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.
DS : Numbers 1
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- Mission2012
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- vinay1983
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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!
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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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
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
- vinay1983
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[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!