positives and negatives

If y is an integer, then the least possible value of |23 - 5y| is
A) 1
B) 2
C) 3
D) 4
E) 5

We can just test each answer choice:

A) 1. So, |23 - 5y| = |23 - 5(1)| = 18
B) 2. So, |23 - 5y| = |23 - 5(2)| = 13
C) 3. So, |23 - 5y| = |23 - 5(3)| = 8
D) 4. So, |23 - 5y| = |23 - 5(4)| = 3
E) 5. So, |23 - 5y| = |23 - 5(5)| = 2

So, when y = 5, |23 - 5y| = |23 - 5(5)| = |-2| = 2 (and 2 is the smallest possible value of |23 - 5y|)

The question asks, "What is the least possible value of |23 - 5y|?
So, the least possible value of |23 - 5y| is 2 (and this occurs when y = 5)

Answer: B

Cheers,
Brent

If y is an integer, then the least possible value of |23 - 5y| is
A) 1
B) 2
C) 3
D) 4
E) 5

The most common incorrect answer here is E, because students misread the question.
They read it as, What value of y minimizes the value of |23 - 5y|?
If this WERE the question, then the answer would, indeed, be E

HOWEVER, the question asks is to determine the minimum possible value of |23 - 5y|

Cheers,
Brent

[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.