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Math Expert V
Joined: 02 Sep 2009
Posts: 58340
What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 65% (01:50) correct 35% (02:09) wrong based on 266 sessions

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What is the sum of all consecutive multiples of 8 between 400 and 600, inclusive?

A. 8000
B. 10,400
C. 12,500
D. 13,000
E. 15,000

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Math Expert V
Joined: 02 Aug 2009
Posts: 7957
Re: What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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Bunuel wrote:
What is the sum of all consecutive multiples of 8 between 400 and 600, inclusive?

A. 8000
B. 10,400
C. 12,500
D. 13,000
E. 15,000

Hi
400 is 8*50 and 600 is 8*75...
Average of 400 and 600= 500, extreme multiples of 8..
# of multiples of 8 =75-50+1=26..

Sum =#*avg= 26*500=13000

D
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Manager  S
Joined: 24 Oct 2013
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Location: India
Concentration: General Management, Strategy
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Re: What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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total terms = 26 - [200/8 + 1]

sum = (400+600)/2 * 26 = 13000

Option D
Manager  Joined: 29 Aug 2008
Posts: 106
Re: What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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2
2
Its a series with a difference of 8 between two consecutive terms.

400/8 = 50th Terms

600/8 = 75th Terms.

Total no of terms = 75-50+1 = 26

Sum of all = n/2(First + last term)

= 26/2(400+600) = 13,000

Option D.
Director  S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
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Re: What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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First term is 400 last term is 600. Difference is 8. n is total number of terms
Therefore 600 = 400 +(n-1)8 or n =26
Therefore the sum = n/2(first term +last term) = 26/2(400+600) =13000. Option D
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Re: What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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Bunuel wrote:
What is the sum of all consecutive multiples of 8 between 400 and 600, inclusive?

A. 8000
B. 10,400
C. 12,500
D. 13,000
E. 15,000

400/8 = 50
600/8 = 75

Thus, there are 25 multiples of 8

Now, the series of numbers is { 400 , 408 , 416 ............ 584 , 592 , 600 }

Or , the sum of the series is 8 ( 50 + 51 + 52........ 73 + 74 + 75 }

Or , the sum of the series is 8 *1625 = 13000

Thus, answer must be (D) 13000
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Target Test Prep Representative D
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Re: What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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2
Bunuel wrote:
What is the sum of all consecutive multiples of 8 between 400 and 600, inclusive?

A. 8000
B. 10,400
C. 12,500
D. 13,000
E. 15,000

We can determine the sum of all multiples of 8 between 400 and 600 inclusive using the following formula:

sum = average x quantity

The quantity is (600 - 400)/8 + 1 = 200/8 + 1 = 25 + 1 = 26.

Since we have a set of evenly spaced integers, we can calculate the average by using the following formula:

Average = (smallest multiple in the set + largest multiple in the set)/2. Thus:

Average = (400 + 600)/2 = 500

Thus, the sum is 500 x 26 = 13,000

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Manager  S
Joined: 03 Jan 2017
Posts: 135
Re: What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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n of multiplies: 600-400=200/8=25+1=26
26*(200+600)/2=1300
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Re: What is the sum of all consecutive multiples of 8 between 400 and 600,  [#permalink]

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_________________ Re: What is the sum of all consecutive multiples of 8 between 400 and 600,   [#permalink] 25 Sep 2018, 20:51
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