[email protected] wrote:Looking for a better explanation for question 51 in the OG guide. I don`t understand why the answer choice is B.
If y is an integer, then the least possible value of |23-5y| =?
Thank-you!
B
If y is an integer, then the least possible value of |23-5y| is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Solution:
To solve this question, we must be sure to 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 possible value that can result from taking an 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, which are 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.
Answer:
B
Another approach to solving this problem is to determine what value of y makes the expression 23 - 5y equal to 0:
23 - 5y = 0
23 = 5y
y = 4.6
However, we know that y must be an integer, so we must round y = 4.6 to y = 5.
We then substitute the value 5 for y into the absolute value equation, as was done earlier, and we obtain the same answer of 2, which is answer choice
B.
