Least possible value

saidov.mikhail wrote:If y is an integer, then the least possible value of |23-5y| is

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Please help me with this one as I don't understand explanation from OG. (It's a question #50 from OG 12th Edition).

As I understood "least possible value" means the value that is the least. How to move further stepwise?

thanks,
misha

Solution:

To solve this question, we must make sure we interpret it correctly. We are not finding the least possible value of y, but rather the least possible value of |23-5y| (the absolute value of 23 – 5y). Remember that the smallest value that can result from taking the absolute value is zero. Thus we need to make 23 - 5y as close to zero as possible.

We know that 5y is a multiple of 5, so let’s first look at the multiples of 5 closest to 23. We have “20” and “25”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 5y = 20, y is 4 and when 5y = 25, y is 5. Let’s start with letting y = 4.

|23-5(4)|

|23-20|

|3| = 3

Next, let’s let y equal 5.

|23-5(5)|

|23-25|

|-2| = 2

We see that the smallest possible value of |23-5y| is 2.

The answer is B