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

tagged by: Brent@GMATPrepNow

This topic has 5 expert replies and 1 member reply

Top Member

Vincen Master | Next Rank: 500 Posts
Joined
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Posted:
458 messages
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What is the sum of the multiples of 7 from 84 to 140?

Mon Sep 25, 2017 5:59 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

The OA is C.

Is there any way to solve it without listing the numbers?

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GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
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Fri Dec 15, 2017 10:23 am
Vincen 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 use the following equation to determine the quantity:

(largest multiple in the set - smallest multiple in the set)/7 + 1 = number of multiples of 7

(140 - 84)/7 + 1

56/7 + 1 = 9

Next, letâ€™s determine the average of this evenly spaced set.

average = (first number + last number)/2

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

Thus, the sum is 9 x 112 = 1,008.

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GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
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GMAT Score:
770
Fri Dec 15, 2017 1:26 pm
Vincen 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

The OA is C.

Is there any way to solve it without listing the numbers?
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

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
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GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
548 messages
Followed by:
3 members
43
Fri Dec 15, 2017 10:23 am
Vincen 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 use the following equation to determine the quantity:

(largest multiple in the set - smallest multiple in the set)/7 + 1 = number of multiples of 7

(140 - 84)/7 + 1

56/7 + 1 = 9

Next, letâ€™s determine the average of this evenly spaced set.

average = (first number + last number)/2

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

Thus, the sum is 9 x 112 = 1,008.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11041 messages
Followed by:
1217 members
5254
GMAT Score:
770
Fri Dec 15, 2017 1:26 pm
Vincen 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

The OA is C.

Is there any way to solve it without listing the numbers?
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

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

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

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
Joined
04 Oct 2017
Posted:
365 messages
Followed by:
7 members
180
Fri Oct 13, 2017 10:28 am
Quote:
What is the sum of the multiples of 7 from 84 to 140, inclusive?
Hi Vincen,
Let's take a look at your question.

First of all we need to find the number of terms between 84 to 140 inclusive.
Since we are talking about multiples of 7, lets find out the term numbers of 84 and 140 in the sequene of multiples of 7.
$$\frac{84}{7}=12$$
84 is 12th term.

$$\frac{140}{7}=20$$
140 is 20th term.

Total number of terms = n = 20 - 12 + 1 = 9

Sum of n terms in geometric series$$=\frac{n}{2}\left(a_1+a_n\right)$$
$$=\frac{9}{2}\left(84+140\right)$$
$$=\frac{9}{2}\left(224\right)$$
$$=\frac{9}{2}\left(84+140\right)$$
$$=9\left(112\right)$$
$$=1008$$

Therefore, Option C is correct.
Hope this helps.

I am available, if you'd like any follow up.

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pannalal Junior | Next Rank: 30 Posts
Joined
20 Sep 2017
Posted:
22 messages
2
Tue Sep 26, 2017 9:48 pm
Vincen 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

The OA is C.

Is there any way to solve it without listing the numbers?
Sum of the multiples of 7 from 84 to 140, inclusive = 84 + 91 + ... + 140.

Number of multiples of 7 from 84 to 140 = 140/7 - 84/7 + 1 = 20 - 12 + 1 = 9.

Now, write these numbers twice, once in ascending order and then in descending order:

S = 84 + 91 + .... + 133 + 140
S = 140 + 133 + .... + 91 + 84

The sum of each pair is 224. As the total number of pairs are 9.

2S = 224*9 or S = 112*9 = 1008.

Thus, the correct answer is C.

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