GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 May 2020, 20:10

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Intern
Status: What to know what someone's dream looks like? Observe a large pile of GMAT books. (c)
Joined: 30 Sep 2010
Posts: 24
The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

09 Oct 2010, 07:16
3
00:00

Difficulty:

5% (low)

Question Stats:

86% (01:09) correct 14% (00:59) wrong based on 346 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 64144
Re: Basic Arithmetic Question (Consecutive Integers)  [#permalink]

### Show Tags

09 Oct 2010, 07:21
4
2
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

Posted from GMAT ToolKit

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

_________________
##### General Discussion
Intern
Status: What to know what someone's dream looks like? Observe a large pile of GMAT books. (c)
Joined: 30 Sep 2010
Posts: 24
Re: Basic Arithmetic Question (Consecutive Integers)  [#permalink]

### Show Tags

09 Oct 2010, 07:23
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]

Posted from GMAT ToolKit
Math Expert
Joined: 02 Sep 2009
Posts: 64144
Re: Basic Arithmetic Question (Consecutive Integers)  [#permalink]

### Show Tags

09 Oct 2010, 07:26
3
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]

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.
_________________
Intern
Status: What to know what someone's dream looks like? Observe a large pile of GMAT books. (c)
Joined: 30 Sep 2010
Posts: 24
Re: Basic Arithmetic Question (Consecutive Integers)  [#permalink]

### Show Tags

09 Oct 2010, 09:13
That helps tremendously. It is these little synaptic peculiarities that make the most difference.

Posted from GMAT ToolKit
Intern
Joined: 29 May 2012
Posts: 1
Re: Basic Arithmetic Question (Consecutive Integers)  [#permalink]

### Show Tags

13 Sep 2012, 06:17
3
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
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16724
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

22 May 2015, 22:23
2
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

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 23 Oct 2016
Posts: 54
GMAT 1: 770 Q50 V47

### Show Tags

28 Aug 2017, 05:13
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.

Math Expert
Joined: 02 Sep 2009
Posts: 64144
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

28 Aug 2017, 06:17
1
grahamtandrew wrote:
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.

Merging topics.

"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.

_________________
Manager
Joined: 23 Oct 2016
Posts: 54
GMAT 1: 770 Q50 V47
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

28 Aug 2017, 07:39
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?

Sent from my iPhone using GMAT Club Forum
Math Expert
Joined: 02 Sep 2009
Posts: 64144
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

28 Aug 2017, 07:42
1
grahamtandrew wrote:
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?

Sent from my iPhone using GMAT Club Forum

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.
_________________
Manager
Joined: 23 Oct 2016
Posts: 54
GMAT 1: 770 Q50 V47
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

28 Aug 2017, 08:19
Bunuel wrote:
grahamtandrew wrote:
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?

Sent from my iPhone using GMAT Club Forum

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.

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
...

VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1090
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

28 Aug 2017, 09:26
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

Sent from my ONE E1003 using GMAT Club Forum mobile app
Manager
Joined: 23 Oct 2016
Posts: 54
GMAT 1: 770 Q50 V47
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

28 Aug 2017, 09:59
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

Sent from my iPhone using GMAT Club Forum
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

31 Aug 2017, 09:16
1
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

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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 23 Oct 2016
Posts: 54
GMAT 1: 770 Q50 V47
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

31 Aug 2017, 09:31
JeffTargetTestPrep,

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

Sent from my iPhone using GMAT Club Forum
Senior Manager
Status: eternal student
Joined: 06 Mar 2018
Posts: 324
Location: Kazakhstan
Concentration: Technology, General Management
Schools: Stanford
GPA: 3.87
Re: The sum of three consecutive integers is 312. What is the  [#permalink]

### Show Tags

15 Mar 2020, 06:28
EMPOWERgmatRichC wrote:
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

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

EMPOWERgmatRichC thank you!
_________________
My SC approach flowchart
My Verbal Flashcards

(no one is ideal, please correct if you see any mistakes or gaps in my explanation, it will be helpful for both of us, thank you)

___________________
"Nothing in this life is to be feared, it is only to be understood"
~ Marie Curie
Re: The sum of three consecutive integers is 312. What is the   [#permalink] 15 Mar 2020, 06:28