Problem Solving

swerve wrote:In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?

A. 35%
B. 45%
C. 55%
D. 65%
E. 75%

The OA is B.

Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks.

See the image below



Adding equation (1) and (2), we get

=> (0.3x + 0.25y) + (0.1x + 0.75y) = x
=> y = 0.6x

We have to get the value of [(0.3x + 0.25y) / x]*100% ---(3)

Plugging-in the value of y = 0.6x in equation (3), we get

[(0.3x + 0.25y) / x]*100% = [(0.3x + 0.25*0.6x) / x]*100% = [(0.3x + 0.15x) / x]*100% = [0.45x / x]*100% = 45%

The correct answer: B

Hope this helps!

-Jay
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swerve wrote:In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?

A. 35%
B. 45%
C. 55%
D. 65%
E. 75%

I thought I'd point out that Jay's and Mitch's Double Matrix approach 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 people, and the two characteristics are:
- has a university diploma or doesn't have a university diploma
- had job of choice or doesn't have job of choice

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

swerve wrote:In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?

A. 35%
B. 45%
C. 55%
D. 65%
E. 75%

Let's let the total number of people be 100.

Since 10% of the people do not have a university diploma but have a job of their choice, 10 people do not have a university diploma but do have a job of their choice.

Since 40% of the people, or 40 people, have a job of their choice, 60 people do not have a job of their choice. So we know that 0.25(60) = 15 people who do not have a job of their choice have a university diploma and thus 45 people who do not have a job of their choice do not have a university diploma.

Since 10 people do not have a university diploma but have a job of their choice and 45 people who do not have a job of their choice do not have a university diploma, it must mean 10 + 45 = 55 people do not have a university diploma. So 45 people, or 45/100 = 45% of the people do have a university diploma.

Answer: B