More than two numbers

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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

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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Source: Beat The GMAT — Data Sufficiency | Tue Jun 16, 2009 6:16 am

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

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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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

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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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

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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