AMC 8 Daily Practice - Multiplication Formula

Complete problem set with solutions and individual problem pages

Problem 3 Easy

What is the value of \frac{10^{2}-9^{2}+8^{2}-7^{2}+6^{2}-5^{2}+4^{2}-3^{2}+2^{2}-1^{2}}{10+9+8+7+6+5+4+3+2+1}？

  • A.

    10

  • B.

    5

  • C.

    3

  • D.

    2

  • E.

    1

Answer:E
Solution

\frac{10^{2} - 9^{2} + 8^{2} - 7^{2} + 6^{2} - 5^{2} + 4^{2} - 3^{2} + 2^{2} - 1^{2}}{10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1}

=\frac{(10 - 9)(10 + 9) +(8 - 7)(8 + 7) + (6 - 5)(6 + 5) + (4 - 3)(4 + 3) + (2 - 1)(2 + 1)}{10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1}

=\frac{(10 + 9) +(8 + 7) + (6 + 5) + (4 + 3) + (2 + 1)}{10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1}

=1

Final Answer: \boxed{1}

Related Problems
Problem 1 AMC 8 Daily Practice - Multiplication Formula
Problem 2 AMC 8 Daily Practice - Multiplication Formula
Problem 4 AMC 8 Daily Practice - Multiplication Formula
Problem 5 AMC 8 Daily Practice - Multiplication Formula
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