It is currently 20 Jan 2018, 23:06

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The sum of the positive integers from 1 to 27 is equivalent

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Feb 2012
Posts: 215

Kudos [?]: 434 [0], given: 121

Concentration: Finance, Economics
The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

19 Aug 2013, 04:05
6
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:34) correct 44% (01:18) wrong based on 416 sessions

### HideShow timer Statistics

The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from

A. -27 to 54
B. 0 to 28
C. 15 to 45
D. 38 to 46
E. 48 to 54
[Reveal] Spoiler: OA

_________________

Kudos if you like the post!

Failing to plan is planning to fail.

Kudos [?]: 434 [0], given: 121

Senior Manager
Joined: 10 Jul 2013
Posts: 324

Kudos [?]: 436 [0], given: 102

Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

19 Aug 2013, 04:55
1
This post was
BOOKMARKED
Stiv wrote:
The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from
A -27 to 54
B 0 to 28
C 15 to 45
D 38 to 46
E 48 to 54

I give kudos to anybody who post quick and efficient way for solving the problem (< 1 min.)

Summation : 27/2 . {2 . 1 + 26 . 1} = 27 . 14

we can eliminate A because there were 27 numbers on the question and the last was 27. After this 27 numbers every number is far more than these 27 numbers. So addition of same number of numbers after 27 must not be equal .
B eliminated by sight.
C contains 31 numbers , each is bigger than 1 to 27 serially. so eliminated.

only last two worth calculation.

Now D, So 9/2 {2 . 38 + (9-1) . 1} = 9 . 42 = 9 . 3 . 14 = 27 . 14 .
it equals the summation of 1 to 27 Answer (D)
_________________

Asif vai.....

Kudos [?]: 436 [0], given: 102

Intern
Joined: 24 Jul 2013
Posts: 3

Kudos [?]: 2 [2], given: 1

Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

19 Aug 2013, 13:39
2
KUDOS
Stiv wrote:
The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from
A -27 to 54
B 0 to 28
C 15 to 45
D 38 to 46
E 48 to 54

I give kudos to anybody who post quick and efficient way for solving the problem (< 1 min.)

Sum of the integers from 1 to 27 is the average of first and last terms multiplied by # of terms. Applying that to the question stem gives you
(28/2) * (27)
-(14) * (27)
-(3 * 3 * 3 * 2 * 7).

Choice A is basically the sum of 27 - 54 which will be too big
Choice B is tempting but after applying the formula you will get (14) * (28)
Choice C will be too big as well, there are 30 terms and each term is bigger than it's corresponding term in the original sequence

Choice D looks like it could work, so apply the formula.

=(84/2) * (46 - 38 + 1)
=(42) * (9)
=(3 * 3 * 3 * 2 * 7)

Kudos [?]: 2 [2], given: 1

Non-Human User
Joined: 09 Sep 2013
Posts: 14211

Kudos [?]: 291 [0], given: 0

Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

25 Aug 2014, 22:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 291 [0], given: 0

Manager
Joined: 07 Feb 2015
Posts: 77

Kudos [?]: 21 [0], given: 28

Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

30 Aug 2015, 06:52
I need some basic help on this one. Can you not start with:

1 + 27 = 28
2 + 26 = 28
3 + 25 = 28
...
...

(28-1+1)/2 = 14 total divisions

28(14) =

Then find the prime factorization and then match that prime factorization with all the answer choices?

Kudos [?]: 21 [0], given: 28

Manager
Status: single
Joined: 19 Jan 2015
Posts: 95

Kudos [?]: 17 [0], given: 1170

Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)
Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

30 Aug 2015, 19:42
sum of consecutive positve integers =n(n+1)/2
=27*28/2
=27*14
=378.
so now we see options
in option A -27 to 54.
if we substitute -27 to 27 sum equal to 0.
thereafter 28to54 is greater than 378.
so option B is 0t0 28.
sum equal 1to 28 it is greater than 1to 27.

option C sum 15 to 45,
total number is 31. medain number is 30.
sum of consecutive no equal to median *total no of terms.
=30*31=910.

option D 38 to 46 total 9 numbers are there.
median no 42*9=378.
option E 48 to 54 total numbers 7 . median no 51*7=357.
It is less than sum.
so option D is correct.

