AMC 10 Step by Step
Log inSign up
Printable

2020 AMC 10B Problem 1

Problem onlyBack to the problem
2020 AMC 10B Problem 1AMC 10 Step by Step
Name:                             Date: October 28, 2026
Algebraic Manipulation · difficulty 1 of 5 · about 1 min · position P1-10

What is the value of 1−(−2)−3−(−4)−5−(−6)?1 - (-2) - 3 - (-4) - 5 - (-6)?

  1. A)−20-20
  2. B)−3-3
  3. C)33
  4. D)55
  5. E)2121

Answer

D

Key insight

Taking away a negative number is the same as adding it, so the expression becomes 1 + 2 - 3 + 4 - 5 + 6.

Solution

1. First clean up the signs. Subtracting a negative number is the same as adding the positive number. For example, 5−(−2)=75 - (-2) = 7, the same as 5+25 + 2.
2. There are three "minus a negative" pieces here:
- −(−2)-(-2) becomes +2+2,
- −(−4)-(-4) becomes +4+4,
- −(−6)-(-6) becomes +6+6.
3. The expression is now
1+2−3+4−5+6.1 + 2 - 3 + 4 - 5 + 6.
4. Add it in small groups so nothing slips:
(1+2)+(−3+4)+(−5+6)=3+1+1=5.(1 + 2) + (-3 + 4) + (-5 + 6) = 3 + 1 + 1 = 5.

The answer is (D) 5\boxed{\textbf{(D)}\ 5}.

Why this works

The only idea here is the sign rule: minus a negative is plus. Rewrite all the signs first, then add in short groups. On the first problem of the contest, being careful matters much more than being fast.

The trap

Treating every minus sign as plain subtraction, getting 1 - 2 - 3 - 4 - 5 - 6 = -19 or another large negative number.

Concise solution

Each "minus a negative" becomes a plus:
1−(−2)−3−(−4)−5−(−6)=1+2−3+4−5+6.1 - (-2) - 3 - (-4) - 5 - (-6) = 1 + 2 - 3 + 4 - 5 + 6.
Group the terms in convenient pairs: (1+2)+(−3+4)+(−5+6)=3+1+1=5(1+2) + (-3+4) + (-5+6) = 3 + 1 + 1 = 5.

The answer is (D) 5\boxed{\textbf{(D)}\ 5}.

Review in the AoPS books

Techniques

Set up the equation/formula and compute; no special trick needed