What is the mode of the list above?

B

1. {0,0,0,0} , {0,2,0,-2}
Insufficient
2. Range = 0 {0,0,0,0}, {-1,-1,-1,-1},{2,2,2,2}
Mode = 4
Sufficient

B

1. {0,0,0,0} , {0,2,0,-2}
Insufficient

2. Range = 0
{0,0,0,0}, {-1,-1,-1,-1},{2,2,2,2}
Mode = 4
Sufficient

The number that occurs the most in the set is called mode. Statement B just says that range = 0 and as you correctly identified , set can be made of different combinations but does not necessarily gives us the mode.
So B is insufficient

You clearly have no idea what the mode is. Mode is the most repeated number in a sequence. And I believe only the first one is sufficient in that sense. (A)

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Is the answer A
St1: {0,0,0,0},{0,1,-1,0} mode 0
st2: range 0 : highest and lowest numbers are equal, so all numbers are equal.Hence the numbers can be anything. Insufficient

from 1:
product of no two elements is +ve : ( -1,0,0,1) (-2,0,0,1)

sufficient
From:range of elements is 0 : it can be any set of number

IMO A

Par of GMAT CLUB'S New Year's Quantitative Challenge Set

Interesting concepts tested in this question.

First, mode is the element of the set which occurs the most number of times in that set. Eg: In a set A= {1, 2, 2, 2, 6 ,7}, the mode is the number that occurs the most times i.e. 2 and not the number of times 2 occurs (i.e. 3)

Lets move to statements.

Statement 1: This means that if any two elements of the set are multiplied, the product is either negative or 0 (this is the important bit!). Now, we can never have a condition where in a set of 4 numbers, product of any two numbers is negative. Eg: Let's say a, b and c are positive and d is negative. Here, a*d will be negative. However, since we can pick any two numbers, what if we pick numbers a and b, then the product will be positive. A similar situation happens if we take more numbers to be negative.

Lets move to testing for 0. Now, product of any two numbers to be 0 will happen only if at least 3 numbers out of the 4 are 0. Thus, clearly 0 is the number that occurs most number of times. Hence, the mode is 0. This statement is sufficient

Statement 2: If range of a set is 0, then all numbers are the same. However, we still don't know what is that number. Hence, we cannot calculate mode.

Statement 2 is insufficient.

Hence, answer is A

What is mode? The number in the list that has the maximum occurrence/frequency; e.g {2,2,2,2,3} has mode 2.

Statement 1. Let's try to create a set where no two numbers will give a positive product: {1, -5, 0, 0}, Clearly 0 is the mode here(Frequency=2).
Another example {4, -8, 0, 0} Sufficient.

Statement 2. let's try to create a set with range=0. What is range: The distance of the max and min element in the set on a number line.
https://www.mathgoodies.com/lessons/vol8/range

Range zero sets
{0,0,0,0}Mode is 0
{4,4,4,4}4 is mode. Clearly not sufficient as we are getting multiple values.

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