Question

Anastasia thinks of a positive integer.
Barry doubles Anastasia's number.
Connor trebles Barry's number.
Damion multiplies Connor's number by 6.

Eve notices that the total of the four numbers is a perfect square.

What is the smallest positive integer that Anastasia could have thought of?

Answer 1

Answer:

6

Step-by-step explanation:

Anastasia thinks of a positive integer, say x

Barry doubles Anastasia's number.

• Barry's Number=2x

Connor trebles Barry's number.

• Connor's Number=3x

Damion multiplies Connor's number by 6.

• Damions Number=6(3x)=18x

Total of the Four Numbers=x+2x+3x+18x=24x

To find the value of x that makes 24x the smallest  perfect square

First, express it as a product of prime factors

$24x=2 X 2 X 2 X 3 X x=2^3X3Xx\\ Multiply both sides by 2 and 3 to make the powers even\\24 X 2 X 3=2^3X3X2 X 3=2^4X3^2\\ 24 X [2 X 3]=144 which is a perfect square\\Therefore, x=6$