amorphous wrote:
If s denotes the sum of the integers from 1 to 30, inclusive and t denotes the sum of the integers from 31 to 60 inclusive. What is t-s?
src: orbit test prep
s = 1 + 2 + 3 + 4 + ..... + 29 + 30t = 31 + 32 + 33 + 34 + ..... + 59 + 60
Notice that we can rewrite the second equation as follows:
t = (30 +
1) + (30 +
2) + (30 +
3) + (30 +
4) + ......+ (30 +
29) + (30 +
30)
In other words, t = (30 + 30 + 30 + 30 + 30 ... + 30 + 30) + (
1 + 2 + 3 + 4 + ..... + 29 + 30)
IMPORTANT: To determine the number of 30's in the above sum, we need to use the following useful formula:
The number of integers from x to y inclusive equals y - x + 1 So, the number of integers from 31 to 60 inclusive equals 60 - 31 + 1 = 30
This means there are thirty 30's in the above sum.
That is: t = (30)(30) + (
1 + 2 + 3 + 4 + ..... + 29 + 30)
So, t - s = [(30)(30) + (
1 + 2 + 3 + 4 + ..... + 29 + 30)] - [
1 + 2 + 3 + 4 + ..... + 29 + 30]
= (30)(30)
= 900
Answer: 900
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep