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Chapter 10: Problem 8

Quantity \(\mathbf{A}\) The greatest number of distinct nonnegative consecutive integers whose sum is less than 22 Quantity_B 6 a. Quantity A is greater b. Quantity B is greater c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
\(\mathbf{A}\) > \(\mathbf{B}\), hence the answer is (a). Quantity A is greater.

Step by step solution

01

Understand the problem

This step involves understanding the question. It asks for the greatest number of distinct nonnegative consecutive integers that can be added together without their sum exceeding 22.
02

Try to solve the problem

Start with the smallest nonnegative integer, which is 0. Add consecutive integers 1, 2, 3, 4, 5, 6 and 7 to 0 but stop at 7. Because adding another consecutive number (8) would result in the sum exceeding 22. Check the sum: 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28, which is greater than 22. Therefore, 7 is not included and the series stops at 6. This means the series of nonnegative integers are 0, 1, 2, 3, 4, 5 and 6.
03

Determine the quantity

The distinct nonnegative consecutive integers that have a sum less than 22 are 0, 1, 2, 3, 4, 5 and 6. This shows one have 7 different number of nonnegative distinct integers. Therefore, Quantity A is 7.

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