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A certain company has 255 employees. If an employee is to be

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by conquistador » Sat Oct 22, 2016 2:02 am
Source: GMAT EP2

A certain company has 255 employees. If an employee is to be selected at random from the company's employees, is the probabalility less than 1/2 that the employee selected will be a woman who has a college degree.

1. 130 of the company's employees do not have a college degree.
2. 125 of the company's employees are men.
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Source: — Data Sufficiency |

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by [email protected] » Sat Oct 22, 2016 9:26 am
Hi Mechmeera,

This question is really just about taking the proper notes and focusing on the question that is ASKED.

We're told that there are 255 total employees. We're asked if the probability of selecting a woman with a college degree from that group is LESS than 1/2. This is a YES/NO question.

1) 130 of the company's employees do not have a college degree.

With this Fact, 130 do NOT have a college degree, which means that 125 DO have a degree.

125/255 IS less than half, regardless of how many of those 125 people are women. Thus, the answer to the question is ALWAYS yes.
Fact 1 is SUFFICIENT

2) 125 of the company's employees are men.

With this Fact, 125 of the employees are men, so 130 are women.

130/255 is MORE than half.

IF... all 130 of the women have a degree, then the answer to the question is NO.
IF... just 1 of the women has a degree, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

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by crackverbal » Mon Oct 24, 2016 10:06 am
Hi Machmeera,

This question is just a data analysis question presented in the guise of a probability. The easiest way to represent data is by either using a Venn diagram or a 2 x 2 matrix. Whenever you have sets of data which are mutually exclusive (for e.g. men and women or have a college degree and do not have a college degree) then you can always represent data using a 2 x 2 matrix.

Now if the probability that the employee selected will be a woman who has a college degree has to be less than 1/2 then the number of women who have a college degree needs to be less than 128 since the total employees is 255. The question now can be rephrased to 'Is the number of women who have a college degree less than 128'

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Statement 1 : 130 of the company's employees do not have a college degree :

If 130 of the employees do not have a college degree then 125 employees have a college degree. This implies that the number of women who have a college degree will always be 125 or lesser. The probability here will always be less than 1/2. We get a definite YES. Sufficient.

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Statement 2 : 125 of the company's employees are men :

If 125 of the employees are men then 130 employees are women. This implies that the number of women who have a college degree can be 130 or lesser. If the number here is 129 or 130, the probability will be greater than 1/2, which gives us a NO and if the number is less than 128 then the probability will be less than 1/2, which gives us a YES. Insufficient.

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OA : A

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by Brent@GMATPrepNow » Mon Oct 24, 2016 10:47 am
I thought I'd point out that crackverbal's "2x2 matrix" approach is also known as the Double Matrix Method. This 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 employees, and the two characteristics are:
- male or female
- has a degree or doesn't have a degree,

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
Brent Hanneson - Creator of GMATPrepNow.com
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