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If the sum of the last 3 integers in a set of 6 consecutive

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If the sum of the last 3 integers in a set of 6 consecutive [#permalink]

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If the sum of the last 3 integers in a set of 6 consecutive integers is 624, what is the sum of the first 3 integers of the set?

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Re: If the sum of the last 3 integers in a set of 6 consecutive [#permalink]

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New post 20 Sep 2013, 15:33
jlgdr wrote:
If the sum of the last 3 integers in a set of 6 consecutive integers is 624, what is the sum of the first 3 integers of the set?


Say the 6 consecutive integers are x-3, x-2, x-1, x, x+1, x+2.

The sum of the last 3 integers = x + (x+1) + (x+2) = 3x + 3 = 624.
The sum of the first 3 integers = (x-3) + (x-2) + (x-1) = 3x -6 = (3x + 3) - 9 = 624 - 9 = 615.
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Re: If the sum of the last 3 integers in a set of 6 consecutive [#permalink]

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New post 22 Sep 2013, 02:58
jlgdr wrote:
If the sum of the last 3 integers in a set of 6 consecutive integers is 624, what is the sum of the first 3 integers of the set?


Let numbers be x, x+1, x+2,x+3,x+4, x+5.

sum of last three = 3x+12 = 624 => 3x= 612.

Sum of first three = 3x+3 = 612+3 = 615.
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Re: If the sum of the last 3 integers in a set of 6 consecutive [#permalink]

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New post 19 Jun 2017, 07:20
jlgdr wrote:
If the sum of the last 3 integers in a set of 6 consecutive integers is 624, what is the sum of the first 3 integers of the set?



To represent a consecutive series (constantly increasing by 1) let the series be

[x-3] + [x-2] + [x- 1] + x + [x+1] + [x+ 2]

x + [x+1] + [x+2] = 624

3x + 3 =624
3x = 621
x= 207

3x -6 =
3(207) -6 = 615

Thus

615

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Re: If the sum of the last 3 integers in a set of 6 consecutive [#permalink]

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New post 19 Jun 2017, 08:06
Look at the 6 consecutive integers: x, x+1, x+2, x+3, x+4, x+5.

First three: x, x+1, x+2
Last three: x+3, x+4, x+5

As we can see, every number in second series is 3 more than every corresponding number in first series. Overall difference = 3*3 = 9 (since there are three numbers in each series)

So sum of first three numbers = 624 - 9 = 615.

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Re: If the sum of the last 3 integers in a set of 6 consecutive [#permalink]

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New post 01 Jan 2018, 01:36
the middle number in the last 3 numbers = 624/3 = 208 ==> the last 3 numbers are:207, 208, 209
the first 3 numbers are: 204, 205, 206
the sum of the first 3 integers: 204+205+206= 615
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Re: If the sum of the last 3 integers in a set of 6 consecutive   [#permalink] 01 Jan 2018, 01:36
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