Absolute Value - please help thanks.

[moonlite]

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

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

OA B

[dmateer25]

Look at the possible answer choices.

You can pretty easily conclude that no integer multiplied by 5 equals 22 or 24. Those are the two numbers that would make the absolute value 1.

So next see if 2 is a possible answer. You need to get 2 or -2 inside the absolute value. That mean 5 times a integer needs to be 21 or 25. Well you can pretty easily see that no integer times 5 equals 21. However, 5 x 5 = 25. Therefore 2 is a possible value.

No need to go any further B is the answer.

|23-5(5)| = |23 - 25| = 2

[logitech]

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

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

OA B

ABSOLUTE value is nothing but a distance from point ZERO.

so for example -2 and 2 are both 2 units far away from 0, this is why they have exactly same absolute values..but since we have to express a distance with a POSITIVE term we need to multiply by -1 to make it POSITIVE

so -2 is (-1) x ( -2) = 2 units away from ZERO

But 2 is positive so we dont need to touch it.

Lets go back to question:

the least possible value of | 23 -5y | is ZERO if there was no information given about about Y because ZERO means this number is sitting ON THE ZERO, so there is no distance...

but the question stem says Y IS A INTEGER...

so 5y will be multiples of 5 ( ....-,10, -5, 0, 5, 10, 15, 20, 25, 30, ....)

Which one would you choose to make 23-5y the smallest number ?

if you choose a negative number 23-(negative) = it will be even bigger

so you want a positive number which is close to 23, and that is 25

| 23 -5y |= | -2 |

and don't get confused because of the negative number it still means 2 units away from ZERO