 It is currently 22 Mar 2019, 14:14 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The sum of the consecutive integers from 2 to 13  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Moderator  Joined: 18 Apr 2015
Posts: 5862
Followers: 94

Kudos [?]: 1151 , given: 5465

The sum of the consecutive integers from 2 to 13 [#permalink]
Expert's post 00:00

Question Stats: 58% (00:39) correct 41% (00:49) wrong based on 77 sessions

 Quantity A Quantity B The sum of the consecutive integers from 2 to 15 34 less than the sum of the consecutive integers from 1 to 17

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________ Director Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 344  , given: 66

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
1
KUDOS
Carcass wrote:

 Quantity A Quantity B The sum of the consecutive integers from 2 to 13 34 less than the sum of the consecutive integers from l to 17

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

What's l in quantity B? Is it 1?
Manager  Joined: 26 Jun 2017
Posts: 104
Followers: 0

Kudos [?]: 39 , given: 38

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
I think the answer is given wrong,
for the QA-- 13-2=11 then 11/2= 5.5, so 5.5 * 15 (pair) = 82.5
for QB 1+17=18, then 17-1=16 (because no mentioning about inclusiveness), so 16/2=8 (pair) and 8*18=144, 144-36=108, B>A
_________________

What you think, you become. Intern Joined: 19 Oct 2017
Posts: 7
Followers: 0

Kudos [?]: 10  , given: 0

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
1
KUDOS
Is the answer C correct here ?
Moderator  Joined: 18 Apr 2015
Posts: 5862
Followers: 94

Kudos [?]: 1151 , given: 5465

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
Expert's post
Yes, it is C.

I give you kudos for the right answer but next time give also us your reasoning.

Regards
_________________ Intern Joined: 23 Nov 2017
Posts: 45
Followers: 0

Kudos [?]: 45  , given: 0

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
2
KUDOS
I dont see how the answer can be C.

I used Gauss equation to solve this and I even counted all numbers from 1 to 17 and from 2 to 13.

Gauss euqation:

S= (N(A + z))/2

S = sum
N = number of terms in the set
A = First number in the set
Z = final number in the set

Quantity A

s = ((12)(2 + 13))/2
s = 90

Quantity A = 90

Qunatity B

s = (17(1 + 17))/2
s = 153

153 - 34 = 119

quantity B = 119

A<B

Am I missing something obvious here? Manager Joined: 22 Feb 2018
Posts: 159
Followers: 2

Kudos [?]: 101  , given: 22

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
1
KUDOS
Some of the consecutive integers equal:
(first number + last number) * [(number of integers) / 2]
and why is that? considering the sequence 1, 2, 3, 4, 5, 6 their sum is (1+6) + (2+5) + (3+4) = 7 + 7 + 7 = 7 * 6/2 = 7 *3 = 21
a1 + a2 + a3 + .... + an-2 + an-1 + an = (an+a1) + (an-1 + a2) +....= n/2 * (an+a1)

so for the integers between 2 and 13 sum is: (2+13) * (13-2+1)/2 = 90. A equals 90.
and for integers between 1 and 17 sum is: (1+17) * 17/2 = 153 and B equals 153 - 34 = 119
so B is bigger than A.

_________________ Manager  Joined: 15 Jan 2018
Posts: 147
GMAT 1: Q V
Followers: 3

Kudos [?]: 182  , given: 0

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
1
KUDOS
(The problem has been edited since this response. In the original problem, Quantity A was the sum of integers from 2 to 13.)

There is definitely something wrong with this problem. Assuming l in quantity B means 1, the answer is given as C, but it should be B. Let's prove it. As several people have shown, you can use the average formula, or Sum/(# of items) = Ave, to find the totals of both sides. I would do it more simply in this case, without the formula.

There is a great deal of overlap between the two sides. After all, the integers 2 through 13 are contained inside the integers from 1 through 17. Let's subtract all numbers that are in both sets from both sides. So what numbers are left over? Quantity A is totally contained within Quantity B, so at this point it's got nothing left and is 0. What about Quantity B?

Quantity B has 1, 14, 15, 16, and 17, while Quantity A does not. Adding these we get 63. (A quick way to add the last four numbers would be to add 14 and 17 to get 31, and double that since 15 + 16 must be the same, to get 62, and then adding 1.) Subtracting 34 from 63 will clearly get us something bigger than 0, so the answer should be B, not C.

