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

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Joined: 23 Jan 2004
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how many numbers between 1 and 99 inclusive can x be drawn [#permalink]

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11 Oct 2004, 17:50
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
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11 Oct 2004, 18:41

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.
CIO
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12 Oct 2004, 07:36
Anonymous wrote:

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.
12 Oct 2004, 07:36
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