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X is positive interger less than 500.When x is divided by 7

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javed
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X is positive interger less than 500.When x is divided by 7 [#permalink] New post   19 May 2007, 05:45
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X is positive interger 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?
A 18
B 20
C 22
D 24
E 25.

OA D

Please explain your answere.

Cheers!

Javed.



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Re: X is positive interger less than 500.When x is divided by 7 [#permalink] New post   19 May 2007, 07:31
Gotcha... !! 24 is the ans.

My answer is a bit rookie but I got the answer.atleast a line of thinking... Correct me if I am wrong anywhere..

I started with a trial and error on the type of such numbers...
8, 29, 50 , 71..... => Such numbers come at a gab of 21 numbers.

So the total number of such numbers should be between 20 and 25.
Applying A.P formula, d = 21, lets say n = 24
So, a24 = 8 + 23.21 = 483.
A number greater than this will cross 500.
Hence , there are 24 numbers that when divided 7 give remainder as 1 and when by 3 give remainder as 2.


Thanks...
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Re: X is positive interger less than 500.When x is divided by 7 [#permalink] New post   19 May 2007, 09:35
Dividing 7 with 3 gives remainder 1. So, 7xn+1 gives a 3m+2 once in three times i.e. for 8, 29, ...

AP formula gives An = A + (n-1)d
500 (or so) = 8 + (n-1)21
492/21 (or so) = (n-1)
23.42 (or so) = (n-1)

But n should be an integer, so n-1 = 23 => n = 24
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Re: X is positive interger less than 500.When x is divided by 7 [#permalink] New post   20 May 2007, 03:46
Thank you guys, OA is D.

Javed.

Cheers!
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Re: X is positive interger less than 500.When x is divided by 7 [#permalink] New post   20 May 2007, 04:45
Amit05 wrote:
Gotcha... !! 24 is the ans.

My answer is a bit rookie but I got the answer.atleast a line of thinking... Correct me if I am wrong anywhere..

I started with a trial and error on the type of such numbers...
8, 29, 50 , 71..... => Such numbers come at a gab of 21 numbers.

So the total number of such numbers should be between 20 and 25.
Applying A.P formula, d = 21, lets say n = 24
So, a24 = 8 + 23.21 = 483.
A number greater than this will cross 500.
Hence , there are 24 numbers that when divided 7 give remainder as 1 and when by 3 give remainder as 2.


Thanks...


how come the bold portion is true. solving this a24= 491
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Re: X is positive interger less than 500.When x is divided by 7 [#permalink] New post   20 May 2007, 08:13
vshaunak@gmail.com wrote:
Amit05 wrote:
Gotcha... !! 24 is the ans.

My answer is a bit rookie but I got the answer.atleast a line of thinking... Correct me if I am wrong anywhere..

I started with a trial and error on the type of such numbers...
8, 29, 50 , 71..... => Such numbers come at a gab of 21 numbers.

So the total number of such numbers should be between 20 and 25.
Applying A.P formula, d = 21, lets say n = 24
So, a24 = 8 + 23.21 = 483.
A number greater than this will cross 500.
Hence , there are 24 numbers that when divided 7 give remainder as 1 and when by 3 give remainder as 2.


Thanks...


how come the bold portion is true. solving this a24= 491


yes, its 491 but still the result holds true since 491 is still less than 500 since we want to have numbers less than 500.

I hope I am clear. Let me know if doubt prevails..
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Re: X is positive interger less than 500.When x is divided by 7 [#permalink] New post   20 May 2007, 10:28
hI, excuse me , what is A.P formula ? thanks a lot
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Re: X is positive interger less than 500.When x is divided by 7 [#permalink] New post   20 May 2007, 12:09
A.P :

An = A1 + (n-1)d

Where, n is the nth term in the series,
A1 is the first term,
d is the difference between 2 consecutive terms of the series.



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Re: X is positive interger less than 500.When x is divided by 7 [#permalink]
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