Kudos [?]: 17 [0], given: 1170

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10724

Kudos [?]: 3780 [3], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

05 Sep 2015, 15:15
3
KUDOS
Expert's post
Hi gmatser1,

I'm going to give you a hint so that you can try this question again....

This question can be solved by 'bunching' (and a bit of pattern matching). To start, we have to figure out the sum of the integers from 1 to 27, inclusive. You are correct that you can start by 'bunching' the terms...

1+27 = 28
2+26 = 28
3+25 = 28
Etc.

Since there are 27 terms, there will be 13 'pairs' and a 'middle' term that does not get paired; the final sum will be 13(28) + 14. At this point, you can do the arithmetic in a couple of different ways.

(13)(28) + 14 =
(26)(14) + 14 =
(26)(14) + 1(14) =
(27)(14) =
378

So, you can either look for an answer that totals 378 OR you can look for an answer that can be 'bunched' into (27)(14).

Using this same type of approach, how would you work through the answer choices?

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Kudos [?]: 3780 [3], given: 173 Manager Joined: 07 Feb 2015 Posts: 77 Kudos [?]: 21 [0], given: 28 Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink] ### Show Tags 06 Sep 2015, 14:01 EMPOWERgmatRichC wrote: Hi gmatser1, I'm going to give you a hint so that you can try this question again.... This question can be solved by 'bunching' (and a bit of pattern matching). To start, we have to figure out the sum of the integers from 1 to 27, inclusive. You are correct that you can start by 'bunching' the terms... 1+27 = 28 2+26 = 28 3+25 = 28 Etc. Since there are 27 terms, there will be 13 'pairs' and a 'middle' term that does not get paired; the final sum will be 13(28) + 14. At this point, you can do the arithmetic in a couple of different ways. (13)(28) + 14 = (26)(14) + 14 = (26)(14) + 1(14) = (27)(14) = 378 So, you can either look for an answer that totals 378 OR you can look for an answer that can be 'bunched' into (27)(14). Using this same type of approach, how would you work through the answer choices? GMAT assassins aren't born, they're made, Rich Thanks! I forgot about that 13th "middle" pair. Could have found that out by mapping it out, but that would have taken way too long. In looking at the answers, the same dynamic applies with D. 46-38= 8 total numbers / 2 = 4 pairs with 42 left in the middle 38+46 = 84 39+45 = 84 40+44= 84 41+43 = 84 42 4(84) + 42 = 378 I think my original statement about prime factorization would be hard using this method. Nevermind! Kudos [?]: 21 [0], given: 28 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 10724 Kudos [?]: 3780 [1], given: 173 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink] ### Show Tags 06 Sep 2015, 18:06 1 This post received KUDOS Expert's post HI gmatser1, You mentioned in your last post how "mapping out" all of the pairs would have taken too long. I agree, but you don't really have to map them all out to see the pattern and the total. Here's how: You know that the first few 'pairs' are.... 1+27 = 28 2+26 = 28 So the 'smaller number' + the 'bigger number' will total 28. Using that logic: 1) What would be the 'bigger number' when the 'smaller number' was 13? 2) Using all of the 'smaller numbers' for reference, how many total 'pairs' would there be? 3) Once you know what 'pairs up' with 13, how hard is it to find any 'leftover' numbers? As you continue to study, you're going to find that most GMAT questions can be answered in a variety of ways. If you find that "your way" of approaching the prompt takes too long, then it might be that you're approaching the prompt in "the long way." GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3780 [1], given: 173

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7868

Kudos [?]: 18494 [4], given: 237

Location: Pune, India
Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

06 Sep 2015, 20:27
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
Stiv wrote:
The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from

A. -27 to 54
B. 0 to 28
C. 15 to 45
D. 38 to 46
E. 48 to 54

Sum of Numbers = Average * Number of numbers
If numbers are from 1 to 27, average will be the middle number 14.
Sum of numbers = 14 * 27

We need to find the option where the sum is the same.

