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

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If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post Updated on: 27 Aug 2018, 05:49
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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.


Am unable to understand how the answer is B
from II u can have a positive and a negative number totaling to 0 eg. 1+(-1).
However if we combine both statements the value of all elements is 0.. Pl Help

Originally posted by devinawilliam83 on 25 Feb 2012, 02:23.
Last edited by Bunuel on 27 Aug 2018, 05:49, edited 2 times in total.
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post 25 Feb 2012, 02:30
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devinawilliam83 wrote:
if there are more than 2 numbers in a list. is each of the number in the list equal to 0?
I. The product of any 2 numbers in the list is equal to 0
II. The sum of any 2 numbers in the list is 0

Am unable to understand how the answer is B
from II u can have a positive and a negative number totaling to 0 eg. 1+(-1).
However if we combine both statements the value of all elements is 0.. Pl Help


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's 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.

Answer: B.

P.S. Please DO NOT reword or shorten the questions you post.
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post 13 Mar 2012, 02:17
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devinawilliam83 wrote:
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.


When I saw the phrase, "more than two numbers in a list", I immediately thought I am going to pick 3-number set. Not more. Reading on, "does each number equal to 0"? So the 3-number set I picked was {0,0,1}.

Option 1 says, "the product of any two numbers equal to 0". In my list, it does. But right away I figured that, because the other two numbers are 0, the product of any two numbers will always be 0. INSUFFICIENT.

Option 2 says, "the sum of any two numbers equal to 0". Aha! With this condition, the 0's in the set will not force the result to be 0. So, only B. SUFFICIENT.
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post 12 Jan 2013, 03:39
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kiyo0610 wrote:
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


FROM ONE

we cant tell whether all set members are 0 or not because if the set contains odd number of elements then for 1 to be true then all elements must be zero but if the number of elements is even , we can ve one element as an intiger for example that is larger or less than 0 and the statment still will hold true ... insuff

from 2
this could only hold true if all elemnts are 0's
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post 13 Jul 2013, 10:11
devinawilliam83 wrote:
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.


Am unable to understand how the answer is B
from II u can have a positive and a negative number totaling to 0 eg. 1+(-1).
However if we combine both statements the value of all elements is 0.. Pl Help



B is the answer. If it is the condition that any of the two numbers have sum zero, then they all have to be zero only.
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post 21 Jul 2014, 04:24
devinawilliam83 wrote:
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.


Am unable to understand how the answer is B
from II u can have a positive and a negative number totaling to 0 eg. 1+(-1).
However if we combine both statements the value of all elements is 0.. Pl Help


It is important to understand what the statements say here. They each say ANY 2 numbers, which means that no matter how many numbers you have and which of these numbers you take, you always get the result as stated in the statements. Let's take a look:

(1) The product of any 2 numbers = 0. If you have 100 numbers and 99 are 0 and 1 is not you will ahve any 2 numbers = 0. If you have 100 = 0 you get the same result. IS.
(2) The sum of any 2 numbers = 0. This can only mean that every number = 0. You are right that 1+ (-1) = 0 bit if you have a third number, e.g. 0 or 3 or 9. you will get a result different from 0. Hence the answer can only be that all the numbers are 0s. Hence B.
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post 19 Nov 2016, 18:24
What if there are four numbers. -1,-3 ,+1,+3. SUM is zero but each number is not.
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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

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New post 29 Mar 2017, 07:50
Hey everyone,
I have a more general question regarding this type of question.
So the question basically says "Is each of the numbers in the list equal to 0?"

Maybe I complicate myself, but I thought that statement I is sufficient, as it provides a clear answer to the question.
--> No, the numbers in the list are not equal to zero.

So my question is, if this kind of question pops up in the GMAT, does the sufficiency of the statements only depend on a positive affirmation of the question?

I hope I could express what I mean (since I'm not native in English :-))?!

Thanks,
Vincent
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post 29 Mar 2017, 08:00
Vincent89 wrote:
Hey everyone,
I have a more general question regarding this type of question.
So the question basically says "Is each of the numbers in the list equal to 0?"

Maybe I complicate myself, but I thought that statement I is sufficient, as it provides a clear answer to the question.
--> No, the numbers in the list are not equal to zero.

So my question is, if this kind of question pops up in the GMAT, does the sufficiency of the statements only depend on a positive affirmation of the question?

I hope I could express what I mean (since I'm not native in English :-))?!

Thanks,
Vincent


For (1):
It's certainly possible all numbers to equal to 0: for example {0, 0, 0} --> answer YES.

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). For example, {0, 0, 1} --> answer NO.

As for your other question: in YES/NO DS questions a definite NO answer to the question is still considered to be sufficient.

Hope it's clear.
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Re: If there are more than two numbers in a certain list, is each of the  [#permalink]

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New post 19 Oct 2018, 08:14
devinawilliam83 wrote:
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.

\(L = \left\{ {\,{x_1}\,,\,{x_2}\,,\, \ldots \,\,,\,\,{x_n}} \right\}\,\,\,\,,\,\,\,n \geqslant 3\)

\(?\,\,\,:\,\,\,{\text{all}}\,\,{\text{zero}}\)

\(\left( 1 \right)\,\,\,{x_j} \cdot {x_k} = 0\,\,\,\,\,\left( {j \ne k} \right)\,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,L = \left\{ {0,0, \ldots ,0,0} \right\}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\
\,{\text{Take}}\,\,L = \left\{ {0,0, \ldots ,0,1} \right\}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\, \hfill \\
\end{gathered} \right.\)

What about statement (2)? Do you "feel" this statement is sufficient... but you cannot be 100% sure?

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\(\left( 2 \right)\,\,\left\{ \begin{gathered}
\,{x_j} + {x_k} = 0 \hfill \\
{x_k} + {x_m} = 0 \hfill \\
\end{gathered} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,\,{x_j} - {x_m} = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{x_j} = {x_m}\,\,\,\,{\text{for}}\,\,\,\underline {{\text{ANY}}} \,\,\,\,{x_j}\,,\,\,{x_k}\,,\,\,{x_m}\,\,\,{\text{in}}\,\,L\)

\(\,\left\{ \begin{gathered}
\,{x_j} = {x_m} \hfill \\
\,0 = {x_j} + {x_m} = 2\,\, \cdot {x_j} \hfill \\
\end{gathered} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{x_j} = 0\,\,\,{\text{for}}\,\,{\text{all}}\,\,j\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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