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.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. 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.

Suggested GMAT Data Sufficiency Samples

• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• How Many Integers are There Between, But Not Including, Integers r and s ? GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• Is (x – 2) (x – 3) > 0? GMAT Data Sufficiency
• If a and b are positive integers, is a/b < 9/11? GMAT Data Sufficiency
• If y = x^2 - 6x + 9, What is the Value of x? GMAT Data Sufficiency
• If [x] Denotes The Greatest Integer Less Than or Equal to x GMAT Data Sufficiency
• Is |x| < 1? GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Is x^2>y^2? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• If 30 is Divided by Half and 10 is Added to the Result, Then What is GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Juan Bought Some Paperback Books That Cost $8 GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency
• 2x+3y GMAT Data Sufficiency
• The Selling Price of an Article is Equal to the Cost of the Article GMAT Data Sufficiency
• Of the 58 Patients of Vertigo Hospital, 45 have Arachnophobia GMAT Data Sufficiency
• If the Lengths of the Legs of a Right Triangle are Integers GMAT Data Sufficiency
• On a Race Track a Maximum of 5 Horses can Race Together at A Time GMAT Problem Solving
• If x is a Positive Integer, is√x an Integer GMAT Data Sufficiency
• If Bob's Age is Three Times David's Age, What is Bob's Age? GMAT Data Sufficiency
• A Circle is Inscribed in a Quadrilateral ABCD Such a Way that it Touches GMAT Data Sufficiency
• What is the Area of a Rectangular Field? GMAT Data Sufficiency
• If x and y are negative integers, then what is the value of xy GMAT Data Sufficiency
• If x is a non-zero integer, what is the value of x GMAT Data Sufficiency
• In the Figure above, FGHI is Inscribed in the Circle with the Centre J GMAT Data Sufficiency
• In the xy- plane, region R consists of all the points (x, y) GMAT Data Sufficiency
• Is 2ab > ab? GMAT Data Sufficiency
• The Restaurant Serves 6 Varieties of Appetizers, 10 Different Entrees GMAT Problem Solving
• What is the Probability That it will Rain Tomorrow GMAT Data Sufficiency
• If r > 0 and s > 0, is r/s < s/r? GMAT Data Sufficiency
• How many integers n are there such that r < n < s? GMAT Data Sufficiency
• By How Many Dollars was The Price of a Certain Portable Tape Recorder GMAT Data Sufficiency
• At a Certain Bookstore, Each Notepad Costs x Dollars GMAT Data Sufficiency
• A Train Traveled from Station A to Station B at an Average Speed of 80 GMAT Data Sufficiency
• A Teacher Distributed a Number of Candies, Cookies, and Toffees GMAT Data Sufficiency
• What is the Perimeter of Quadrilateral Q? GMAT Data Sufficiency
• What is the Perimeter of Rectangle ABCD GMAT Data Sufficiency
• Mr. Alex Usually Starts at 9:00am and Reaches His Office Just GMAT Data Sufficiency
• If x and y Represent Number on The Number Line, is x + y = 0 GMAT Data Sufficiency
• Is 9 the HCF of p and q? GMAT Data Sufficiency