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How many numbers with remandiers

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Senior | Next Rank: 100 Posts
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by moliver » Fri Oct 09, 2009 4:16 am
Hi! Help with this problem please! Thanks.

x is a positive integer less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many such numbers are possible?
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by mp2437 » Fri Oct 09, 2009 5:37 am
24? I began with 8, and found the next one at 29, then next one of 50..The pattern is to add 21 to each preceding number.

8,29,50,71,92....470,491
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by vaibhav.iit2002 » Sun Oct 11, 2009 9:39 am
IMO 24

nos are in form of 21n+8 [n>=0]
500=21x23+17 , hence max value of x=21x23+8

total 24

But is there a way in which we can directly conclude that no. will be of form 21n+8, without searching through pattern?
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