(Algebra) The positive integers from 1 up are arranged, as shown in the table above.

[Max@Math Revolution]

Q1. (Algebra)

The positive integers from 1 up are arranged, as shown in the table above. Nine numbers in the form of a square are chosen from the arrangement. x is the upper-left most number in the square, and the sum of the 9 numbers is 171. What is the value of x?

A. 10
B. 11
C. 18
D. 19
E. 23

[Max@Math Revolution]

Solution:

Square form: An Equal number of rows and columns make a square. To form a square of 9 numbers: 3 by 3 square has to be selected.

When we select the first row, it will have 3 numbers as per the table. So,

• We will select the 1st, 2nd, and 3rd numbers.
  The next row selection will give us the 8th, 9th, and 10th numbers.
  The third row will give us the 15th, 16th, and 17th numbers.

Given: x is the upper-left most number, so the 1st number is x = 1, and the sum of the 9 numbers is 171.

=> 1st number: x
=> 2nd number: x + 1
=> 3rd number: x + 2 ….. and so on.

So, we get x + (x + 1) + (x + 2) + (x + 7) + (x + 8) + (x + 9) + (x + 14) + (x + 15) + (x + 16) = 171.

=> 9x + 72 = 171
=> 9x = 99
=> x = 11

Therefore, B is the correct answer.

Answer: B