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The sum of three consecutive integers is 312. What is the

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The sum of three consecutive integers is 312. What is the [#permalink] New post 09 Oct 2010, 08:16
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The sum of three consecutive integers is 312. What is the sum of the next three consecutive integers?

A) 315
B) 321
C) 330
D) 415
E) 424
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Re: Basic Arithmetic Question (Consecutive Integers) [#permalink] New post 09 Oct 2010, 08:21
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Robiou wrote:
The sum of three consecutive integers is 312. What is the sum of the next three consecutive integers?

A) 315
B) 321
C) 330
D) 415
E) 424

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a+(a+1)+(a+2)=3a+3=312;
(a+3)+(a+4)+(a+5)=(3a+3)+9=312+9=321.

Answer: B.
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Re: Basic Arithmetic Question (Consecutive Integers) [#permalink] New post 09 Oct 2010, 08:23
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?

[url=Posted from [url= ToolKit[/color][/url]

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Re: Basic Arithmetic Question (Consecutive Integers) [#permalink] New post 09 Oct 2010, 08:26
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Robiou wrote:
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?

[url=Posted from [url= ToolKit[/color][/url]

Image Posted from GMAT ToolKit


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.

Hope it helps.
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Re: Basic Arithmetic Question (Consecutive Integers) [#permalink] New post 09 Oct 2010, 10:13
That helps tremendously. It is these little synaptic peculiarities that make the most difference.

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Re: Basic Arithmetic Question (Consecutive Integers) [#permalink] New post 13 Sep 2012, 07:17
I solved this in a little different way

The sum of three consecutive (x+y+Z) = 312
Average = 312/3 = 104,
x = 103, y= 104 & z= 105
sum of next three numbers = 106+107+108 = 321
Re: Basic Arithmetic Question (Consecutive Integers)   [#permalink] 13 Sep 2012, 07:17
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