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
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Least possible value
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saidov.mikhail
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|a-b| = the DISTANCE between a and b.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
Thus, |23-5y| = the distance between 23 and 5y.
To minimize this distance, the value of 5y must be AS CLOSE AS POSSIBLE to 23.
Options:
If y=4, then 5y = 20.
If y=5, then 5y = 25.
If y=6, then 5y = 30.
The LEAST possible distance between 23 and 5y will be yielded by the option in red.
If y=5, then |23-5y| = |23-25| = 2.
The correct answer is B.
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freyesinsb
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The question stem asks not for the value of y but for the least possible value of the following expression:freyesinsb wrote:Doesn't that make the answer E? If Y=5?
|23-5y|.
When y=5, we get the least possible value of |23-5y|:
|23-5y| = |23-5*5| = |23-25| = |-2| = 2.
Thus, the least possible value of |23-5y| is 2 (answer choice B).
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Solution: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
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
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