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Re: PS: 0 to 50 inclusive, remainder [#permalink]
24 Mar 2009, 23:16

1

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C:17

I brute forced this one. All the multiples of 3 + 1 will have a remainder of 1: 4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49 - 16 numbers total But then I thought, no way it's this easy and thought about 1. 1/3 would also have a remainder of 1, making the answer 17.

Re: PS: 0 to 50 inclusive, remainder [#permalink]
25 Mar 2009, 00:21

2

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My ans is also C.17.

Explanation:

1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on. Hence we have an arithmetic progression: 1, 4, 7, 10,..... 49, which are in the form 3n+1. Now we have to find out number of terms. tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference. so, 49 = 1+(n-1)3 or, (n-1)3 = 48 or, n-1 = 16 or, n = 17

an-I know that 51/17=3, in order to have a reminder +1, i will take x=16 an=16*3+1=49

Could you please explain this in detail??

I have meant that 51=3*x, than x=17, since we have limits from 0 to 50 inclusive the last number in sequence is 49 which is =16*3+1, as 50=16*3+2.
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well Bibha, I would like to expalin this in a logical manner rather than by mathematical expression. each no. which is 1 more than multiple of three would be in this series. so upto 50 there are 16 such no.s so correspondingly there are 16 no.s which are 1 more than a multiple of three and the last being 49. reply me if it is not clear.

Does it mean that if zero is included in any similar problem like this then we should consider it, no matter what the divisor is??? Ex- if question say any no. between 0 and 50, inclusive, divisible by 3 Answer will still be 17 Is it right
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Does it mean that if zero is included in any similar problem like this then we should consider it, no matter what the divisor is??? Ex- if question say any no. between 0 and 50, inclusive, divisible by 3 Answer will still be 17 Is it right

0 is a multiple of every integer (except zero itself), so there are \frac{48-0}{3}+1=17 numbers divisible by 3 in the range 0-50 inclusive (check this: totally-basic-94862.html?highlight=range).

But in original question 0 is not considered as one of the numbers: the lowest value of n is 1 (for p=0) and the highest value of n is 49 (for p=16), so total of 17 such numbers.
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There are 48/3=16 numbers that are divisible by 3 (0 is excluded). If we add 1 to each and every of these number, we still have 16 numbers that have a remainder of 1 when divided by 3 (say 4, 7, 10,..., 49). But we have not counted 0 yet, 0+1 equals 1, 1 has a remainder of 1 when divided by 3.

Re: PS: 0 to 50 inclusive, remainder [#permalink]
31 Aug 2010, 22:56

I think we can find this very quickly by using this: approximately 1/3 of the numbers from 0-50 are div by 3 so, (50/3) +1 = 16 + 1 = 17 approximately 1/2 of the numbers are div by 2 => (50/2 ) + 1 = 26 approximately 1/4 of the numbers are div by 4 => (50/4) + 1 =13 approximately 1/5 of the numbers are div by 5 => (50/5) + 1 =11 approximately 1/6 of the numbers are div by 6 => (50/6) + 1 = 9 I saw this on Bunuel's post somewhere and I thought to myself, how did he know? so I tried to calculate it and voila!, it is true...didn't try with range starting with non-zero numbers though don't forget to add one..before you are done!

Re: PS: 0 to 50 inclusive, remainder [#permalink]
31 Aug 2010, 23:12

when 1 is devided by 3 remainder is 1, and when 3 is devided remainder 0. 16*3=48. so upto 48 there will be 16 number which will give remainder 1 after 48, there is only 1 number up to 50 which will give 1 remainder so the answer 17

Re: PS: 0 to 50 inclusive, remainder [#permalink]
06 Jan 2012, 19:57

First, lets look at the range. With 1 remainder, 4-49.

So, number of elements = (49-3)/3 + 1 = 16

Now, lets not forget 1, since 1/3 -> 1 as remainder (Good one!)

So, 16 +1 = 17
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