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# How many integers from 0 to 50, inclusive, have a remainder

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Director
Joined: 09 Aug 2006
Posts: 754

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How many integers from 0 to 50, inclusive, have a remainder [#permalink]

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27 Jun 2007, 04:00
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How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

A.14
B.15.
C.16
D.17
E.18

Kudos [?]: 255 [0], given: 0

Senior Manager
Joined: 04 Jun 2007
Posts: 345

Kudos [?]: 33 [0], given: 0

Re: PS: Remainder when Divided by 3 [#permalink]

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27 Jun 2007, 05:26
GK_Gmat wrote:
How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

A.14
B.15.
C.16
D.17
E.18

Between 0 and 50 (inclusive) the first and last numbers satisfying the given conditions are 1 and 49. Therefore, all other numbers, along with these will form an arithmetic progression with common difference 3.
So, we have: 49 = 1 + (n-1)*3 which gives n=17.
Hence, D.

Kudos [?]: 33 [0], given: 0

CIO
Joined: 09 Mar 2003
Posts: 461

Kudos [?]: 71 [0], given: 0

Re: PS: Remainder when Divided by 3 [#permalink]

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27 Jun 2007, 06:08
GK_Gmat wrote:
How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

A.14
B.15.
C.16
D.17
E.18

I get the same answer, but i use a different method. When we have a list of consecutive numbers and we want to count the numbers, it's always:

Subtract
Divide (by d)

So the list goes from 1 to 49:

Subtract: 49 - 1 = 48
Divide by d: 48/3 = 16
Add 1: 16 + 1 = 17

I just find it's easier for students to remember that method than to remember a formula.

Humble opinion.

Kudos [?]: 71 [0], given: 0

Director
Joined: 06 Sep 2006
Posts: 734

Kudos [?]: 49 [0], given: 0

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27 Jun 2007, 09:23
(48 - 0)/3 + 1
17
D.

No. of term b/w consecutive numbers = (Last - First)/Difference + 1

Difference is 1 for sequence like 1,2, 3,...
Difference is 2 for odd/even

Kudos [?]: 49 [0], given: 0

Director
Joined: 01 May 2007
Posts: 795

Kudos [?]: 379 [0], given: 0

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11 Nov 2007, 16:10
I solved this the following way... does this make sense?

51 = 3q + 1

q = 16.6667 or round to 17.

I got 51 by getting 50-0 plus one (since we said zero to 50 inclusive.)

Kudos [?]: 379 [0], given: 0

Director
Joined: 13 Dec 2006
Posts: 506

Kudos [?]: 243 [0], given: 0

Location: Indonesia

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11 Nov 2007, 17:58
Hi,

guys why am I getting 16 instead of 17, as you have got....

In my opinion the first number between 0 to 50, which will give remainder of 1 when divided by 3 is 4. and the last number is 49.

in other words 16* 3 = 48, add one to 48 will give 49. which will be the last number.

so answer should be 16... let me know, where am I wrong? My answer is C=16

Amardeep

Kudos [?]: 243 [0], given: 0

Director
Joined: 08 Jun 2007
Posts: 575

Kudos [?]: 109 [0], given: 0

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11 Nov 2007, 18:09
Amardeep Sharma wrote:
Hi,

guys why am I getting 16 instead of 17, as you have got....

In my opinion the first number between 0 to 50, which will give remainder of 1 when divided by 3 is 4. and the last number is 49.

in other words 16* 3 = 48, add one to 48 will give 49. which will be the last number.

so answer should be 16... let me know, where am I wrong? My answer is C=16

Amardeep

The first number should be 1 . Remember 0 is multiple of all numbers.
3*0 + 1 = 1

Kudos [?]: 109 [0], given: 0

11 Nov 2007, 18:09
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