A. -27 to 54
-27 to -1 will cancel out numbers from 1 to 27. So the sum would be the sum of numbers from 28 to 54. These will be 27 numbers but with a much higher average. So ignore this option.

B. 0 to 28
Here the sum will be 28 more than our desired sum. Ignore this option.

C. 15 to 45
Here we have 31 numbers with an average much more than 14. So the sum will be much more than the desired sum. Ignore.

D. 38 to 46
Here we have 9 numbers with an average of 42 (the middle number).
Sum = 42 * 9 = 14 * 27 (matches)

E. 48 to 54
Just to complete the calculations, let me show you how you can compare this option too.
Here we have 7 numbers with an average of 51.
Sum = 7 * 51 = 14 * 51/2 = 14 * 25.5. This is less than the desired sum.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18494 [4], given: 237

Senior Manager
Joined: 08 Jun 2015
Posts: 365

Kudos [?]: 27 [0], given: 106

Location: India
GMAT 1: 640 Q48 V29
Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

20 May 2016, 07:10
D it is ... good explanations above
_________________

" The few , the fearless "

Kudos [?]: 27 [0], given: 106

Current Student
Joined: 18 Oct 2014
Posts: 902

Kudos [?]: 472 [0], given: 69

Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

20 May 2016, 07:41
Stiv wrote:
The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from

A. -27 to 54
B. 0 to 28
C. 15 to 45
D. 38 to 46
E. 48 to 54

Sum of integers from 1 to 27= 27*28/2= 27*14 (Units digit will be 8)

A. -27 to 54
Effectively it will be sum of integers from 28 to 54 (It will definitely be greater than the sum of integers from 1 to 27)

B. 0 to 28
Integer 28 will be added more to the sum of integers from 1 to 27

C. 15 to 45
There are total 31 integers, and by looking closely at the numbers, we realize that most of the numbers are greater than 27 and hence the sum will also be greater

D. 38 to 46

By adding units digit of given numbers (8+9+0+1+2+3+4+5+6), we get 8 as the unit digit of resulting number. This is the answer.

E. 48 to 54
We do not get 8 as unit digit in this case as we got in option D
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Kudos [?]: 472 [0], given: 69

Math Expert
Joined: 02 Aug 2009
Posts: 5536

Kudos [?]: 6443 [0], given: 122

Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

20 May 2016, 08:47
Stiv wrote:
The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from

A. -27 to 54
B. 0 to 28
C. 15 to 45
D. 38 to 46
E. 48 to 54

Hi,

the property which I will use is that SUM of consecutive integers is Number of imtegers * average or center number..
sum of the positive integers from 1 to 27 = 27 * \frac{1+27}{2} = 27*14...
so the sum has to be EVEN and multiple of 7 and 27..

lets see the choices-

A. -27 to 54 --------- number of integers = 27+54+1 = 82.. this means the SUM will be multiple of PRIME 41... NO

B. 0 to 28-----------number of integers = 28+1 = 29.. this means the SUM will be multiple of PRIME 29... NO

C. 15 to 45-----------number of integers = 45-15+1 = 31.. this means the SUM will be multiple of PRIME 31... NO

D. 38 to 46-----------number of integers = 46-38+1 = 9..so we see the average now =$$\frac{46+38}{2}= 42$$..this means the SUM will be =9*42 = 9*6*7 = 27*14...YES

E. 48 to 54-----------number of integers = 54-48+1 = 7.... so we see the average now =$$\frac{48+54}{2}= 51$$..this means the SUM will be =51*7 OR an ODD number and also not a multiple of 27...NO

