The question given below is a sample question in Numbers and operation. These are typical word problems in Arithmetic that are tested in SAT.
Question
If 3 students are made to sit in a row, then 9 students do not have a seat. Alternatively, if 9 students are made to sit in a row, then 5 rows are empty. How many students have to be seated in a row so that an equal number of students sit in all the rows and all the students are seated?
A. 5
B. 4
C. 8
D. 7
E. 6
Correct answer is 4. Choice B.
Explanatory Answer
Let there be "n" rows in the class.
Arrangement I
When 3 students are made to sit in a row, 3n students will be seated.
In this arrangement 9 students do not have a seat.
Therefore, there are (3n + 9) students in the class
Arrangement II
When 9 students are made to sit in a row, then 5 rows are empty.
i.e., the students have been seated in n - 5 rows.
Therefore, there are 9*(n - 5) students in the class.
As the number of students in the class is a constant, irrespective of the arrangement, we get 3n + 9 = 9*(n - 5)
i.e., 3n + 9 = 9n - 45
or 6n = 54 or n = 9
There are 9 rows in the class.
As there are 9*(n - 5) students, we get 9*(9 - 5) = 36 students.
If 36 students have to be seated in 9 rows, such that equal number of students sit in each of the rows, then we have to seat
= 4 students to a row.
