2015 AMC 8

Complete problem set with solutions and individual problem pages

Problem 14 Medium

Which of the following integers cannot be written as the sum of four consecutive odd integers?

  • A.

    16

  • B.

    40

  • C.

    72

  • D.

    100

  • E.

    200

Answer:D

Solution 1

Let our 4 numbers be n, n+2, n+4, n+6, where n is odd. Then, our sum is 4n+12. The only answer choice that cannot be written as 4n+12, where n is odd, is \boxed{\textbf{(D)} 100}.

 

Solution 2

If the four consecutive odd integers are 2n-3,~ 2n-1, ~2n+1 and 2n+3; then, the sum is 8n. All the integers are divisible by 8 except \boxed{\textbf{(D)}~100}.

Related Problems
Problem 12 2015 AMC 8
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