AMC 8 Daily Practice Round 9

Complete problem set with solutions and individual problem pages

Problem 20 Medium

Given that the \text{L.C.M.} of 2 consecutive even numbers is 10 times of the larger number. What is the square difference between these two integers?

  • A.

    12

  • B.

    28

  • C.

    60

  • D.

    76

  • E.

    84

Answer:E

Let a be half of the larger integer.

2\times a\times (a-1)=2\times a\times 10

~~~~~~~~~~~~~~~~~a-1=10

~~~~~~~~~~~~~~~~~~~~~~~~a=11，

∴ These two integers are 20 and 22.

{{22}^{2}}-{{20}^{2}}

=84

The answer is \text{E}.

Related Problems
Problem 18 AMC 8 Daily Practice Round 9
Problem 19 AMC 8 Daily Practice Round 9
Problem 21 AMC 8 Daily Practice Round 9
Problem 22 AMC 8 Daily Practice Round 9
Think Academy Powered by ChatGPT