Set A Consists of k Distinct Numbers GMAT Data Sufficiency

Question: Set A consists of k distinct numbers. If n numbers are selected from the set one-by-one, where n ≤ k, what is the probability that numbers will be selected in ascending order?

(1) Set A consists of 12 even consecutive integers.
(2) n=5.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

Set A consists of k distinct numbers.
n numbers are selected from the set one-by-one, where n≤k,

Find out:

The probability that numbers will be selected in ascending order.

Statement 1 alone: Set A consists of 12 even consecutive integers.

That is k =12.
n ≤ k so n can be any number ranging from 1 to 12.
Hence the probability will vary over 1,½,⅓ ...........1/12.
Therefore, Statement one alone is insufficient.

Statement 2 alone: n=5

k ≥ 5
thus k can be any value from (6,∞) indicating so many distinct numbers.
However, whatever the number of items there, we are choosing only 5 out of them these 5 can have 5! combinations.
Out of these combinations, we could have the only way to order them in ascending order.
Therefore the probability that numbers will be selected in ascending order is 1/5!
Hence, Statement two alone is sufficient.

Approach Solution 2:

The problem statement informs that:

Given:

Set A consists of k distinct numbers.
n numbers are selected from the set one-by-one, where n≤k,

Find out:

The probability that numbers will be selected in ascending order.

Statement 1: Set A consists of 12 even consecutive integers.
It implies the value of K=12, then the value of n =1,2,3,.......12.

Let n=3, which means there are 3 numbers in this selection.
This selection (of 3 numbers) can be arranged in 3! ways.
These arrangements can be done in ascending order in only one way.
Probability is=1/3!

Let n=5 then probability =1/5! ,
If n=6, probability=1/6! and so on... till n=12
Hence for different values of n, we will get different probabilities.
Hence statement 1 is not sufficient.

Statement 2: n=5
It says n=5, (So we are not worried about K, since we need to select 'n' numbers from the set of K numbers)
Probability= 1/5!
(Therefore in statement 1, the value of n is not fixed. It can vary from 1 to 12. Here in statement 2, given n=5)
Hence, statement 2 alone is sufficient.

Approach Solution 3:

The problem statement declares that:

Given:

Set A consists of k distinct numbers.
n numbers are selected from the set one-by-one, where n≤k,

Find out:

The probability that numbers will be selected in ascending order.

Statement 1: Set A consists of 12 consecutive integers.
We know the total number of integers in the set, but we have no idea about how many we have to select.
Hence, statement one alone is INSUFFICIENT

Statement 2: n = 5
This implies how many numbers we need to select.
Total ways of selecting 5 numbers = 5! = 120
Out of all these selections, in only 1, the numbers will be in ascending order.
Hence required selection = 1
Therefore, Probability = 1/120

Hence, statement two alone is SUFFICIENT.

“Set A consists of k distinct numbers”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “Kaplan GMAT Math Workbook”. The GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions come up with a problem statement that is followed by two factual statements. GMAT data sufficiency includes 15 questions which are two-fifths of the total 31 GMAT quant questions.

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Set A Consists of k Distinct Numbers GMAT Data Sufficiency

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