did everything correctly + 20% who got neither of the questions correctly + 5% answered the second question correctly bur first question incorrectly + 25% answered the first question correctly and second question incorrectly. This adds up to all the combinations at 100% so this works.
ReplyDelete75%+55%+20%=150%
ReplyDelete50% of students got both questions correct.
given that 20% didn't answer either of the questions correctly, 75% out of the remaining 80% answered the first question correctly and 55% answered the second correctly. the answer to what percentage of students answered both correctly can range from 50% to 55%, since the 55% for the second question could be the same students that answered the first correctly, (55% inside of the 75%), but could also be 50% in the 75% and 5% in the 5% (remaining since it's 75% out of 80%.)
ReplyDeleterajmohamed
Hope and Calista :) :)
ReplyDeleteFirst we made a Venn diagram and drew a 'universe' around it holding the data of all percentages from above. The question told us that 20% of the students answered incorrectly for both, so we subtracted this from 100% giving us 80%. Therefore, we knew that the amount of students that answered #1, #2 as well as both had to equal 80%. To find the amount of students who did #1 correctly, we did 80%-55%, giving us 25%. Next, we did the same to the other side, except we subtracted 75% from 80% to give us the percentage of students who did the 2nd question properly (5%). Next we added 25% and 5% together and subtracted it from 80%. This gave us the percentage of students who answered both questions correctly. The final percentage was 50%.
First, we simplify, 3/4 people got the first question right, 11/20 got the second, and 1/5 didn't answer either correct. 3 x 11, 4 x 20 = 33/80 percentage of people would get both questions correct. The people wrong doesn't really matter because the percentage of people who got both questions correct are out of the total amount anyway.
ReplyDelete33/80 = 0.4125 = 41.25%
Since 20% of the students didn't answer either of the questions correctly only 80% could have. However, only 55% answered the second question correctly so 55% is the maximum number of students who answered both the questions correctly. However, since 75%, not the remaining 80%, answered question 1 correctly (5% didn't answer question 1 right), then we can remove 5% from 55% because they would have only got question 2 correct. Therefore, 50% of students answered both correctly.
ReplyDeleteTo check:
50% answered both correctly.
25% answered only question 1 correctly (75 - 50 = 25)
5% answered only question 2 correctly (55 - 50 = 5)
20% didn't answer either question correctly.
Added together: 50% + 25% + 5% + 20% = 100% so I am right
Good job y'all. It was 50%. So, 50% of the students who wrote the test answered both questions correctly.
ReplyDeleteThere's one way to solve it explained here: https://www.khanacademy.org/test-prep/gmat/problem-solving/v/gmat-math-39 Start at 6:48 of the video.