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OG 12th misprint? Arithmetic: Absolute value; integer ops

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by pinaychic21 » Sun Mar 06, 2011 7:27 pm
I am hoping I am not driving myself nuts with all the studying and just over looking this problem:

Page 159, #50

If y is an integer, then the least possible value of |23-5y| is

A) 1
B) 2
C) 3
D) 4
E) 5

I chose E, but the book's explanation says B, though they worked the problem as I had, and the correct answer was 5 which is clearly E. Am I in the twilight zone??
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by Anurag@Gurome » Sun Mar 06, 2011 7:35 pm
pinaychic21 wrote:I am hoping I am not driving myself nuts with all the studying and just over looking this problem:

Page 159, #50

If y is an integer, then the least possible value of |23-5y| is

A) 1
B) 2
C) 3
D) 4
E) 5

I chose E, but the book's explanation says B, though they worked the problem as I had, and the correct answer was 5 which is clearly E. Am I in the twilight zone??
Obviously, l23-5yl is least when 5y is closest to 23.
Multiple of 5 closest to 23 is 25 and this makes y as 5.
Or l23-5yl is least as l23-25l = 2.
Answer is B).
Last edited by Anurag@Gurome on Sun Mar 06, 2011 7:37 pm, edited 1 time in total.
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by yellowho » Sun Mar 06, 2011 7:36 pm
its not asking y, its asking for the lowest value of |23-5y|.

plug in 5 for y and you get 2.
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by pinaychic21 » Sun Mar 06, 2011 8:09 pm
Anurag@Gurome wrote:
pinaychic21 wrote:I am hoping I am not driving myself nuts with all the studying and just over looking this problem:

Page 159, #50

If y is an integer, then the least possible value of |23-5y| is

A) 1
B) 2
C) 3
D) 4
E) 5

I chose E, but the book's explanation says B, though they worked the problem as I had, and the correct answer was 5 which is clearly E. Am I in the twilight zone??
Obviously, l23-5yl is least when 5y is closest to 23.
Multiple of 5 closest to 23 is 25 and this makes y as 5.
Or l23-5yl is least as l23-25l = 2.
Answer is B).
Thanks, there I go not reading the explanation properly again =/
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by sanju09 » Sun Mar 06, 2011 11:51 pm
pinaychic21 wrote:I am hoping I am not driving myself nuts with all the studying and just over looking this problem:

Page 159, #50

If y is an integer, then the least possible value of |23-5y| is

A) 1
B) 2
C) 3
D) 4
E) 5

I chose E, but the book's explanation says B, though they worked the problem as I had, and the correct answer was 5 which is clearly E. Am I in the twilight zone??
Since 23 is not a multiple of 5 hence no integer for y can turn 23 - 5 y equal to zero, but we can still look for the multiple of 5 that is closest to 23. Do not take 20 as 5 y for the minimization, take 25 rather, because |23 - 20| = 3 whereas |23 - 25| =[spoiler]2.



B[/spoiler]
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