A group of students, no two of whom are the same height, are lined up

Question

A group of students, no two of whom are the same height, are lined up next to one another. What is the probability that they are lined up in order from shortest to tallest, from left to right?

(1) There are four students in the group.

(2) Three of the students in the group are females.

CrackverbalGMAT · Answer

Probability = \frac{Favorable \space Outcomes}{Total \space Outcomes}

Favorable outcomes = 1 as there is only 1 way in which we can order them from shortest to tallest. To get the probability we need the Total outcomes.

Statement 1:  There are four students in the group.

This statement gives us the Total outcomes = 4!

The probability = 1/24

Therefore Statement 1 Alone is Sufficient  . Answer options could be A or D

Statement 2:   Three of the students in the group are females.

This does not give us the total outcomes as we don't know how many males are there.

Therefore Statement 2 Alone is Insufficient  .

Option A

Arun Kumar

IanStewart · Answer

With 4 students, there are 4! = 24 ways to line up the students, so using Statement 1, the answer is 1/24.

Kinshook · Answer

Given: A group of students, no two of whom are the same height, are lined up next to one another. 
Asked: What is the probability that they are lined up in order from shortest to tallest, from left to right?

(1) There are four students in the group.
Favorable ways = 1
Total ways = 4!
Probability that they are lined up in order from shortest to tallest, from left to right = 1/4! = 1/24
SUFFICIENT

(2) Three of the students in the group are females.
The statement does not provide any useful information regarding the probability.
NOT SUFFICIENT

IMO A

CEdward · Answer

A group of students, no two of whom are the same height, are lined up next to one another. What is the probability that they are lined up in order from shortest to tallest, from left to right?

(1) There are four students in the group.

n = 4

So that means there are 4! ways to order the students. Only 1 of those ways is such that they are ordered from shortest to tallest in ascending order.

P = favourable outcomes / total possible outcomes = 1 / 4! = 1/24

Sufficient

(2) Three of the students in the group are females.

We don't know how many males there are.

Insufficient.

Answer is A.

A group of students, no two of whom are the same height, are lined up

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

A group of students, no two of whom are the same height, are lined up

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards