From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency

Question: From a group of M employees, N will be selected, at random, to sit in a line of N chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Andrew is seated somewhere to the right of employee Georgia?

Statement #1: N = 15
Statement #2: N = M

Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.
Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.
BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
Each statement ALONE is sufficient to answer the question.
Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

“From a group of M employees, N will be selected, at random,”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

Given the restriction of Andrew being to the right of Georgia, it is obvious that the answer is divided by two!

In statement 1 its given that, N = 15
The way of selection is C(M,N) = C(M,15)
M is unknown according to the above equation so it is insufficient.

In statement 21 its given that, N=M
The way of selection is C(M,N) = C(M,M) = 1
So the answer = 1/2! = 1/2 and it is sufficient.

As you can see,
Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

Correct Answer: B

Approach Solution 2:

Lets solve this question using brute force calculations,

The Statement 1 is insufficient because we need to know M in order to calculate the probability.

Lets move to statement 2

N= M

This turns to sit N people into N chairs
For Andrew is seated somewhere to the right of employee Georgia, we have (1+ 2+ 3+....+ (n-1)) possibilities
To understand it better this, lets say 4 people sit in 4 chairs
Put Georgia in seat 1, then Andrew can be seated in 2,3, and 4 ( 3 possibilities)
Put Georgia in seat 2, then Andrew can be seated in 3,4 ( 2 possibilities)
Put Georgia in seat 3, then Andrew can be seated in 4 only (1 possibility)
Add 1+2+3

After Georgia and Andrew are seated, we are left with (n-2)! possible combination
In this case, after Georgia and Andrew are seated, there are two seats left, we have 2! possible combination)
The total possible combinations for N people in N chairs is N!
The possible combinations that meet the requirement is (1+2+3+...(N-1))* (N-2)! = [(N-1)*N/2] * (N-2)!
The probability = [(N-1)*N/2] * (N-2)!/N! = [(N-1)*N/2]/ [(N-1)*N] = ½
Which is sufficient.

As you can see,
Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

Correct Answer: B

Approach Solution 3:

The restriction of Andrew being to Georgia's right makes it clear that the answer is divided by two!

It is stated in assertion 1 that N = 15.
The selection process is C(M,N) = C. (M,15)
The above equation indicates that M is insufficient because it is unknown.

N=M is stated in statement 21.
The selection process is C(M,N) = C(M,M) = 1.
Therefore, 1/2! = 1/2 is a sufficient response.

As you can see, statement 2 Alone IS Sufficient to answer the question, but statement 1 ALONE is not sufficient.

Correct Answer: B

Some suggested GMAT Data Sufficiency Questions

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From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency

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