Number 3

Number Theory Level 2

How many integers that are multiples of 3 are there between 1,000 and 1,000,000?


The answer is 333000.

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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6 solutions

Rajnish Kaushik
Apr 24, 2014

1000000-1000=999000 999000/3=333000

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Kunal Sharma
Apr 30, 2014

First multiple of 3 between 1000 and 1000000 = a = 1002

Last multiple = l = 999999

d = 3

l = a + (n-1)d

999999 = 1002 + (n-1)*3

n = 333000

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ryan Redz
Jun 5, 2014

999,999 - 1,002 = 998,997/3 + 1 = 333,000

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Vishnudatt Gupta
May 4, 2014

arithmetic sequence a + (n-1)b 1002 + (n-1)3 = 999999

1002 + 3n - 3 = 999999

999 + 3n = 999999

3n = 999999-999

n = = 333000

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Dian Fadilla
Apr 30, 2014

arithmetic sequence

a + (n-1)b

1002 + (n-1)3 = 999999

1002 + 3n - 3 = 999999

999 + 3n = 999999

3n = 999999-999

n = 999000 3 \frac{999000}{3} = 333000

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Rahma Anggraeni
Apr 30, 2014

1 , 000 , 000 3 \frac{1,000,000}{3} - 1 , 000 3 \frac{1,000}{3} <<< use the whole number only

333,333 - 333 = 333,000

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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