According to a survey, 7 percent of teenagers have not used a computer

Question

According to a survey, 7 percent of teenagers have not used a computer to play games, 11 percent have not used a computer to write reports, and 95 percent have used a computer for at least one of the above purposes. What percent of the teenagers in the survey have used a computer both to play games and to write reports?

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

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

pushpitkc · Accepted Answer

Given:   7 percent of teenagers have not used a computer to play games.

The percentage of teenagers who have used a computer to play games is 93% 
Since 11 percent have not used a computer to write reports, the percentage of
teenagers who have used a computer to write reports is 89%

It has been given that teenagers who have used the computer for at least one of
the purposes - 95% (making the number of teenagers not using computers - 5%)

P(Total) = P(Play games) + P(Write Reports) - P(Both) + P(Neither)

Substituting values, we will get 100 = 93 + 89 - x + 5 | x = 182 + 5 - 100 = 87

Therefore, the percentage of teenagers who use the computer for both purposes is  87%(Option D)

GMATinsight · Answer

Please solution using grid as mentioned below:

Answer: Option D

funsogu  Please check answer to your question (asked in PM) here. a+b+c = 95 which gives us d = 100-95=5

I hope this helps!!!

GMATinsight · Answer

The best way to solve this is by forming a grid but I am solving this in different way here.

Total teenager who used computer to play games = 100-7 = 93 = a+b
where b is the students who play games as well as write report on computer
Total teenager who used computer to write reports = 100-11 = 89 = b+c

Also, a+b+c = 95
i.e. c = 95-93 = 2
i.e. b = 89-2 = 87

Answer: Option D

dave13 · Answer

something didnt work out ...hmm 100 = group 1 + group 2 -(both)+neither 100 = 7+11-(95-x)+0

GMATinsight · Answer

Problem starts with your group1 and group 2 probably

Check the grid and see if it makes sense

dave13 · Answer

hello GMATinsight : i still have questions if you dont mind

Total teenager who used computer to write reports = 100-11 = 89 = b+ c what does C represent? Another question if 95 percent have used a computer for at least one of the above purposes , then it means that either student used computer only for one of purposes or used computers for both purposes, IF MY UNDERSTANDING IS CORRECT then Why are you subtracting from 100 and not from 95 ? One more question if 95 percent have used a computer for at least one of the above purposes THEN 5% DIDNT USE COMPUTER AT ALL ?

GMATinsight · Answer

If you check the grid solution mentioned above then your doubt can be answered.

c = People who use computer for reading but nor for games

also, your understanding of 95% is correct. This number represents the people who use computer for atleast one of these activities which is why we can say that rest 5% (100-95) as shown in grid also do NOT use computer for wither of the two activities.

demawtf · Answer

Games 
 No Games 
 TOT 
 
  Reports 
 X 
 2 
 89 (100-11) 
 
  No Reports 
  
 5 (100-95) 
 11 
 
  TOT 
 93 (100-7) 
 7 
 100

89-2=87 =X

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According to a survey, 7 percent of teenagers have not used a computer

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	Games	No Games	TOT
Reports	X	2	89 (100-11)
No Reports		5 (100-95)	11
TOT	93 (100-7)	7	100

GMAT Problem Solving (PS) Questions

According to a survey, 7 percent of teenagers have not used a computer

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards