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If 25% of a company's employees are

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If 25% of a company's employees are

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If 25% of a company's employees are women older than 30, what percent of the men employees are 30 or younger?

1.Half of the women employees are 30 or younger
2.35% of the company's employees are men of 30 or younger

OA: C

Can somebody explain via 2*2 or Venn diagram?

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NandishSS wrote:
If 25% of a company's employees are women older than 30, what percent of the men employees are 30 or younger?

1.Half of the women employees are 30 or younger
2.35% of the company's employees are men of 30 or younger

OA: C

Can somebody explain via 2*2 or Venn diagram?
Set up your double-set matrix and designate the total 'T.' We'll start with this:




Statement 1 tell us that half of the women are 30 or younger. Well, that means there are the same number of women 30 or younger as over 30. If there are .25T older than 30, there will be .25T under
30, giving us a total of .5T women, and thus .5T men. But not enough to find the percent of male employees who are 30 or younger. S1 is not sufficient. Now our matrix looks like this:





Statement 2 tells us that the Men/30 or over cell is .35T. By itself, not sufficient. Our matrix would look like this:




Together we know that there are .5T men and .35T of those are 40 or over, thus leaving .15T who are under 30. Thus the percent of men under 30 would be .15T/.5T = 30%. We have a unique value, this together the statements are sufficient. The answer is C


Our final matrix looks like this:



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NandishSS wrote:
If 25% of a company's employees are women older than 30, what percent of the men employees are 30 or younger?

1.Half of the women employees are 30 or younger
2.35% of the company's employees are men of 30 or younger
Let the total number of employees = 100.
Since 25% of the employees are women older than 30, the following matrix is yielded:


What percent of the men employees are 30 or younger?
Question stem, rephrased:
What is the value of (men 30 or younger)/(all men)?

Statement 1: Half of the women employees are 30 or younger.
Since half of the women are 30 or younger, the 25 women who are older than 30 must constitute the remaining half of the women, implying that there are a total of 50 women.
The following matrix is yielded:

No way to determine the value of (men 30 or younger)/(all men).
INSUFFICIENT.

Statement 2: 35% of the company's employees are men of 30 or younger.
The following matrix is yielded:

No way to determine the value of (men 30 or younger)/(all men).
INSUFFICIENT.

Statements combined:
The following matrix is yielded:

Thus:
(men 30 or younger)/(all men) = 35/50.
SUFFICIENT.

The correct answer is C.

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GMAT/MBA Expert

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I thought I'd point out that Mitch's approach (known as the Double Matrix Method) 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 employees, and the two characteristics are:
- female or male
-aged 30 or younger or older than 30

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: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

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

Easy Problem Solving questions
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

Medium Problem Solving questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/920
- http://www.beatthegmat.com/posted-speed-limit-t272374.html
- http://www.beatthegmat.com/motel-t271938.html
- http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html
- http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html
- http://www.beatthegmat.com/at-least-100-students-at-a-certain-high-school-study-japanes-t274669.html
- http://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/946
- http://www.beatthegmat.com/ratio-problem-t268339.html
- http://www.beatthegmat.com/overlapping-sets-question-t265223.html
- http://www.beatthegmat.com/fractions-t264254.html
- http://www.beatthegmat.com/overlapping-sets-t264092.html
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/943
- http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
- http://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- http://www.beatthegmat.com/sets-matrix-ds-t271914.html
- http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
- http://www.beatthegmat.com/a-manufacturer-t270331.html
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- http://www.beatthegmat.com/double-set-matrix-question-t271423.html
- https://youtu.be/dOZ9KM1m5Hs
- http://www.beatthegmat.com/sets-t269449.html
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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