Bunuel 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
Another approach is to
check each answer choice to see if it COULD be the smallest possible value of |23 - 5y|
Let's start with answer choice A, since it is the smallest answer.
A) 1Is it possible that |23 - 5y| = 1 if y MUST BE AN INTEGER?
Let's solve it.
If |23 - 5y| = 1, then 23 - 5y = 1 or 23 - 5y = -1
Take 23 - 5y = 1 and subtract 23 from both sides to get: -5y = -22
Solve to get: y = 4.4 NOT an integer
Take 23 - 5y = -1 and subtract 23 from both sides to get: -5y = -24
Solve to get: y = 4.8 NOT an integer
So, if y is an INTEGER, it's IMPOSSIBLE for |23 - 5y| to equal 1
ELIMINATE A
B) 2Is it possible that |23 - 5y| = 2 if y MUST BE AN INTEGER?
Let's solve it.
If |23 - 5y| = 2, then 23 - 5y = 2 or 23 - 5y = -2
Take 23 - 5y = 2 and subtract 23 from both sides to get: -5y = -21
Solve to get: y = 4.2 NOT an integer
Take 23 - 5y = -2 and subtract 23 from both sides to get: -5y = -25
Solve to get: y = 5 AN INTEGER
AHA! It IS POSSIBLE for |23 - 5y| to equal 2
Answer: B
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