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Can a list contain duplicates?

by mshameen » Tue Feb 01, 2011 6:49 am
If there are more than two numbers in a certain list, is each of the numbers in the list equal to O?
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.

This is a data sufficiency question and the right answer is B i.e. Statement 2 alone is sufficient. However, the question no where states that the numbers have to be positive. What if the list contains 4 numbers as follows: +7, -7, +7, -7. Sum would be 0, but we cannot tell of all numbers are 0s or just pairs of positive and negative numbers.
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by GMATGuruNY » Tue Feb 01, 2011 7:18 am
mshameen wrote:If there are more than two numbers in a certain list, is each of the numbers in the list equal to O?
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.

This is a data sufficiency question and the right answer is B i.e. Statement 2 alone is sufficient. However, the question no where states that the numbers have to be positive. What if the list contains 4 numbers as follows: +7, -7, +7, -7. Sum would be 0, but we cannot tell of all numbers are 0s or just pairs of positive and negative numbers.
Statement 1: The product of any two numbers in the list is equal to 0.
The numbers could be {0,0,0}. The product of any 2 numbers is 0*0.
Does each number = 0? Yes.
The numbers could be {0,0,1}. The product of every pair {0*0, 0*1} is 0.
Does each number = 0? No.
Insufficient.

Statement 2: The sum of any two numbers in the list is equal to 0.
In order for the sum of any two numbers chosen to be 0, all the numbers must be 0. Otherwise, there will be at least one pair whose sum is not 0.
{0,0,0} works because the sum of any pair is 0+0 = 0.
{0,0,1} doesn't work because the sum of 0+1 ≠ 0.
Since, to satisfy statement 2, all the numbers must be 0, sufficient.

The correct answer is B.

Your example {7, -7, 7, -7} doesn't satisfy statement 2 because 7+7≠0 and -7 + -7 ≠ 0. To satisfy statement 2, the sum of any two numbers in the list must be 0.
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