At a certain hospital, 75% of the interns

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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Sat Nov 19, 2016 6:30 pm

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

Please help me with the problem. I tried setting up matrix but I am really confused with the language of the question!

Thanks

Source: Beat The GMAT — Problem Solving | Sat Nov 19, 2016 6:30 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Nov 19, 2016 6:45 pm

I posted a solution here:
https://www.beatthegmat.com/tired-vs-not ... 59469.html

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Nov 19, 2016 7:07 pm

Here's another approach that uses the Double Matrix Method: https://www.beatthegmat.com/hospitals-t283256.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Sat Nov 19, 2016 8:57 pm

Thanks to both of you for your input.

It is a very straight forward question but I was very confused with the language of the question.

-> 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts
-> 80% of the interns receive fewer than 6 hours of sleep

I thought it was providing contradictory information so could not fit this information in the matrix. But now i get the difference between the two!

Matt@VeritasPrep: GMAT Instructor; Posts: 2629; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Nov 25, 2016 3:13 pm

It might be easier to see the distinction if we label each group.

< 6 hours AND tired = x
> 6 hours AND not tired = y
< 6 hours AND not tired = z
> 6 hours AND tired = w

We're told that:

x = .75 * (x + y + w + z)

y = .7 * (y + w)

x + z = .8 * (x + y + w + z)

From there, the algebra is tedious, but relatively straightforward. (Of course, on test day I wouldn't recommend algebra, but it does make the prompt intelligible.)

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