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how many numbers between 1 and 99 inclusive can x be drawn

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Intern
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how many numbers between 1 and 99 inclusive can x be drawn [#permalink] New post 11 Oct 2004, 16:50
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how many numbers between 1 and 99 inclusive can x be drawn such that X^2 + X is divisible by 3.
Please show the work and explain whatever number property rule can get you to the answer.

Thanks
Joined: 31 Dec 1969
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 [#permalink] New post 11 Oct 2004, 17:41
answer = 66

x^2 + x = x(x+1) must be div by 3 => x must be a multiple of 3 or one less than a multiple of 3

From 1-99 there are 99 nos.
Can divide these into 33 sets of 3 consecute nos each....
{1,2,3} {4,5,6}........{97,98,99}
in each set, the last 2 nos are ok for our x
Therefore among all 33 sets, 2*33 = 66 values are ok for x.
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 [#permalink] New post 12 Oct 2004, 06:36
Anonymous wrote:
answer = 66

x^2 + x = x(x+1) must be div by 3 => x must be a multiple of 3 or one less than a multiple of 3

From 1-99 there are 99 nos.
Can divide these into 33 sets of 3 consecute nos each....
{1,2,3} {4,5,6}........{97,98,99}
in each set, the last 2 nos are ok for our x
Therefore among all 33 sets, 2*33 = 66 values are ok for x.


Exactly, I agree with this.
  [#permalink] 12 Oct 2004, 06:36
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how many numbers between 1 and 99 inclusive can x be drawn

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