Art of Problem Solving

2014 CEMC Gauss (Grade 8) Problems/Problem 5: Difference between revisions

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<math>|1110| = 1110</math>
<math>|1110| = 1110</math>


The smallest of these numbers is <math>1001</math>. Thus, the answer is $-100
The smallest of these numbers is <math>1001</math>. Thus, the answer is <math>\boxed {\textbf {(D) } -1001}</math>.

Revision as of 13:33, 23 April 2025

Problem

Which of the following integers is closest to zero?

$\text{ (A) }\  -1101\qquad\text{ (B) }\ 1011\qquad\text{ (C) }\ -1010\qquad\text{ (D) }\ -1001\qquad\text{ (E) }\ 1110$

Solution

We need to find the number that has the least distance to 0. To do this, we can take the absolute value of each number, and see which number is the lowest:

$|-1101| = 1101$

$|1011| = 1011$

$|-1010| = 1010$

$|-1001| = 1001$

$|1110| = 1110$

The smallest of these numbers is $1001$. Thus, the answer is $\boxed {\textbf {(D) } -1001}$.