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# What is the sum of the multiples of 7 from 84 to 140, inclus

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Director
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What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink]

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23 May 2007, 20:47
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Question Stats:

77% (02:11) correct 23% (01:35) wrong based on 445 sessions

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What is the sum of the multiples of 7 from 84 to 140, inclusive?

A. 896
B. 963
C. 1008
D, 1792
E. 2016
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Jul 2013, 11:01, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Director
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23 May 2007, 21:35
LM wrote:
What is the sum of the multiples of 7 from 84 to 140, inclusive?
896
963
1008
1792
2016

Please explain some FAST SHORT method

= [(140 + 84)/2] [(140/7) - (84/7 + (1)]
= 1008
Director
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23 May 2007, 21:55
Himalayan wrote:
LM wrote:
What is the sum of the multiples of 7 from 84 to 140, inclusive?
896
963
1008
1792
2016

Please explain some FAST SHORT method

= [(140 + 84)/2] [(140/7) - (84/7 + (1)]
= 1008

Wonderful!!! Thanks a lot!! Could you please explain too?
Director
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23 May 2007, 22:00
LM wrote:
Himalayan wrote:
LM wrote:
What is the sum of the multiples of 7 from 84 to 140, inclusive?
896
963
1008
1792
2016

Please explain some FAST SHORT method

= [(140 + 84)/2] [(140/7) - (84/7 + (1)]
= 1008

Wonderful!!! Thanks a lot!! Could you please explain too?

Okayyy I got it!! you are using AP series formula!!
Manager
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23 May 2007, 23:57
all you have to do on a quick test like gmat is this:

84, 91, 98, 105, 112, 119, 126, 133, 140.

i wouldn't even list 'em out on the test.

(84 + 140) / 4.5 = answer
Director
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26 May 2007, 19:17
ethan_casta wrote:
all you have to do on a quick test like gmat is this:

84, 91, 98, 105, 112, 119, 126, 133, 140.

i wouldn't even list 'em out on the test.

(84 + 140) / 4.5 = answer

What is 4.5? Why are you dividing by 4.5 and where did you get that? How do you reach the answer with your method in short time.
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Re: What is the sum of the multiples of 7 from 84 to 140, [#permalink]

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22 Jul 2013, 10:57
2
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You could also add up the last digit of the multiples:

4 + 1 + 8 + 5 + 2 + 9 + 6 + 3 + 0 = ..8 --> last digit of solution must be 8 --> 1008 --> Answer C
Intern
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Re: What is the sum of the multiples of 7 from 84 to 140, [#permalink]

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22 Jul 2013, 10:59
By the way,

Difficulty: 500-600
Tag: Consecutive Integers
Source: Manhattan GMAT
OA:
[Reveal] Spoiler:
Intern
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Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink]

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22 Jul 2013, 13:19
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The formula we want to use in this type of problem is this:
Average*Total Numbers=Sum

First, find the average by taking the sum of the F + L number and divide it by 2:
A = (F + L)/2

Second, find the total numbers in our range by dividing our F and L numbers by 7 and add 1.
(140/7) - (84/7) + 1

Multiply these together so what we show Average*Total Numbers=Sum
(84 + 140)/2 * (140/7) - (84/7) + 1 = Sum
112 * 9 = 1008
C
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Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink]

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22 Jul 2013, 22:44
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Expert's post
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LM wrote:
What is the sum of the multiples of 7 from 84 to 140, inclusive?

A. 896
B. 963
C. 1008
D, 1792
E. 2016

Alternatively, note that 84 = 7*12 and 140 = 7*20

7*12 + 7*13 + ... 7*20 = 7*(12 + 13 + 14 .. + 20)
12 to 20 are 9 consecutive numbers so their sum will be (middle number) * 9 = 16*9 = 144

