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Chapter 10: Problem 8

Quantity \(\mathbf{A}\) The greatest number of consecutive nonnegative integers which have a sum 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
Maximal sum of consecutive numbers less than 22 is achieved for n=6 (the integers from 0 to 6 sum up to 21 which is less than 22). Thus, Quantity A is equal to Quantity B, and hence the correct answer is 'C. The two quantities are equal'.

Step by step solution

01

Determine Quantity A

To determine quantity A, we have to add up consecutive nonnegative integers starting from 0 (i.e., 0, 1, 2, 3, ....), until the sum becomes just less than 22. This essentially means summing up the first 'n' integers, given by the formula \(\frac{n(n+1)}{2}\), where 'n' is the number of terms. To find 'n', you can continue adding consecutive integers starting from zero until the sum becomes less than 22. The number of terms added will then give 'n'.
02

Evaluate Quantity B

Quantity B is already given as 6.
03

Compare Quantity A and Quantity B

After finding the value of Quantity A (which is the maximum number of consecutive integers that can be added up to a sum less than 22) and having Quantity B as 6, you need to compare these two quantities.

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Most popular questions from this chapter

Quantity_A \(4\left(\frac{1}{2} x+2 y\right)\) Quantity \(\mathbf{B}\) \(2 x+8 y\) 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.

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