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If the sum of the last 3 integers in a set of 7 consecutive integers

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jlgdr
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If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink] New post   20 Sep 2013, 16:29
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If the sum of the last 3 integers in a set of 7 consecutive integers is 258, what is the sum of the first 4 integers?

A. 84
B. 114
C. 230
D. 246
E. 330
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Re: If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink] New post   20 Sep 2013, 16:37
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Let x, x+1,x+2 be the sum of last 3 consecutive integers which equals 258. X is thus 255/3=85. The other 4 nos are 81,82,83,84. Kudo me if you like the answer.
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Re: If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink] New post   20 Sep 2013, 16:38
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jlgdr wrote:
If the sum of the last 3 integers in a set of 7 consecutive integers is 258, what is the sum of the first 4 integers?

Any fast approaches are more than welcome.


Say 7 consecutive integers are x-3, x-2, x-1, x, x+1, x+2, x+3.

The sum of the last 3 integers = (x+1) + (x+2) + (x+3) = 3x + 6 = 258 --> x = 84
The sum of the first 4 integers = (x-3) + (x-2) + (x-1) + x = 4x - 6 = 330.
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Re: If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink] New post   11 Dec 2013, 16:53
tapanrajurkar wrote:
Let x, x+1,x+2 be the sum of last 3 consecutive integers which equals 258. X is thus 255/3=85. The other 4 nos are 81,82,83,84. Kudo me if you like the answer.


Trying to get more creative than this. :-D

Cheers!
J :)
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Re: If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink] New post   01 Jan 2018, 02:50
the middle number in the last 3 numbers = 258/3 = 86 ==> the last 3 numbers are:85, 86, 87
the first 4 numbers are: 81, 82, 83, 84
the sum of the first 4 integers: 81+82+83+84= 330
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Re: If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink] New post   01 Jan 2018, 23:43
jlgdr wrote:
If the sum of the last 3 integers in a set of 7 consecutive integers is 258, what is the sum of the first 4 integers?

Any fast approaches are more than welcome.


let x=first integer
258=3x+15
x=81
mean of first four integers=82.5
4*82.5=330
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Re: If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink] New post   14 Feb 2020, 09:11
jlgdr wrote:
tapanrajurkar wrote:
Let x, x+1,x+2 be the sum of last 3 consecutive integers which equals 258. X is thus 255/3=85. The other 4 nos are 81,82,83,84. Kudo me if you like the answer.


Trying to get more creative than this. :-D

Cheers!
J :)


Any set of consecutive integers (evenly spaced) has Mean = Med. So sum of the last 3 integers is 258 --> Med = Mean = 258/3 = 86. Then, u can easily find that the set is 81,82,83,84,85,86,87. Calculate the sum of the first 4 integers --> 330

Hope this helps.
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Re: If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink] New post   17 Feb 2020, 13:40
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Re: If the sum of the last 3 integers in a set of 7 consecutive integers [#permalink]
17 Feb 2020, 13:40
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