Olympiad Maths Prep

Track / Stage 3 / 56 of 260 #56 of 2000

Problem 56

AMC 10/12, early questions
Number theory Difficulty 3.3 Find the answer

Given that aa is the largest negative integer, bb is the smallest positive integer, and cc is the number with the smallest absolute value, then a+cb=a+c-b=____.

Official solution

Given that aa is the largest negative integer, bb is the smallest positive integer, and cc is the number with the smallest absolute value, we can determine the values of aa, bb, and cc as follows:

- Since aa is the largest negative integer, a=1a = -1.
- Since bb is the smallest positive integer, b=1b = 1.
- Since cc is the number with the smallest absolute value, c=0c = 0.

Now, we need to find the value of a+cba+c-b. Substituting the values of aa, bb, and cc we get:

a+cb=1+01=11=2 a+c-b = -1 + 0 - 1 = -1 - 1 = -2

Therefore, the answer is 2\boxed{-2}.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.