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

Question

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

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

KarishmaB · Accepted Answer

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

husker2010 · Answer

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

Himalayan · Answer

=    
= 1008

LM · Answer

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

LM · Answer

Okayyy I got it!! you are using AP series formula!!

ethan_casta · Answer

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

LM · 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.

kingflo · Answer

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

kingflo · Answer

By the way,

Difficulty: 500-600
Tag: Consecutive Integers
Source: Manhattan GMAT
OA:  Answer C

MzJavert · Answer

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.

Asifpirlo · Answer

solution;
(140-84)/7 = 8
so total number = 8+1 = 9
summation= 9/2 {2*84+(9-1)*7} = 1008 = C

coolpintu · Answer

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.

shelrod007 · Answer

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

pacifist85 · Answer

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.

(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.

leonidbasin1 · Answer

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?

KarishmaB · Answer

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

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

Sum =   * 9 = (84 + 140) * 4.5 = 1008

LogicGuru1 · Answer

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

ANSWER IS C

KarishmaB · Answer

Also, check https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/03 ... gressions/ It discusses the various Arithmetic Progression concepts.

Nunuboy1994 · Answer

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"

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards