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If there are more than two numbers in a certain list, is eac

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Joined: 27 Oct 2009
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If there are more than two numbers in a certain list, is eac  [#permalink]

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06 Jan 2011, 14:56
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45% (medium)

Question Stats:

56% (01:05) correct 44% (01:02) wrong based on 105 sessions

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If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0?

(1) The product of any two numbers in the list is equal to 0
(2) The sum of any two numbers in the list is equal to 0

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Re: Product or Sum with 0  [#permalink]

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06 Jan 2011, 15:10
1
If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0?

Note that we are told that there are more than 2 numbers in the list.

(1) The product of any two numbers in the list is equal to 0 --> it certainly possible all numbers to equal to 0 but it's also possible one number to be different from 0 and all other numbers to equal to 0 (in this case the product of ANY two numbers in the list will also be equal to 0). Not sufficient.

(2) The sum of any two numbers in the list is equal to 0 --> as there are more than 2 numbers in the list then all numbers must equal to 0 (if we were not told that there are more than 2 numbers in the list then it would be possible to have a list like {-1, 1} but as there are more than 2 numbers then in order the sum of ANY two numbers in the list to be equal to 0 all numbers must equal to zero). Sufficient.

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If there are more than two numbers in certain list  [#permalink]

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28 Apr 2015, 07:32
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 zero
2). The sum of any two numbers in the list equal to 0.

Spoiler: :: OA
B
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Posts: 54544
Re: If there are more than two numbers in a certain list, is eac  [#permalink]

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28 Apr 2015, 07:35
sauravleo123 wrote:
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 zero
2). The sum of any two numbers in the list equal to 0.

Spoiler: :: OA
B

Merging topics. Please refer to the solution above.
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Re: If there are more than two numbers in a certain list, is eac  [#permalink]

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28 Apr 2015, 20:26
Hi All,

When dealing with questions that talk about groups of unknown numbers, it often helps to come up with some examples that fit the limited information that you have. In that way, you can TEST VALUES by considering what the group of numbers COULD contain.

Here, we're told that the group of numbers consists of MORE than 2 numbers (so 3 or more numbers). We're asked if EACH of the numbers is 0. This is a YES/NO question.

Fact 1: The product of any two numbers in the list is equal to zero

Since the product of ANY number and 0 is 0, this means that the list COULD contain a non-0 number....In the second option, choosing any 2 numbers WILL result in a product that = 0.

IF the group of numbers is....
{0, 0, 0} then the answer to the question is YES
{0, 0, 1] then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: The sum of any two numbers in the list equal to 0.

Since we're dealing with MORE than 2 numbers, this Fact provides a specific 'restriction' - we CAN'T have ANY non-0 numbers because then would could end up with a sum that is NOT 0.

IF...
{0, 0, 0} then the answer to the question is YES

IF....
{-1, 1, 1} then we could end up with (1) + (1) = 2, which does NOT fit the given Fact. Thus, this example is NOT possible and neither is any other example that could lead to a Non-0 sum. By extension, that means that EVERY number in the group MUST be 0.
Fact 2 is SUFFICIENT

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Re: If there are more than two numbers in a certain list, is eac  [#permalink]

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15 May 2015, 01:46
I missed this question

very simple, but enough to kiss us
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Re: If there are more than two numbers in a certain list, is eac  [#permalink]

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20 Mar 2019, 01:17
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Re: If there are more than two numbers in a certain list, is eac   [#permalink] 20 Mar 2019, 01:17
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