Total sum = 7*144 = 1008
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 22 Apr 2013 Posts: 88 Followers: 1 Kudos [?]: 34 [1] , given: 95 Re: simpler method [#permalink] ### Show Tags 07 Aug 2013, 07:41 1 This post received KUDOS LM wrote: ethan_casta wrote: all you have to do on a quick test like gmat is this: 84, 91, 98, 105, 112, 119, 126, 133, 140. i wouldn't even list 'em out on the test. (84 + 140) / 4.5 = answer What is 4.5? Why are you dividing by 4.5 and where did you get that? How do you reach the answer with your method in short time. It's multiply by 4.5. (84 + 140) * 9/2 == 224*4.5 == 1008 The 9 in the formula is the number of consecutive items in the list. _________________ I do not beg for kudos. Senior Manager Joined: 10 Jul 2013 Posts: 334 Followers: 3 Kudos [?]: 362 [0], given: 102 Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink] ### Show Tags 07 Aug 2013, 10:10 1 This post was BOOKMARKED LM wrote: What is the sum of the multiples of 7 from 84 to 140, inclusive? A. 896 B. 963 C. 1008 D, 1792 E. 2016 solution; (140-84)/7 = 8 so total number = 8+1 = 9 summation= 9/2 {2*84+(9-1)*7} = 1008 = C _________________ Asif vai..... Intern Joined: 05 Apr 2010 Posts: 15 Followers: 0 Kudos [?]: 12 [0], given: 4 Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink] ### Show Tags 07 Aug 2013, 10:28 1 This post was BOOKMARKED Asifpirlo wrote: LM wrote: What is the sum of the multiples of 7 from 84 to 140, inclusive? A. 896 B. 963 C. 1008 D, 1792 E. 2016 solution; (140-84)/7 = 8 so total number = 8+1 = 9 summation= 9/2 {2*84+(9-1)*7} = 1008 = C All perfect till no of terms. I suggest following for sum. sum = number of terms * (avg of first and last term) = 9 * (84+140)/2 = 1008. May help save a second or two. Manager Joined: 23 Jan 2013 Posts: 172 Concentration: Technology, Other Schools: Haas GMAT Date: 01-14-2015 WE: Information Technology (Computer Software) Followers: 3 Kudos [?]: 48 [0], given: 41 Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink] ### Show Tags 31 Mar 2014, 11:48 All numbers are consecutive and with a spacing of 7 . So average would be (140 + 84 )/2 = 112 . Sum of 9 numbers = 9 * average = 9 * 112 = 1008 Senior Manager Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 441 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Followers: 2 Kudos [?]: 122 [0], given: 169 Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink] ### Show Tags 13 Feb 2015, 12:20 If it doesn't occur to us to use the (first+last)/2 we can always go up 7, starting with 84 until 140. Adding them up wouldn't take longer. That if panic hits and we cannot think of the easiest way, which I guess would be "(first+last)/2". (first+last)/2 --> gives the mean. we know that 9 is the N. So, we then use: M= S/N --> 112 = S / 9 --> S = 9*112 --> S = 1008. GMAT Club Legend Joined: 09 Sep 2013 Posts: 15431 Followers: 649 Kudos [?]: 207 [1] , given: 0 Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink] ### Show Tags 18 Apr 2016, 22:31 1 This post received KUDOS 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. _________________ Intern Joined: 16 Jan 2016 Posts: 22 Location: United States (CA) Leonid: B Concentration: Operations, General Management GPA: 3.6 WE: Operations (Other) Followers: 0 Kudos [?]: 5 [0], given: 29 Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink] ### Show Tags 05 Sep 2016, 19:10 I do not get the 4.5 part?? all you have to do on a quick test like gmat is this: 84, 91, 98, 105, 112, 119, 126, 133, 140. i wouldn't even list 'em out on the test. (84 + 140) / 4.5 = answer Can someone please explain this? _________________ I Write... http://www.misterethoughts.blogspot.com Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7372 Location: Pune, India Followers: 2287 Kudos [?]: 15099 [0], given: 224 Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink] ### Show Tags 05 Sep 2016, 22:23 leonidbasin1 wrote: I do not get the 4.5 part?? all you have to do on a quick test like gmat is this: 84, 91, 98, 105, 112, 119, 126, 133, 140. i wouldn't even list 'em out on the test. (84 + 140) / 4.5 = answer Can someone please explain this? This is incorrect. The concept used is Sum = Average * Number of elements Average = (84+140)/2 Number of elements = 9 Sum = [(84+140)/2] * 9 = (84 + 140) * 4.5 = 1008 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Director
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What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink]

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06 Sep 2016, 00:39
LM wrote:
What is the sum of the multiples of 7 from 84 to 140, inclusive?

A. 896
B. 963
C. 1008
D, 1792
E. 2016

Lets use the simplest statistical concept:- Mean

$$Mean = \frac{Sum}{Total Terms}$$

Easy way to find mean is$$\frac{First + Last}{2}$$

$$\frac{84+140}{2} = \frac{224}{2} = 112$$

therefore
$$112= \frac{SUM}{Total Terms}$$

Total Terms are $$\frac{(Last -First)}{Gap}+ 1$$

Total Terms = $$\frac{140-84}{7} +1 = \frac{56}{7} + 1 = 8+1 = 9$$

112= $$\frac{SUM}{9}$$

SUM = 112*9 = 1008

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Re: What is the sum of the multiples of 7 from 84 to 140, inclus [#permalink]

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06 Sep 2016, 02:26
VeritasPrepKarishma wrote:
leonidbasin1 wrote:
I do not get the 4.5 part??

all you have to do on a quick test like gmat is this:

84, 91, 98, 105, 112, 119, 126, 133, 140.

i wouldn't even list 'em out on the test.

(84 + 140) / 4.5 = answer

This is incorrect.
The concept used is
Sum = Average * Number of elements

Average = (84+140)/2
Number of elements = 9

Sum = [(84+140)/2] * 9 = (84 + 140) * 4.5 = 1008

Also, check http://www.veritasprep.com/blog/2012/03 ... gressions/
It discusses the various Arithmetic Progression concepts.
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Re: What is the sum of the multiples of 7 from 84 to 140, inclus   [#permalink] 06 Sep 2016, 02:26
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