D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Kudos [?]: 6443 [0], given: 122

Board of Directors
Joined: 17 Jul 2014
Posts: 2719

Kudos [?]: 463 [0], given: 211

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

12 Oct 2016, 17:52
Stiv wrote:
The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from

A. -27 to 54
B. 0 to 28
C. 15 to 45
D. 38 to 46
E. 48 to 54

i did the direct way...and it took more than 2 minutes...
A -> from 1 to 27 is 27*28/2 = 378. since we have -27, it's -378. -27 is inclusive, so subtract from -378-27, and get -351. sum from 0 to 54 = 54*55/2 = 27*55 -> last digit is 5...since we would add with -351, the last digit would be 4...so not good.
B -> 0 to 28 -> 28*29/2 = 14*29 -> way too big.
C -> sum from 0 to 14 = 14*15/2 = 7*15 = XX5. 0 to 45 is 45*46 = 23*45 -> last digit is 5. since we would subtract XX5, the last digit would be 0 and not 8. out.
D -> from 0 to 37 = 37*38/2 = 37*19 = smth smth last digit =3. 46*47/2 = 23*47 -> last digit =1. hm...if XX1 - XX3 -> we'll get last digit 8..this might be the answer...
E -> from 0 to 47 = 47*48/2 = 47*29 -> last digit is 3 (smth XX3). 0 to 54 = 54*55/2 = 27*55 = XX5..last digit 5...from 5 subtract 3 and get 2..we need 8
looks like only D works!

Kudos [?]: 463 [0], given: 211

Intern
Joined: 12 Feb 2015
Posts: 37

Kudos [?]: 2 [0], given: 259

Location: India
GPA: 3.84
Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

25 Aug 2017, 23:36
The sum of consecutive integers is given by n(n+1)/2...so how to calculate as per this?

acc to me,a option says -27 to 54,in which -26 to 26 will eventually cancel and remaining sum for 27 to 53 inclusive with 27 terms comes out to be 27*28/2...27*14 which is what coming previously(in the question)

Kudos [?]: 2 [0], given: 259

Intern
Joined: 12 Feb 2015
Posts: 37

Kudos [?]: 2 [0], given: 259

Location: India
GPA: 3.84
Re: The sum of the positive integers from 1 to 27 is equivalent [#permalink]

### Show Tags

25 Aug 2017, 23:43
chetan2u wrote:
Stiv wrote:
The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from

A. -27 to 54
B. 0 to 28
C. 15 to 45
D. 38 to 46
E. 48 to 54

Hi,

the property which I will use is that SUM of consecutive integers is Number of imtegers * average or center number..
sum of the positive integers from 1 to 27 = 27 * \frac{1+27}{2} = 27*14...
so the sum has to be EVEN and multiple of 7 and 27..

lets see the choices-

A. -27 to 54 --------- number of integers = 27+54+1 = 82.. this means the SUM will be multiple of PRIME 41... NO

B. 0 to 28-----------number of integers = 28+1 = 29.. this means the SUM will be multiple of PRIME 29... NO

C. 15 to 45-----------number of integers = 45-15+1 = 31.. this means the SUM will be multiple of PRIME 31... NO

D. 38 to 46-----------number of integers = 46-38+1 = 9..so we see the average now =$$\frac{46+38}{2}= 42$$..this means the SUM will be =9*42 = 9*6*7 = 27*14...YES

E. 48 to 54-----------number of integers = 54-48+1 = 7.... so we see the average now =$$\frac{48+54}{2}= 51$$..this means the SUM will be =51*7 OR an ODD number and also not a multiple of 27...NO

D

should we always consider the range as inclusive,even when not specified?

Kudos [?]: 2 [0], given: 259

Re: The sum of the positive integers from 1 to 27 is equivalent   [#permalink] 25 Aug 2017, 23:43
Display posts from previous: Sort by