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2020 AMC 10B Problem 1

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2020 AMC 10B Problem 1AMC 10 Step by Step
Name:                             Date: September 13, 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

Subtracting a negative is adding, so the expression is 1 + 2 - 3 + 4 - 5 + 6, which pairs up neatly.

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}.

Why this works

The only content is the sign rule a−(−b)=a+ba - (-b) = a + b. Once the signs are cleaned up, grouping the terms into small pairs keeps the running total trivial and prevents slips. On the first problem of a contest, accuracy matters far more than speed.

The trap

Treating every minus sign as subtraction and computing 1 - 2 - 3 - 4 - 5 - 6 = -19 or a similar large negative.

Common mistakes

  • Treating every minus sign as subtraction and computing 1 - 2 - 3 - 4 - 5 - 6 = -19 or a similar large negative.
  • Flipping the signs of the positive terms as well, which produces −1+2+3+4+5+6=19-1 + 2 + 3 + 4 + 5 + 6 = 19 or 2121, choice (E).

Techniques

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