A Team of 8 Students Goes On An Excursion, In Two Cars, Of Which One GMAT Problem Solving

‘A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4’ is the topic from the GMAT Quantitative problem set. GMAT quantitative reasoning section tests the candidate's ability to solve mathematical and quantitative problems, interpret graph data, and mathematical reasoning. The question in this section comes with five options. Candidates need to choose the one which is correct. GMAT Quant syllabus has mainly the two categories-

Problem Solving: This question type in GMAT Quantitative analyses candidates logical and analytical reasoning skills. In this section, candidates indicate the best five answer choices.
Data Sufficiency: This question type in GMAT Quantitative analyses candidates’ quantitative problems and identifies relevance with the data given.

Topic: A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. If internal arrangement inside the car does not matter then the number of ways in which they can travel, is

91
122
126
3920
4120

Read more articles on GMAT samples

A recent survey showed that 50 percent of people polled believe that elected officials should resign if indicted for a crime	From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee.	12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles
From her Collection of 9 Different Hats Ellen Wants to Wear one Different Hat to School Each Day During a Four Day Week	According to a recent study, retirees in the United States are four times more likely to give regular financial aid to their children as to receive it from them.	The Speed of a Railway Engine is 42 Km per hour When No Compartment is Attached, and the Reduction in Speed is Directly Proportional to the Square Root of the Number of Compartments Attached.
The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated	The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size.	There are 6 Tasks and 6 Persons. Task 1 Cannot be Assigned Either to Person 1 or to Person 2; Task 2 Must be Assigned to either Person 3 or Person 4
A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?	If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k?	An Inlet Pipe can Fill in an Empty Cistern in 30 minutes Whereas a leak in the Bottom of the Cistern can Empty a Filled Tank in 40 minutes
Iqbal Dealt Some Cards to Mushtaq and Himself From a Full Pack of Playing Cards and Laid the Rest Aside	The interview is an essential part of a successful hiring program because, with it, job applicants who have personalities that are unsuited to the requirements of the job will be eliminated from consideration.	A Four Digit Number is Formed By Repeating a Two Digit Number Such as 2525, 3232, etc.
The Present Age Of A Father Is 3 Years More Than Three Times The Age Of His Son	If a and b are integers, and b > 0, does (a - 1)/(b + 1) = a/b ?	If P and Q are positive integers, is P divisible by 12?

Answer: C

Model Answer:

There is only one approach to solve the problem.

Explanation:
Given:

8 students goes on an excursion, in two cars
one can seat 5 and the other only 4.

Condition:

The internal arrangement inside the car does not matter

Find out:

The number of ways in which they can travel

Let’s first assume that the students are indistinguishable.
Then the problem becomes: How many ways can 2 positive integers (where the first addend can’t be more than 4 and the second can’t be more than 5) add up to 8?
There are two ways we can attain this:

3 + 5 = 8
4 + 4 = 8

Now, obviously the students (and in general, people) are distinguishable, and they can exchange seats. Hence, the internal arrangement will change. Considering this, we have to take each of the two cases above:
Considering Case 1: 3 + 5 = 8
That is, the first car gets 3 students and the second 5 students. Since the students are distinguishable, the number of choices the first car has is 8C3 and the number of choices the second car has is 5C5 (after 3 students have been chosen to sit in the first car).
Therefore, the number of ways the 8 students can be distributed into 2 cars in this case is
8C3 x 5C5
= (8 x 7 x 6)/(3 x 2) x 1
= 8 x 7
= 56.
Considering Case 2: 4 + 4 = 8
That is, the first car gets 4 students and the second 4 students. Since the students are distinguishable, the number of choices the first car has is 8C4 and the number of choices the second car has is 4C4 (after 4 students have been chosen to sit in the first car).
Therefore, the number of ways the 8 students can be distributed into 2 cars in this case is
8C4 x 4C4
= (8 x 7 x 6 x 5)/(4 x 3 x 2) x 1
= 2 x 7 x 5
= 70.
Thus, the total number of ways in both cases is 56 + 70 = 126.
Hence, C is the correct answer.

SHARE ON FACEBOOK SHARE ON TWITTER

A Team of 8 Students Goes On An Excursion, In Two Cars, Of Which One GMAT Problem Solving

Fees Structure

Comments

SUBSCRIBE TO OUR NEWS LETTER