Venn diagrams/Sets

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surajgarg: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Mon May 10, 2010 11:55 pm; Thanked: 4 times

by surajgarg » Sat Jul 17, 2010 12:21 pm

1. At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?

A. 6
B. 14
C. 19
D. 20
E. 81

OA - C

2. Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?

A. 22(2/9)%
B. 16(2/3)%
C. 11(1/9)%
D. 10%
E. 5%

OA - D

Pls provide explanations for the above problems.

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Source: Beat The GMAT — Problem Solving | Sat Jul 17, 2010 12:21 pm

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sat Jul 17, 2010 12:26 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sat Jul 17, 2010 5:19 pm

surajgarg wrote:1. At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?
A. 6
B. 14
C. 19
D. 20
E. 81
OA - C

Let number of interns = 100
Then 80 interns receive fewer than 6 hours of sleep.
75 interns receive less than 6 hours of sleep and report tired feeling, so only 5 interns do not report tired feeling.
70 interns receive greater than or equal to 6 hours of sleep, do not report tired feeling.
Number of interns receiving greater than or equal to 6 hours of sleep = 100 - 80 = 20
70% of 20 report no tired feeling, so number of interns who do not report tired feeling = 70% of 20 = 14

Therefore, percent of the interns report no feelings of tiredness = 14 + 5 = 19

The correct answer is [spoiler](C)[/spoiler].

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sat Jul 17, 2010 5:38 pm

surajgarg wrote: 2. Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?

A. 22(2/9)%
B. 16(2/3)%
C. 11(1/9)%
D. 10%
E. 5%
OA - D
Pls provide explanations for the above problems.

Let there are 100 lights.
Then 80 lights should be on and 20 should be off at 8 p.m.
Then 40% of 20 = 8 lights should be off but are on.
10% of the lights that are supposed to be on are actually off implies 10% of 80 = 8
Number of lights that are on = 80 + 8 - 8 = 80
Therefore, percent of lights which are on but should be off = (8/80) * 100 = 10%

The correct answer is (D).

Rahul Lakhani
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Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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+91-99201 32411 (India)

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

by outreach » Sat Jul 17, 2010 9:56 pm

1

75=receive fewer than 6 hours of sleep and report feeling tired during their shifts
80=interns receive fewer than 6 hours of sleep
20=interns receive more than 6 hours of sleep
14=interns who receive 6 or more hours of sleep report no feelings of tiredness

Q=interns report no feelings of tiredness during their shifts

80-75+14=19

2

80=lights at Hotel California are on at 8 p.m
40% of 20=8=lights that are supposed to be off are actually on
10% of 80=8=lights that are supposed to be on are actually off

no of lights that should be on =80-8-8=80

d

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