According to a report, 7% of students did not use a computer to play

Question

According to a report, 7% of students did not use a computer to play games, 11% did not use a computer to write reports, and 95% did use a computer for at least one of the purposes. What percent of the students according to the report did use a computer for both the purposes – play games and write reports?

(A) 13%
(B) 56%
(C) 77%
(D) 87%
(E) 91%

Show Answer

Official Answer

D

(A) 13%
(B) 56%
(C) 77%
(D) 87%
(E) 91%

Kinshook · Answer

Given: According to a report, 7% of students did not use a computer to play games, 11% did not use a computer to write reports, and 95% did use a computer for at least one of the purposes.

Asked: What percent of the students according to the report did use a computer for both the purposes – play games and write reports?

According to a report, 7% of students did not use a computer to play games, 11% did not use a computer to write reports, and 95% did use a computer for at least one of the purposes.

Play games  ~ Play games  Total  
  Write reports      100%-11%=89%  
  ~Write reports    100%-95%=5%  11%  
  Total  100%-7%=93%  7%  100%

Play games  ~ Play games  Total  
  Write reports   93%-6%=87%     89%  
  ~Write reports  11%-5%=6%  5%  11%  
  Total  93%  7%  100%

IMO D

azamatboden · Answer

100 = 93+89+x+5
X=87

mooby_1234 · Answer

Another possible method for this could be -

We know that:
11% of students did not use computer to write reports = 'students who only used for gaming + respective share of students who didn't use computers'
7% of students did not use computer for gaming = 'students who only used for reports + respective share of students who didn't use computers'

Adding both statements: 
18% = students who only used for gaming + students who only used for reports + 2* (share of students who didn't use computers at all, as from adding the above this is found to be counted twice, therefore 5% + 5% ie. 10%)

So, this gives us:
18% = students who only used for gaming + students who only used for reports + 10%

Now, subtracting the share of students who didn't use computers at all (ie. 10%) will give the share of students who used computers for either only gaming or for only reports:
Students who only used for gaming + students who only used for reports = 18% -10% 
Which is 8%

We also know that the total students who used computers are 95%. Therefore:

Total students who used computer = (Those who only used for reports + Those who only used for gaming) + Those who used for both

95% = 8% + those who used for both

Ans: Therefore, those who used for both = 95%-8%, which is 87%. So option D

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According to a report, 7% of students did not use a computer to play

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	Play games	~ Play games	Total
Write reports			100%-11%=89%
~Write reports		100%-95%=5%	11%
Total	100%-7%=93%	7%	100%

GMAT Problem Solving (PS) Questions

According to a report, 7% of students did not use a computer to play

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My Rewards