DS : Numbers 1

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Mission2012: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sun Aug 19, 2012 10:04 pmFollowed by: 2 members; Thanked: 10 times

by Mission2012 » Wed Aug 28, 2013 7:37 am

If N different positive integers are added and the sum is denoted as S, and if S=NX, is X an integer?

(1) N is odd.

(2) All N numbers are consecutive integers.

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Source: Beat The GMAT — Problem Solving | Wed Aug 28, 2013 7:37 am

vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Wed Aug 28, 2013 7:50 am

Statement 1: N is odd

3, 5, 7 If consecutive integers are taken

1+2+3=6=S 1+2+5+8+7=23=S 23=5X X not a integer

So S=3X i.e 6=3X
X=2

N=5 1+2+3+4+5=15 S=NX 15=5X X=5

If suppose the following numbers are taken(since statement 1 does not say anything about the sequence of the numbers)

S=1+2+4=7 N =3 7=3X X is not a integer
Statement 2
Suppose N=2

Then 1+2=3

S=3 N =2
So X=1.5

N=3

1+2+3=6=S 6=3X X=2

Not sufficient

Combine

Numbers are odd and in sequence

1+2+3=6=S N=3 6=3X X=2

1+2+3+4+5=15 N=5 15=5X X=3

1+2+3+4+5+6+7=28 N=7 28=7X X=4

OA C

I hope I am correct!

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Aug 28, 2013 11:50 am

Hi vinay1983,

Your solution is correct; nicely proven!

This question hides an important number property rule involving consecutive integers: When dealing with an ODD number of CONSECUTIVE integers, the average is ALWAYS equal to the "middle" term. The wording of this prompt essentially asks you if the average of a group of numbers is an integer, so this rule applies.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Wed Aug 28, 2013 9:28 pm

[email protected] wrote:Hi vinay1983,

Your solution is correct; nicely proven!

This question hides an important number property rule involving consecutive integers: When dealing with an ODD number of CONSECUTIVE integers, the average is ALWAYS equal to the "middle" term. The wording of this prompt essentially asks you if the average of a group of numbers is an integer, so this rule applies.

GMAT assassins aren't born, they're made,
Rich

Thanks a lot Rich.You see this is the 1st problem I have solved correctly in this forum on my own reasoning.

I now know that if I apply my mind I can BEAT THE GMAT!

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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