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More than two numbers

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by gmat740 » Tue Jun 16, 2009 6:16 am
If there are more than two numbers in certain list, is each of the numbers in the list equal to 0?
1). The product of any two numbers in the list equal to 0.
2). The sum of any two numbers in the list equal to 0.


[spoiler]IMO-C
OA-B[/spoiler]
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by ssmiles08 » Tue Jun 16, 2009 8:06 am
IMO B.

1)
suppose there are 3 numbers on the list.

they can be 0, 5, 0 or they can be 0, 0, 0.

the product of any two combination will result in 0.

but each of the numbers do not always = 0.

2)
again suppose there 3 numbers on the list.

The only way the sum of any two combinations that will result in 0 is 0,0,0.

(B)
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by gmat740 » Wed Jun 17, 2009 4:15 am
2)
again suppose there 3 numbers on the list.

The only way the sum of any two combinations that will result in 0 is 0,0,0.

(B)
How about consider numbers as : 0, -3,+3

so as per B) Sum = 0, but individually the numbers are not 0

There can be numerous combinations like this
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by ssmiles08 » Wed Jun 17, 2009 5:27 am
gmat740 wrote:
How about consider numbers as : 0, -3,+3

so as per B) Sum = 0, but individually the numbers are not 0

There can be numerous combinations like this
The numbers you chose are not a valid set b/c if I pick any two numbers from your set and I choose -3 and 3:

the product of -3*3 = -9 which does not satisfy requirement 1.

from the same set if I chose (-3,3) for requirement 2, I get -3+3 = 0
but if I chose (0,3) I get 0+3 = 3 which does not satisfy requirement 2.

-hope this helps.
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