210 college students were asked in a survey if

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210 college students were asked in a survey if they preferred Lindows- or Winux-based computers. 85 students claimed that they preferred Winux to Lindows. One-fourth as many of the students who preferred Lindows to Winux had no preference. How many of the students in the survey preferred Lindows- to Winux-based computers?

A. 25
B. 50
C. 75
D. 100
E. 125

OA:D

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by GMATGuruNY » Tue Mar 21, 2017 6:29 am
NandishSS wrote:210 college students were asked in a survey if they preferred Lindows- or Winux-based computers. 85 students claimed that they preferred Winux to Lindows. One-fourth as many of the students who preferred Lindows to Winux had no preference. How many of the students in the survey preferred Lindows- to Winux-based computers?

A. 25
B. 50
C. 75
D. 100
E. 125
Use a DOUBLE-MATRIX to organize the data.
Let L = prefer Lindows, NL = do not prefer Lindows, W = prefer Winux, NW = do not prefer Winux.

210 college students were asked in a survey if they preferred Lindows- or Winux-based computers.
The following matrix is yielded:
Image
Since it is not possible to prefer BOTH L AND W -- a student who likes L more than W cannot also like W more than L -- the box in the upper left corner = 0.

85 students claimed that they preferred Winux to Lindows.
The following matrix is yielded:
Image

One fourth as many of the students who preferred Lindows to W had no preference.
No preference = NL AND NW = the center box.
Since (NL AND NW) is equal to 1/4 of L, the following maxtrix is yielded:
Image

The middle row implies the following:
x + (1/4)x = 125
(5/4)x = 125
x = (125*4)/5 = 100.

The correct answer is D.
Last edited by GMATGuruNY on Tue Mar 21, 2017 10:07 am, edited 1 time in total.
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by Brent@GMATPrepNow » Tue Mar 21, 2017 6:44 am
I thought I'd point out that Mitch's Double Matrix technique can be used for most questions featuring a population in which each member has two characteristics associated with it.

Here, we have a population of students, and the two characteristics are:
- prefer Lindows or do not prefer Lindows
- prefer Winux-based or do not prefer Winux-based

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
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- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
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by [email protected] » Tue Mar 21, 2017 8:45 am
Hi NandishSS,

While you can treat this question as if it were an Overlapping Sets question, it doesn't match the traditional 'design' of those types of prompts. With some basic note-taking and algebra, you can answer this question rather easily.

Here, we have 3 groups:
1) Those who prefer W to L
2) Those who prefer L to W
3) Those who have no preference

When you add up these 3 values, the total is 210 students. We're told that the first group is 85 students, so the last two groups must total 210 - 85 = 125 students. Next we're told that the 3rd group is 1/4 the side of the 2nd group. Mathematically, we can write that as...

X = Those who prefer L to W
(1/4)(X) = Those who have no preference

X + X/4 = 125
5X/4 = 125
5X = 500
X = 100

The number of students who prefer L to W is...

Final Answer: D

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