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Re: How many integers from 0 to 50, inclusive, have a remainder [#permalink]
06 Feb 2013, 02:24

The range of given numbers is 50-0+1=51 Any number when divided by 3 can give remainders from the list {0,1,2}. This patten will repeat for every 3 numbers. Hence divide the range by number of available remainders. i.e 51/3=17

Re: PS: 0 to 50 inclusive, remainder [#permalink]
06 May 2013, 04:41

abhishekik wrote:

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

Hello,

I like this solution using the arithmetic progression but in the expression tn=a+(n-1)d why n-1 and not n ?

As I know Un= U0 + n r where U0 is the first terme and r is the common difference.

Thx in advance for the lighting ! _________________

Re: How many integers from 0 to 50, inclusive, have a remainder [#permalink]
24 May 2014, 05:54

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Re: How many integers from 0 to 50, inclusive, have a remainder [#permalink]
16 Jun 2015, 07:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many integers from 0 to 50, inclusive, have a remainder [#permalink]
01 Jul 2015, 15:55

Calculated the same. \(\frac{Last R1 - First R1}{3} +1 = \frac{(49 - 1)}{3} +1 = 16 + 1 = 17\).

Testing the answer choices if another multiple is needed or if there are one too many. This proved that C was the correct answer.

A. 15 * 3 = 45. 50-45 = R5. Too low. B. 16 * 3 = 48. 50-48 = R2. C. 17 * 3 = 51. 50-51 = R1, which is in line with what the question asks. D. 18 * 3 = 54. 54-50= R4. Too high E. 19 * 3 = 57. 57-50= R7.Too high _________________

Kr, mejia401

+1 Kudos if my comment was helpful. Thanks! Failure forges confidence, confidence multiplies success.

gmatclubot

Re: How many integers from 0 to 50, inclusive, have a remainder
[#permalink]
01 Jul 2015, 15:55

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