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If S denotes the sum of the integers from 1 to 30, inclusive and t den

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Bunuel
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If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   11 Dec 2018, 00:28
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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?

A. 800
B. 900
C. 1000
D. 1100
E. 1200
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Archit3110
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If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   Updated on: 12 Dec 2018, 06:37
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Bunuel 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?

A. 800
B. 900
C. 1000
D. 1100
E. 1200



sn= n/2 ( 2a+(n-1)d)

1-30

30/2 ( 2*1+(29)*1)
= 465

similarly for 31-60
n= 60-31+1 = 30
so
30/2(2*31+29*1)

1365

difference 1365-465 = 900 IMO B

Originally posted by Archit3110 on 11 Dec 2018, 04:01.
Last edited by Archit3110 on 12 Dec 2018, 06:37, edited 1 time in total.
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hibobotamuss
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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   12 Dec 2018, 05:55
Archit3110 why have you taken A to be 30 and not 31 for the second calculation? Here: 30/2(2*30+29*1)
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Archit3110
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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   12 Dec 2018, 06:00
hibobotamuss wrote:
Archit3110 why have you taken A to be 30 and not 31 for the second calculation? Here: 30/2(2*30+29*1)


No of digits would be (60-31) +1 : 30..

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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   12 Dec 2018, 06:02
Archit3110 Yes but isnt a suppose to be the first term in the formula and not the number of terms?
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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   12 Dec 2018, 06:02
30/2(2*31+29*1) Shouldnt it be this?
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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   12 Dec 2018, 06:14
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Okay, one way to go about this is using big formulae for arithmetic progressions.

Let us see another way. :-D

t = 31+ 32 + ..+ 59 + 60
s = 1 + 2 + ... + 29 + 30

So t -s = (31 - 1) + ( 32 - 2) + ... + (59 - 29) + (60 - 30)
30 terms and each equals 30

Hence t - s = 30*30 = 900

Option (B) is our bet.

Best,
Gladi

Bunuel 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?

A. 800
B. 900
C. 1000
D. 1100
E. 1200
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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   12 Dec 2018, 06:29
hibobotamuss wrote:
Archit3110 Yes but isnt a suppose to be the first term in the formula and not the number of terms?


Formula is
sn= n/2 ( 2a+(n-1)d)

a first term which, n no of terms and d is difference between in series amongst two no which should be same

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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   12 Dec 2018, 06:32
Exactly, and here the first term is 31, so why have you taken it as 30?
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If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   12 Dec 2018, 06:38
hibobotamuss wrote:
Exactly, and here the first term is 31, so why have you taken it as 30?


It was a typo .. edited ?
Total stays same so does the answer... ,

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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   30 Jun 2020, 05:13
set S = 1 to 30 total 30 terms n= number of terms a = first term l= last term
sum of AP= n/2 (a +l ) = 30/2 (1+30)=15*31=465
set T = 31 to 60 total 30 terms
sum of AP=n/2(a+l)=30/2 (31+60)=15*91=1365

T-S=1365-465=900

ANS : B
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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink] New post   11 Jun 2023, 02:07
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Re: If S denotes the sum of the integers from 1 to 30, inclusive and t den [#permalink]
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