M7MBA wrote: ↑Sun Jun 27, 2021 12:15 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
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
