If the sum of the first \(30\) positive odd integers is \(k,\) what is the sum of the first \(30\) non-negative even

[M7MBA]

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

Source: e-GMAT

[Brent@GMATPrepNow]

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

Source: e-GMAT

k = 1 + 3 + 5 + 7 + . . . . . . + 57 + 59

Sum of the first 30 non-negative even integers = 0 + 2 + 4 + 6 + . . . . . . . . + 56 + 58

Notice the following: 0 + 2 + 4 + 6 + . . . . . . . . + 56 + 58 = (1 - 1) + (3 - 1) + (5 - 1) + (7 - 1) + . . . . . . . + (57 - 1) + (59 - 1)
= (1 + 3 + 5 + 7 + . . . . . . + 57 + 59) - (1 + 1 + 1 + 1 + . . . . . + 1 + 1)

ASIDE: since we're finding the sum of 30 integers, we know there are 30 1's in the sum of 1's
So, we can keep going....
= (1 + 3 + 5 + 7 + . . . . . . + 57 + 59) - (30)
= (k) - (30)

Answer: B

Cheers,
Brent