AMC 10 Daily Practice Round 4

Complete problem set with solutions and individual problem pages

Problem 16 Easy

Let a be a real number. If \left| a \right|=-a, what is the simplified value of \left| a-1 \right|-\left| a-2 \right|?

  • A.

    -3

  • B.

    -1

  • C.

    1

  • D.

    2a-3

  • E.

    3-2a

Answer:B

Given \left| a \right| = -a, we can deduce that a \leqslant 0 (since the absolute value of a number is non-negative, and here it equals the negative value of a).

Now, let's simplify the expression \left| a-1 \right|-\left| a-2 \right|:

\left| a-1 \right| - \left| a-2 \right| = - (a-1) + (a-2) = -1.

Hence, the simplified value of the expression is -1.

The correct answer is \boxed{\text{B}}.

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