How many of the 42 people in a group are employed students?

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How many of the 42 people in a group are employed students?

(1) 29 of the 42 people are employed.
(2) 24 of the 42 people are students.

The OA is E.

The answer is straight E. Even when taken together we have:

{Total} = {Students} + {Employed} - {Both} + {Neither} --> we want to calculate: {Both}, # of employed students.
{42} = {24} + {29} - {Both} + {Neither} --> {Both} = 11 + {Neither}, since we don't know # of people who are neither employed nor students, we can not answer the question.

Has anyone another strategic approach to solving this DS question? Regards!

[[email protected]]

Hi All,

We're told that there are 42 people in a group. We're asked for the number that are EMPLOYED STUDENTS. This is an example of an Overlapping Sets question - and while it's typical to use the Overlapping Sets Formula or the Tic-Tac-Toe board to solve these types of question, this one can be approached with a bit of logic (and very little math is actually needed).

1) 29 of the 42 people are employed.

Fact 1 tells us that 29 of the people are EMPLOYED, but we do NOT know how many of those 29 are students, so the answer to the question could be any integer from 0 to 29, inclusive.
Fact 1 is INSUFFICIENT

2) 24 of the 42 people are students.

Fact 2 tells us that 24 of the people are STUDENTS, but we do NOT know how many of those 24 are employed, so the answer to the question could be any integer from 0 to 24, inclusive.
Fact 2 is INSUFFICIENT

Combined, we know...
-The answer is any integer form 0 to 29, inclusive
-The answer is any integer form 0 to 24, inclusive
Thus, the answer could be any integer form 0 to 24, inclusive - but we don't know the exact number.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

How many of the 42 people in a group are employed students?

(1) 29 of the 42 people are employed.
(2) 24 of the 42 people are students.

Here's a step-by-step approach using the Double Matrix method.

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

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