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?
multiples of 7
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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
Answer C .
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
Answer C .
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In other words, 84 + 91 + 98 + . . . 140 = ?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
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
Last edited by Brent@GMATPrepNow on Fri Feb 12, 2016 8:13 pm, edited 1 time in total.
Hi Brent,Brent@GMATPrepNow wrote:In other words, 84 + 91 + 98 + . . . 140 = ?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
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
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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You're absolutely right. Good catch.prada wrote:
you mean 7 in lieu of 3?
I edited my response accordingly.
Cheers,
Brent
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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.
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.
Solution: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?
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.
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.
Answer: C
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.
Answer: C
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'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
Answer: C
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