wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room.
How many different arrangements are possible?


A

20

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

21

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

22

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

23

No worries! We‘ve got your back. Try BYJU‘S free classes today!
E

none

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

21


Three conditions have to be satisfied:
1. The number of students per row has to be at least 3.
2. Number of row has to be at least 3.
3. Equal number of students has to be seated in a row.

Arrangement 1: 3 students to a row; 12 rows.
Arrangement 2: 4 students to a row; 9 rows.
Arrangement 3: 6 students to a row; 6 rows.
Arrangement 4: 9 students to a row; 4 rows.
Arrangement 5: 12 students to a row; 3 rows.

Observe that the number of students in a row is a factor of 36.
So, list down factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
And then start from 3 and quickly find out if the number of rows is at least 2.

Both the conditions are satisfied for the following factors : 3, 4, 6, 9, and 12. i.e., 5 arrangements.


flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon