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# What is the sum of the multiples of 3 from 11–110, inclusive?

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Math Expert
Joined: 02 Sep 2009
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What is the sum of the multiples of 3 from 11–110, inclusive?  [#permalink]

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23 Jan 2019, 02:15
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Difficulty:

25% (medium)

Question Stats:

79% (02:01) correct 21% (01:23) wrong based on 51 sessions

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What is the sum of the multiples of 3 from 11–110, inclusive?

A 1,980

B 2,057

C 3.228

D 4,573

E 6,050

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Re: What is the sum of the multiples of 3 from 11–110, inclusive?  [#permalink]

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23 Jan 2019, 02:33
1
$$12+15+18+ ... +108$$
Last term $$T_n=108=a+(n-1)d$$
$$a=12 , d=3$$
$$108=12+(n-1)3$$
$$n-1 = 96/3 = 32$$
$$n=33$$
Total sum $$S_n=n/2 [first term + last term]$$

$$Sum = 33/2 * [12+108] = 33/2 * 120 = 1980$$
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Re: What is the sum of the multiples of 3 from 11–110, inclusive?  [#permalink]

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23 Jan 2019, 07:53
1
Bunuel wrote:
What is the sum of the multiples of 3 from 11–110, inclusive?

A 1,980

B 2,057

C 3.228

D 4,573

E 6,050

multiples of 3 would be 12,15... 108
total multiples ; 108-12 = 96/3 = 32+1 = 33 ; +1 since we are adding inclusive terms

sum formula
sn=n/2 + ( 2a + (n-1) d)

n = 33
a=12
d=3
s33= 33/2 + ( 2*12 + 32* 3)
= 1980
IMO A
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Re: What is the sum of the multiples of 3 from 11–110, inclusive?  [#permalink]

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27 Jan 2019, 19:20
Bunuel wrote:
What is the sum of the multiples of 3 from 11–110, inclusive?

A 1,980

B 2,057

C 3.228

D 4,573

E 6,050

We find the greatest multiple of 3 and the smallest multiple of 3 for the range of values given. We see that the average of the multiples of 3 from 11 to 110, inclusive, is:

(108 + 12)/2 = 60

The number of multiples of 3 from 11 to 110, inclusive, is:

(108 - 12)/3 + 1 = 96/3 + 1 = 33

Since sum = average x quantity, the sum of those multiples is:

60 x 33 = 1,980

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Re: What is the sum of the multiples of 3 from 11–110, inclusive?   [#permalink] 27 Jan 2019, 19:20
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