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
positives and negatives
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We can just test each answer choice:If y is an integer, then the least possible value of |23 - 5y| is
A) 1
B) 2
C) 3
D) 4
E) 5
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
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The least possible value of |23-5y| occurs when 23 is close to 5y in value[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, the possible values of 5y are 0,5,10,15,20,25,30 etc.
Out of the list 5y = 25 is closest to 23
The second closest is 5y = 20
|23-5y|= |23-25|=2 = b
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Alternative approach
Least value occurs when |23-5y|=0
23-5y = 0
23 = 5y
y = 23/5 = 4.6
y is between 4 and 5
Since y is an integer, 4.6 is closer to 5 than it is to 4, so y = 5
|23-5(5)|=2=b
Least value occurs when |23-5y|=0
23-5y = 0
23 = 5y
y = 23/5 = 4.6
y is between 4 and 5
Since y is an integer, 4.6 is closer to 5 than it is to 4, so y = 5
|23-5(5)|=2=b
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The most common incorrect answer here is E, because students misread the question.If y is an integer, then the least possible value of |23 - 5y| is
A) 1
B) 2
C) 3
D) 4
E) 5
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|
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Brent
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If y is an integer, then the least possible value of |23-5y| is[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
(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.
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