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## multiples of 7

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 6 member replies
j_shreyans Legendary Member
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#### multiples of 7

Mon Sep 08, 2014 10:17 pm
What is the sum of the multiples of 7 from 84 to 140, inclusive?

A)896
B)963
c)1008
D)1792
E)2016

OAC

How to approach this kind of question?

Joined
30 Aug 2017
Posted:
27 messages
Tue Sep 05, 2017 9:44 pm
j_shreyans 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

OAC

How to approach this kind of question?
Solution:

Sum of the multiples of 7 from 84 to 140, inclusive,
84 + 91 + 98 + 105 + ... +140

This above series represents an arithmetic series with a common difference d = 7.
We know that sum of a finite arithmetic series can be calculated using the formula,

Sum = (First term + Last term)(n/2) where n is the number of terms in the series.
Therefore, to find sum, we need to find the number of terms in the series above.

We know that the terms in the arithmetic sequence are the multiples of 7. Therefore,
First term = 84 = 7 x 12 = 12th multiple of 7
Last term = 140 = 7 x 20 = 20th multiple of 7

The number of terms in the series 84 + 91 + 98 + 105 + ... +140
= 9 (84 and 140 inclusive)
Therefore, n = 9

Now,
Sum = (First term + Last term)(n/2)
Sum = (84 + 140)(9/2)
Sum = (224)(9/2)
Sum = (224 x 9) / 2
Sum = 2016 / 2
Sum = 1008

Therefore, Option C is the correct answer.

Joined
30 Aug 2017
Posted:
27 messages
Tue Sep 05, 2017 9:58 pm
A streamlined solution:
84 / 7 = 12
140 / 7 = 20
So, it would be seven multiple of 12, 13, 14, 15, 16, 17, 18, 19 and 20.
Thus the sum of the multiples of 7 from 84 to 140, inclusive, is:
7(12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20) = 7 (144) = 1008.

abhasjha Master | Next Rank: 500 Posts
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Mon Sep 08, 2014 10:27 pm
This question tests your knoweldge of AP series

84 = 12x7 .. so 84 is 12the term
140= 20 X7 ..... 140 is 20th term ....

so total number of terms between 84 and 140 = 9 . ( using the formula total numbers between b and a inclusisve is( b-a ) +1

now the sum of an AP series is... n/2 ( first term + last Term ) = 9/2 (84 +140 ) = 1008

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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GMAT Score:
770
Mon Sep 08, 2014 10:30 pm
j_shreyans 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

In other words, 84 + 91 + 98 + . . . 140 = ?

Since the values are EQUALLY SPACED, we can use the rule: SUM = [(FIRST + LAST)/2][# of values]

NUMBER of values
Here's a nice rule: If x and y are multiples of k, then the number of multiples of k from x to y inclusive = [(y-x)/k] + 1
So, for example, the NUMBER multiples of 3 from 6 to 21 inclusive = [(21 - 6)/3] + 1 = [15/3] + 1 = 6

So, the NUMBER multiples of 7 from 84 to 140 inclusive = [(140 - 84)/7] + 1
= [56/7] + 1
= 9

------------------------------------

Now apply the formula:
SUM = [(FIRST + LAST)/2][# of values]
= [(84 + 140)/2][9]
= [224/2][9]
= [112][9]
= 1008
= C

Cheers,
Brent

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Last edited by Brent@GMATPrepNow on Fri Feb 12, 2016 8:13 pm; edited 1 time in total

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prada Senior | Next Rank: 100 Posts
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08 Dec 2010
Posted:
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Fri Feb 12, 2016 4:06 pm
Brent@GMATPrepNow wrote:
j_shreyans 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

In other words, 84 + 91 + 98 + . . . 140 = ?

Since the values are EQUALLY SPACED, we can use the rule: SUM = [(FIRST + LAST)/2][# of values]

NUMBER of values
Here's a nice rule: If x and y are multiples of k, then the number of multiples of k from x to y inclusive = [(y-x)/k] + 1
So, for example, the NUMBER multiples of 3 from 6 to 21 inclusive = [(21 - 6)/3] + 1 = [15/3] + 1 = 6

So, the NUMBER multiples of 7 from 84 to 140 inclusive = [(140 - 84)/3] + 1
= [56/7] + 1
= 9

------------------------------------

Now apply the formula:
SUM = [(FIRST + LAST)/2][# of values]
= [(84 + 140)/2][9]
= [224/2][9]
= [112][9]
= 1008
= C

Cheers,
Brent
Hi Brent,

I think here
So, the NUMBER multiples of 7 from 84 to 140 inclusive = [(140 - 84)/3] + 1

you mean 7 in lieu of 3?

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Brent@GMATPrepNow GMAT Instructor
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Fri Feb 12, 2016 8:14 pm
you mean 7 in lieu of 3?
You're absolutely right. Good catch.
I edited my response accordingly.

Cheers,
Brent

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Check out the online reviews of our course
Come see all of our free resources

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waleedijaz Newbie | Next Rank: 10 Posts
Joined
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Posted:
1 messages
Sat Apr 30, 2016 4:07 am
You're absolutely right. Good catch???

waleeed

YTarhouni Newbie | Next Rank: 10 Posts
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Tue Sep 05, 2017 6:45 pm
When it comes to calculating the number of item in a sequence of multiples, i find it easy to divide first term and last term by the multiple then apply the formula of (last-First+1).

In this case:
84/7=12
140/7=20
#items=20-12+1=9
from here you can follow any approach that makes you comfortable.

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Scott@TargetTestPrep GMAT Instructor
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Mon Sep 11, 2017 10:19 am
j_shreyans 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

OAC
'

We can use the following formula:

sum = average x quantity

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

average = (smallest integer in set + greatest integer in set)/2

average = (84 + 140)/2 = 224/2 = 112

quantity = (140 - 84)/7 + 1 = 56/7 + 1 = 9

Thus:

sum = 112 x 9 = 1008

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