from 0 to 50, inclusive

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

from 0 to 50, inclusive

by sanju09 » Thu Mar 26, 2009 6:20 am

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?
A. 15
B. 16
C. 17
D. 18
E. 19

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Source: Beat The GMAT — Problem Solving | Thu Mar 26, 2009 6:20 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pm; Thanked: 104 times; Followed by:1 members

by scoobydooby » Thu Mar 26, 2009 6:29 am

the numbers are of the form: 3k+1

1st number: 3.0+1=1
2nd number: 3.1+1=4
3rd number: 3.2+1=7
number closest to 50 divisible by 3=48, so the last number is 49 (1 more than a multiple of 3)

we have a series 1+4+7+..+49... (an AP, with a=1, d=3, Tn=49)
Tn=a+(n-1)d
49=1+(n-1)3
48/3=16=n-1
or n=17

C

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truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Thu Mar 26, 2009 2:08 pm

I'm going with B.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: from 0 to 50, inclusive

by Stuart@KaplanGMAT » Thu Mar 26, 2009 2:48 pm

sanju09 wrote:How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?
A. 15
B. 16
C. 17
D. 18
E. 19

When you divide by any number n, there are n possible remainders. For example, when we divide by 3, the 3 possible remainders are 0, 1 and 2. When we divide by 4, the 4 possible remainders are 0, 1, 2 and 3.

So, in this question there are 3 possible remainders.

From 0 to 50 inclusive there are 51 numbers. 51/3 = 17, therefore there are 17 numbers in the set that give each remainder. Finito, choose (C).

If 3 didn't divide evenly into 51, then we'd have to see if we had a "bonus" number in the set; but on this particular question, we see that 51 is evenly divisible by 3 and, if we understand the underlying concepts, get the correct answer in approximately 14 seconds!