I started with Statement 2. We can now find the probability that a single man will win (10/50), but that does not tell us anything about married men or single women. Insufficient.

Statement 1 tells us that we have 30 women (and thus 20 men) and 25 married employees (and thus 25 single employees). However, we still don't have enough to find probabilities for married men or single women. Insufficient.

When we put them together, we can determine the number of married men (20 men - 10 single = 10 married) and the number of single women (25 single - 10 single men = 15 single women). Sufficient.

Because you have complementary (no overlaps) groups (single OR married, male OR female), a matrix is a good way to keep track of the info given.

psm12se wrote:Please guide me on how to approach this problem.

The probability can be answered if we know the number of married men and the number of single women in the company.

(1) Since there are 30 women in the company, hence there must be 20 men there. How many of the men are married, we don't know. Also 25 workers are unmarried (single), how many of them are women, we don't know. This statement is visibly insufficient.

(2) As there are 10 single men in the company, this alone doesn't tell us a thing about the number of married men and the number of single women in the company. Insufficient

When taken together, we come to know that the number of married men is 20 - 10 = 10, and the number of single women is 25 - 10 = 15, hence probability can be answered. [spoiler]Together sufficient

Chose C
[/spoiler]

This is an EITHER/OR group problem.
Every employee is EITHER a man OR a woman.
Every employee is EITHER married OR single.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.

Since the total number of workers = 50, we get the following grid:

In the grid above, the entries in any given row or column must add up to the TOTAL of that row or column:
In the top row, married women + married men = total married.
In the middle column, married women + single women = total women.

Question stem, rephrased: What is the difference between the number of married men and the number of single women?

Statement 1:

No information about the number of married men.
INSUFFICIENT.

Statement 2:

No information about the number of married men or the number of single women.
INSUFFICIENT.

Statements combined:

Thus, single women - married men = 15-10 = 5.
SUFFICIENT.

The correct answer is C.

Brent@GMATPrepNow wrote:I thought I'd point out that Mitch's "group grid" approach (aka Double Matrix Method) can 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
- married or not married

To learn more about this technique, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with the Double Matrix Method, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- 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/ds-french-ja ... 22297.html

Difficult Problem Solving questions
- 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.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://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

Wow, that's a great set of problems. I love the matrix approach.