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

Question

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

Bunuel · Accepted Answer

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

Answer: B.

anasahmed · Answer

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

Robiou · Answer

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?

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Bunuel · Answer

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.

Robiou · Answer

That helps tremendously. It is these little synaptic peculiarities that make the most difference.

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EMPOWERgmatRichC · Answer

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.

A+B+C = 312
312 + 9 = 321

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

grahamtandrew · Answer

In my life, I have used the word consecutive to refer to things that follow immediately after another. For example, I would have said that 3,4,5 are consecutive integers but that 3,5,7 are not consecutive.

Kaplan math workbook defines consecutive as: a list of numbers is consecutive if the numbers occur either at a fixed interval, or exhibit a fixed pattern. Thant implies 3,5,7 are consecutive. Kaplan gives an example of consecutive numbers: -6,-4,-2,0,2,4.

I've been trying to get used to this new definition. However, in the math workbook (9th edition page 32) Kaplan has the following question:

The sum of three consecutive integers is 312. What is the sum of the next three consecutive integers?
-315
-321
-330
-415
-424

I saw this problem and thought, I can solve this if I use my old definition of consecutive (following immediately after another) but using the definition Kaplan gave me (occurring at regular intervals) I do not have enough information to solve this.

Am I missing something? What do I do about this? Help appreciated.

Bunuel · Answer

Merging topics.

Your doubt is addressed above:
"Consecutive integers" ALWAYS mean integers that follow each other in order with common difference of 1:  ... x-3, x-2, x-1, x, x+1, x+2, ... .

For example:

-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 .

So, you are right and Kaplan is not.

P.S. Please follow  the rules  when posting a question.

grahamtandrew · Answer

Thanks for taking the time to respond and help me out. I still am a little confused though.

I'm trying to understand if consecutive means "immediately following on another" or "intervaled". If you're telling me that consecutive integers means "immediately following eachother intervals" than should I assume that consecutive means "immediately following"? Or should I assume that consecutive means "intervaled" but that placing the word integers after consecutive alters (or adds specificity to) the definition of consecutive to imply the "immediately following" portion of the definition?

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Bunuel · Answer

I think I answered this above.

"Consecutive integers" ALWAYS mean integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, ....

..., -3, -2, -1, 0, 1, 2, 3, 4, ... are consecutive integers.

grahamtandrew · Answer

Thanks again for reiterating the meaning of the phrase "consecutive integers." I think I have a very clear picture of what that phrase means. What I was asking in the last question was more of what does "consecutive" mean. If the phrase "consecutive integers" means "integers immediately following one another" then I could infer that consecutive means "immediately following one another." However, that is a clear contradiction to what Kaplan says. So another explanation could be that consecutive means "in regular intervals" but that the phrase "consecutive integers" is commonly understood to add additional specificity and that the phrase implies the immediately following.
 
Essentially there are a whole bunch of phrases that could involve the word consecutive:

consecutive integers (which thanks to you I know it means immediately following one another integers)
consecutive numbers
a, b, and c are consecutive
...

I still want to know the meaning of the word consecutive. If anyone knows, please help.

arvind910619 · Answer

The answer is B 
Let the number be X ,X+1,X+2 
Their sum =312
3x+3=312
x=103 
So next three numbers are 106,107,108 so their sum equals =321

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grahamtandrew · Answer

Arvind thanks but I think we all know how to solve the problem. The question is more on the definition of consecutive and how it applies to other questions. The question was what "consecutive integer" means but Bunuel cleared that up. Now we just need someone who know what consecutive means

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JeffTargetTestPrep · Answer

We can create the following equation:

x + x + 1 + x + 2 = 312

3x + 3 = 312

3x = 309

x = 103

So, the sum of the next three integers is 106 + 107 + 108 = 321.

Alternate Solution:

If the sum of x, x + 1, and x + 2 is 312, then the sum of x + 3, x + 4, and x + 5 will be 9 more than 312, since each integer in the second list is 3 more than the corresponding integer in the first list. Thus, the sum of the next three integers is 312 + 9 = 321.

Answer: B

grahamtandrew · Answer

JeffTargetTestPrep,

I think everyone in this thread knows how to solve the problem. The discussion is on the meaning of consecutive. Thanks anyway

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GKomoku · Answer

EMPOWERgmatRichC thank you!

HWPO · Answer

Bunuel  , would you explain why the following won't work, please?

X + (X+1) + (X+2) = 312

(X+4) + (X+5) + (X+6) =  ?

Each of the terms in the second equation is +4 from the first equation so altogether +12. Why wouldn't it be 324?

sumit0011 · Answer

Using Vedic Maths, we can solve the problem as follows:

Let's assume the first consecutive integer as x.
The second consecutive integer will be x + 1.
The third consecutive integer will be x + 2.

According to the problem, the sum of these three consecutive integers is 312. So, we can write the equation as:

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

Simplifying the equation, we have:

3x + 3 = 312

Subtracting 3 from both sides, we get:

3x = 309

Dividing both sides by 3, we find:

x = 103

Therefore, the first consecutive integer is 103, the second consecutive integer is 104, and the third consecutive integer is 105.

Bunuel · Answer

If three consecutive integers are x, x + 1, and x + 2, the next three will be x + 3, x + 4, and x + 5. So, we'd have 312 + 3*3 = 321.

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

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