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If list Q contains more than two numbers, are all the numbers in Q equ

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Bunuel
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If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   14 Jul 2020, 01:43
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If list Q contains more than two numbers, are all the numbers in Q equal?

(1) The sum of all the numbers in Q is zero.

(2) The product of any two numbers in Q is zero.



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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   14 Jul 2020, 02:03
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Quote:
If list Q contains more than two numbers, are all the numbers in Q equal?

(1) The sum of all the numbers in Q is zero.

(2) The product of any two numbers in Q is zero.


statement 1:
Q = {-1,0,1} or {0,0,0}
not sufficient

statement 2:
Q = {0,0,1} or {0,0,0}
not sufficient

combining both statements, only possible case remains where all the numbers are zero.
ans: C
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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   14 Jul 2020, 02:09
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Statement 1: Sum of all numbers of set Zero.
The set could be consecutive set from Negative to positive with zero as median or Consist all zeroes (Insufficient)

Statement 2: Product of two numbers is zero, then either all numbers are zero or it contain any other integer or non integer value. (Insufficient)

Statement 1&2: Both are giving a set value consisting only zeroes. (Sufficient)

Answer is C

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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   14 Jul 2020, 02:55
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If list Q contains more than two numbers, are all the numbers in Q equal?

(1) The sum of all the numbers in Q is zero.

(2) The product of any two numbers in Q is zero.

1)it can be (-2,0,2) or (0,0,0) not sufficient
2)it can be (1,0,0) or (0,0,0) not sufficient
combine
only (0,0,0) is possible
Ans: C
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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   14 Jul 2020, 05:33
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Quote:

If list Q contains more than two numbers, are all the numbers in Q equal?

(1) The sum of all the numbers in Q is zero.

(2) The product of any two numbers in Q is zero.


(1) insufic
{-1-1,1,1} not all equal
{000} all equal

(2) insufic
{1,0,0} any p of two is 0
{0,0,0} any p of two is 0

(1/2) sufic
only case where any p of two is 0 and sum all terms 0,
is when terms are all equal, in this case {000…}

Ans (C)
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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   14 Jul 2020, 14:17
Answer is C
If both the statements are used together that implies -> all numbers are 0
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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   14 Jul 2020, 20:30
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IMO C

(1) The sum of all the numbers in Q is zero.

Set 1: = {-2, -1 , 0, 1, 2}
Sum=0
Set 2: = {0, 0, 0, 0, 0}
Sum=0

Not Sufficient.

(2) The product of any two numbers in Q is zero.

Set 1= { 0, 0, 0, 2}
Product any two = 0
Set 2= {0, 0, 0, 0, 0}
Product any two = 0

Not Sufficient.

Together: ab = 0, (a+b)=0 => a=0, b=0
So, Set 2 ={0, 0, 0, 0...} Possible
All elements equal.

Sufficient.
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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   14 Jul 2020, 20:42
If list Q contains more than two numbers, are all the numbers in Q equal?

(1) The sum of all the numbers in Q is zero.

(2) The product of any two numbers in Q is zero.

1) More than 1 unique set are possible. (-2, 2, 0) or, (0,0,0). Not suffcient

2) Only possible when all the elements of the set are 0. Sufficient.

B is the answer.
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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink] New post   19 Apr 2023, 10:41
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Re: If list Q contains more than two numbers, are all the numbers in Q equ [#permalink]
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