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If s denotes the sum of the integers from 1 to 30, inclusive

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If s denotes the sum of the integers from 1 to 30, inclusive [#permalink] New post 15 May 2018, 09:03
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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?


[Reveal] Spoiler:
900


src: orbit test prep
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Re: If s denotes the sum of the integers from 1 to 30, inclusive [#permalink] New post 15 May 2018, 20:25
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I got the answer right but anyone still have a method? The way I thought this would be is when we subtract s from t, each integer would come down to 30. For example, since it is (1+2+3...+30) - (31+32+33...60), subtract 1 from 31, 2 from 32, 3 from 33.. 30 from 60, etc. Now we are left with 30 30s. So 30x30=900.
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Re: If s denotes the sum of the integers from 1 to 30, inclusive [#permalink] New post 15 May 2018, 21:01
Your approach is fine. This is one method you could apply for the answer.
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Re: If s denotes the sum of the integers from 1 to 30, inclusive [#permalink] New post 15 Jan 2020, 16:50
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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?


[Reveal] Spoiler:
900


src: orbit test prep


s = 1 + 2 + 3 + 4 + ..... + 29 + 30
t = 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
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: If s denotes the sum of the integers from 1 to 30, inclusive   [#permalink] 15 Jan 2020, 16:50
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