Number properties

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ellexay: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Jan 24, 2009 7:45 am; Thanked: 1 times

by ellexay » Tue Feb 10, 2009 5:22 pm

51. 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

Soln: if we arrange this in AP, we get
4+7+10+.......+49

so 4+(n-1)3=49: n=16
C is my pick

I don't know what the OA is, but can someone tell me if C is indeed correct?

Thank you.

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Source: Beat The GMAT — Problem Solving | Tue Feb 10, 2009 5:22 pm

DeepakR: Master | Next Rank: 500 Posts; Posts: 158; Joined: Tue Sep 30, 2008 8:47 amFollowed by: 1 member; Thanked: 23 times; GMAT Score:660

by DeepakR » Tue Feb 10, 2009 5:32 pm

I think you have to include the number 1 as well.
1,4,7..49 hence a=1 and tn=49 so 49=1+(n-1)3. Therefore n=17 Ans.) D

- Deepak

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ellexay: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Jan 24, 2009 7:45 am; Thanked: 1 times

by ellexay » Tue Feb 10, 2009 5:37 pm

Deepak,

I thought the question wanted integers that, when divided by 3, leave R1. That way, 1 wouldn't be included in the answer set.

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billzhao: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Mon Feb 02, 2009 6:36 am; Thanked: 10 times

by billzhao » Tue Feb 10, 2009 7:32 pm

I think that 1 should be included in the set because:
1. 1 is an integer
2. 1 is in the range from 0 to 50
3. 1 gives an remainder of 1 when dividing 3.

Yiliang

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sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

by sureshbala » Tue Feb 10, 2009 9:26 pm

billzhao wrote:I think that 1 should be included in the set because:
1. 1 is an integer
2. 1 is in the range from 0 to 50
3. 1 gives an remainder of 1 when dividing 3.

Perfect....1 must be included.

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x2suresh: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Aug 07, 2008 5:32 am; Thanked: 16 times

by x2suresh » Tue Feb 10, 2009 9:32 pm

agree with D

1 should be included.

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raunekk: Legendary Member; Posts: 1159; Joined: Wed Apr 16, 2008 10:35 pm; Thanked: 56 times

by raunekk » Tue Feb 10, 2009 9:44 pm

wats d OA??

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Wed Feb 11, 2009 12:57 am

Here is an easy way.

50/3 = 16 integers.
However, this does not include 1, coz 1 divided by 3 has remainder =1.
So add 1.
==> 17 ie D

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ellexay: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Jan 24, 2009 7:45 am; Thanked: 1 times

by ellexay » Wed Feb 11, 2009 6:19 am

Thanks to all! I understand now.

Unfortunately, the source from which I got this problem didn't have the OA for this one =(

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