paresh_patil wrote:How many of 42 people in a group are employed students?

1) 29 out of 42 are employed.

2) 24 out of 42 are student.

(Source: GMATPrep)

This is a great candidate for a technique called the Double Matrix Method. It can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- employment status (employed or unemployed)
- schooling (student or non-student)

There are 42 people altogether, so our first diagram looks like this:


Notice that I placed a star in the top-left box. The target question asks us to determine the number of people in this box.

Statement 1: 29 out of 42 are employed.
We get:

Since we cannot find the number of people in the top-left box, statement 1 is NOT SUFFICIENT

Statement : 24 out of 42 are students.
We get:

Since we cannot find the number of people in the top-left box, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We get:

Since we still cannot find the number of people in the top-left box, the combined statements are NOT SUFFICIENT

Answer: E

For more information about the Double Matrix Method and some additional practice questions, check out these 3 BTG video articles:

- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

Whenever problems with two sets (Say A and B) are involved always remember there are four scenarios - only A, only B, both and none.

Now,

• A = only A + both
  B = only B + both

Hence,

• Either A or B = A + B - both
  Total = Either A or B + None = A + B - Both + None

For example, int his case a person in that group can be any one of the following...

• Student but unemployed
  Employee but not student
  Employed student
  Neither student nor employed

Now, if we look at the statements we can see none of them are talking about the none scenario which is a possible case here.

Hence, taking both statements together,
43 = Employed + Students - Employed Students - Neither students nor employed

Hence, employed students = 43 - (29 + 24 + Neither students nor employed)

As we don't know the number of persons who are neither students nor employed, we cannot determine the number of employed students in the group.

The correct answer is E.