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

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Director
Joined: 03 Sep 2006
Posts: 789
What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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Updated on: 22 Jul 2013, 10:01
5
17
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:41) correct 24% (02:06) wrong based on 523 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

Originally posted by LM on 23 May 2007, 19:47.
Last edited by Bunuel on 22 Jul 2013, 10:01, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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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, 21:44
12
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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Director
Joined: 26 Feb 2006
Posts: 859

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23 May 2007, 20:35
1
1
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
Joined: 03 Sep 2006
Posts: 789

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23 May 2007, 20:55
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
Joined: 03 Sep 2006
Posts: 789

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23 May 2007, 21:00
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
Joined: 13 Feb 2007
Posts: 63

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23 May 2007, 22:57
1
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, 18:17
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, 09:57
3
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
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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, 09:59
By the way,

Difficulty: 500-600
Tag: Consecutive Integers
Source: Manhattan GMAT
OA:
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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, 12:19
2
2
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
Manager
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Posts: 81

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07 Aug 2013, 06:41
1
1
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.
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Re: What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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07 Aug 2013, 09:10
1
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
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Re: What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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07 Aug 2013, 09:28
1
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.
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Schools: Berkeley Haas
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Re: What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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31 Mar 2014, 10:48
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
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Re: What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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13 Feb 2015, 11:20
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.
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Re: What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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05 Sep 2016, 18:10
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

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

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05 Sep 2016, 21:23
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

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

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Updated on: 13 Sep 2018, 02:52
1
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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Originally posted by LogicGuru1 on 05 Sep 2016, 23:39.
Last edited by LogicGuru1 on 13 Sep 2018, 02:52, edited 1 time in total.
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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, 01:26
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]

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19 Jun 2017, 05:16
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

We can apply an AP (Arithmetic Progression) formula for the sum of terms- this formula is applicable when a series of numbers is increasing by a fixed number (1 , 2 ,3 ...5 , 10 ,15.....120, 140, 160 etc). Where this formula wouldn't work is with a series of randomly increasing numbers such as 7, 11, 15. But anyways here is the formula

N= number of items in the series

n/2 (First term + Last term) = Sum of Series

there are 9 multiples of 7 between 84 and 140 so

9/2 (84 + 140) -

Thus

"D"
Re: What is the sum of the multiples of 7 from 84 to 140, inclus &nbs [#permalink] 19 Jun 2017, 05:16

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