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What is the sum of all multiples of 3 between 1 and 200?

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Bunuel
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What is the sum of all multiples of 3 between 1 and 200? [#permalink] New post   08 Jan 2024, 02:30
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What is the sum of all multiples of 3 between 1 and 200?

A. 3,300
B. 6,600
C. 6,633
D. 10,100
E. 20,100


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C
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cdrectenwald
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Re: What is the sum of all multiples of 3 between 1 and 200? [#permalink] New post   08 Jan 2024, 03:58
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I got c:

first term: 3
last term: 198
# number of terms: (198-3)/3 + 1= 66
sum: 66/2 X (3+198) = 6633
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Maheshkv
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Re: What is the sum of all multiples of 3 between 1 and 200? [#permalink] New post   08 Jan 2024, 04:34
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first number = 3, last number = 198

arithmetic progression with common diff of 3, hence sum would be (66*(3+198))/2 =6633

Sum of n terms of AP = (number of terms * (first + last term))/2
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Re: What is the sum of all multiples of 3 between 1 and 200? [#permalink] New post   08 Jan 2024, 07:43
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Bunuel wrote:
What is the sum of all multiples of 3 between 1 and 200?

A. 3,300
B. 6,600
C. 6,633
D. 10,100
E. 20,100

\(3 + 6 + 9.......... + 195 + 198\)

\(= 3(1 + 2 + 3...........63 + 64 + 65 + 66)\)

\(= 3(\frac{66*67}{2})\)

\(= 6633\), Answer must be (C)
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Re: What is the sum of all multiples of 3 between 1 and 200? [#permalink] New post   08 Jan 2024, 10:45
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Bunuel wrote:
What is the sum of all multiples of 3 between 1 and 200?

A. 3,300
B. 6,600
C. 6,633
D. 10,100
E. 20,100


This is a PS Butler Question



OA is C

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getsetfly
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Re: What is the sum of all multiples of 3 between 1 and 200? [#permalink] New post   16 Jan 2024, 03:17
cdrectenwald wrote:
I got c:

first term: 3
last term: 198
# number of terms: (198-3)/3 + 1= 66
sum: 66/2 X (3+198) = 6633



Hey, can you please tell me when we need to do +1 to find the number of terms and when not.....thanks!!
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Bunuel
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Re: What is the sum of all multiples of 3 between 1 and 200? [#permalink] New post   16 Jan 2024, 14:06
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getsetfly wrote:
cdrectenwald wrote:
I got c:

first term: 3
last term: 198
# number of terms: (198-3)/3 + 1= 66
sum: 66/2 X (3+198) = 6633



Hey, can you please tell me when we need to do +1 to find the number of terms and when not.....thanks!!


  • \(Number \ of \ multiples \ of \ x \ in \ the \ range = \)

    \(=\frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1\).

Example 1: how many multiples of 5 are there between -7 and 35, not inclusive?

Last multiple of 5 IN the range is 30;
First multiple of 5 IN the range is -5;

\(\frac{30-(-5)}{5}+1=8\).

Example 2: How many multiples of 4 are there between 12 and 96, inclusive?
\(\frac{96-12}{4}+1=22\).

Example 3:
How many multiples of 7 are there between -28 and -1, not inclusive?
Last multiple of 7 IN the range is -7;
First multiple of 7 IN the range is -21;

\(\frac{-7-(-21)}{7}+1=3\).

Hope it helps.
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Re: What is the sum of all multiples of 3 between 1 and 200? [#permalink]
16 Jan 2024, 14:06
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