BONUS PROBLEM: If the answer were legitimately C, what would l have to be? The only way C could be correct is if l were not 1, but some other integer. If we set the two quantities equal to each other we will get:

90 = ((l + 17)/2)(17 - l + 1) - 34

The two parenthesis on the right represent the average of the integers and the number of integers, respectively. Next, we have:

124 = .5(l + 17)(18 - l)

248 = (l + 17)(18 - l)

This will be a quadratic equation:

248 = 18l - l^2 + 17x18 - 17l

248 = l - l^2 + 306

l^2 - l - 58 = 0

This quadratic can't be factored with integers. 8 comes closest but it doesn't quite work. So basically this proves that there is no way for the two quantities to be equal. There's probably a typo somewhere, even besides the l.
_________________

-
-
-
-
-

Need help with GRE math? Check out our ground-breaking books and app.

Last edited by SherpaPrep on 06 Mar 2018, 08:39, edited 1 time in total. Moderator  Joined: 18 Apr 2015
Posts: 5862
Followers: 94

Kudos [?]: 1151  , given: 5465

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
1
KUDOS
Expert's post
Sorry guys. Thanks for your precious replies.

there was a typo in the first quantity.

The sum of the consecutive integers from 2 to 15

Thank you so much.

Regards
_________________ Manager  Joined: 15 Jan 2018
Posts: 147
GMAT 1: Q V
Followers: 3

Kudos [?]: 182  , given: 0

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
2
KUDOS
There are several ways to go about this problem. (The new, edited one.) You can actually add up all the integers in both sides using some variation of the average formula, but this seems needlessly complicated. We can clearly see that Quantity B is mostly overlapped with Quantity A. If we subtract out every integer on both sides, we will vastly simplify the problem. Subtracting the integers from 2 to 15 on both sides leaves us with 0 under Quantity A and under Quantity B, we're left with 1, 16, and 17. These add up to 34 and since we must subtract 34 from Quantity B, we'll wind up with 0 on both sides. Thus the answer is C.
_________________

-
-
-
-
-

Need help with GRE math? Check out our ground-breaking books and app. Intern Joined: 06 Feb 2018
Posts: 8
Followers: 0

Kudos [?]: 5  , given: 1

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
1
KUDOS

Let's take option A:
Sum of consecutive integers from 2->15 is = Sum of consecutive integers from 1->15 -1 i.e (15)(15+1)/2 -1 => 119

Now option B:
Sum of consecutive integers from 1->17 is =(17)(17+1)/2 => 153, 153-34 =>119

Thus, C Manager Joined: 27 Feb 2017
Posts: 189
Followers: 0

Kudos [?]: 49  , given: 15

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
1
KUDOS
so first, in option B, it is 1 to 17. About solving the problem, we do not want to waste much time on test day and also get the right answer. So think this way- both A and B have a set in common that is 2 to 15. Now, the remaining number in B are 1+16+17 which equals 34. So when we subtract 34 from sum of 1 to 17, as given, we will get the same answer as sum of 2 to 15.
Intern Joined: 14 Jun 2018
Posts: 36
Followers: 0

Kudos [?]: 7 , given: 100

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
Carcass wrote:
Sorry guys. Thanks for your precious replies.

there was a typo in the first quantity.

The sum of the consecutive integers from 2 to 15

Thank you so much.

Regards

According to the rule: sum of consecutive integers is a1+an/2 * n. So quantity A will be as follows:

Quant A: (2+15)/2 * 14 = 119 not 119.

Quant B: (1+17)/2 * 17 = 153 - 35 = 119.

Answer should not be equal?

Last edited by Avraheem on 14 Jul 2018, 00:51, edited 1 time in total. Intern  Joined: 04 May 2017
Posts: 36
Followers: 0

Kudos [?]: 22  , given: 6

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
1
KUDOS
Apply the formula for sum of a arithmetic progression (https://www.wikiwand.com/en/Arithmetic_progression#/Sum)

QA = (2+15)/2*(12-2+1) = 109 = QB = (17+1)/2*17-34 = 109

-> C.
_________________

Do not pray for an easy life, pray for the strength to endure a difficult one - Bruce Lee Intern Joined: 09 Jul 2018
Posts: 10
Followers: 1

Kudos [?]: 10  , given: 0

Re: The sum of the consecutive integers from 2 to 13 [#permalink]
2
KUDOS
Quote:
 Quantity A Quantity B The sum of the consecutive integers from 2 to 15 34 less than the sum of the consecutive integers from l to 17

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

B = [1 + (the sum of the consecutive integers from 2 to 15) + 16 + 17] - 34.
Since the values in red all cancel out, we get:
B = the sum of the consecutive integers from 2 to 15.
Thus, A and B are equal.

[Reveal] Spoiler:
C

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY at gmail
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY at gmail Re: The sum of the consecutive integers from 2 to 13   [#permalink] 09 Jul 2018, 08:15
Display posts from previous: Sort by

# The sum of the consecutive integers from 2 to 13  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.