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
210 college students were asked in a survey if
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Use a DOUBLE-MATRIX to organize the data.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
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:
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:
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:
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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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
- https://www.beatthegmat.com/posted-speed ... 72374.html
- 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,
Brent
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
- https://www.beatthegmat.com/posted-speed ... 72374.html
- 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,
Brent
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich