M7MBA wrote: ↑Thu Dec 17, 2020 11:43 am
If the sum of the first \(30\) positive odd integers is \(k,\) what is the sum of the first \(30\) non-negative even integers?
A. \(k-29\)
B. \(k-30\)
C. \(k\)
D. \(k+29\)
E. \(k+30\)
Answer:
B
Solution:
The first 30 positive odd integers are: 1, 3, 5, …, 59.
The first 30 non-negative even integers are: 0, 2, 4, …, 58.
We see that each of the first 30 non-negative even integers is 1 less than its counterpart in the first 30 positive odd integers. Therefore, the sum of the first 30 non-negative even integers will be 30 x 1 = 30 less than the sum of the first 30 positive odd integers. Since the sum of the first 30 positive odd integers is given to be k, the sum of the first 30 non-negative even integers is therefore k - 30.
Answer: B
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