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My confusion with this question comes from the explanation given (Kaplan Math Workbook).

They state that we can set up the problem as follows:

x + (x+1) + (x+2) = 312 = 3x + 3

therefore, the next three integers would be:

(x+3) + (x+4) + (x+5) = 3x + 12.

12 is 9 greater than 3 from the previous equation so:

3x + 12 = 312 + 9, or 321.

However, what dictates that the consecutive integers have to be single digit increments. Doesn't consecutive integers also include 2,4,6 and 3,6,9? That would change the whole answer. What am I missing?

My confusion with this question comes from the explanation given (Kaplan Math Workbook).

They state that we can set up the problem as follows:

x + (x+1) + (x+2) = 312 = 3x + 3

therefore, the next three integers would be:

(x+3) + (x+4) + (x+5) = 3x + 12.

12 is 9 greater than 3 from the previous equation so:

3x + 12 = 312 + 9, or 321.

However, what dictates that the consecutive integers have to be single digit increments. Doesn't consecutive integers also include 2,4,6 and 3,6,9? That would change the whole answer. What am I missing?

When we see "consecutive integers" it ALWAYS means integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, ....

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.

Re: The sum of three consecutive integers is 312. What is the [#permalink]
10 Oct 2013, 09:01

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Re: The sum of three consecutive integers is 312. What is the [#permalink]
21 May 2015, 02:04

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Re: The sum of three consecutive integers is 312. What is the [#permalink]
22 May 2015, 22:23

Expert's post

Hi All,

This question can be solved in a number of different ways, depending on what type of logic/math you find easiest to deal with. There is a great 'logic pattern' here that can help you to avoid almost all of the math....

We're told that the sum of three consecutive integers is 312. We're asked for the sum of the next three consecutive integers....

Since the numbers are consecutive, we know that each number is 1 greater than the number that comes immediately before it. By extension, the 4th number is 3 greater than the 1st number, the 5th number is 3 greater than the 2nd number and the 6th number is 3 greater than the 3rd number.

If we call the three integers A, B and C, the next three integers would be A+3, B+3, and C+3. Thus, the sum of the next 3 numbers is 3+3+3 = 9 greater than the sum of A, B and C.

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