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 – Creator of greenlighttestprep.com

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