What is the mode of the list above?

Question

GMAT CLUB TESTS' FRESH QUESTION:

{a, b, c, d}
What is the mode of the list above?

(1) The product of no two elements of the list is positive

(2) The range of the elements of the list is 0

M36-70

Bunuel · Accepted Answer

Official Solution:

\{a, \ b, \ c, \ d \} 
 
  What is the mode of the list above? 
 
(1) The product of no two elements of the list is positive
 
The above means that the product of numbers in all two-number groups possible from the list is 0 or negative:  ab \leq 0 ,  ac \leq 0 ,  ad \leq 0 ,  bc \leq 0 , ...
 
Can the list contain two or more positive numbers? No. Because in this case we can have a group of two positive numbers which will give the positive product. 
 
Can the list contain two or more negative numbers? No. Because in this case we can have a group of two negative numbers which will give the positive product. 
 
So, the list should contain at most one positive number, at most one negative number and the remaining numbers must be 0. We can have the following four cases:
 
 \{0, \ 0, \ 0, \ 0 \} 
 
 \{negative, \ 0, \ 0, \ 0 \} 
 
 \{0, \ 0, \ 0, \ positive \} 
 
 \{negative, \ 0, \ 0, \ positive \} 
 
The mode of each of the possible lists above is 0. Sufficient.
 
(2) The range of the elements of the list is 0
 
The range of 0 means that the list contains four equal numbers but we don't know what number this is. Not sufficient.

Answer: A

Leo8 · Answer

A? mode = 0
 1) The product of no two elements of the list is positive

statement 2 is a subset of statement 1: hence 2 can't be sufficient

pratik2018 · Answer

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

pratik2018 · Answer

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

Leo8 · Answer

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

Skoup · Answer

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)

Posted from my mobile device

elPatron434 · Answer

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

Archit3110 · Answer

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

Bunuel · Answer

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

GMATin · Answer

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

LeoN88 · Answer

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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What is the mode of the list above?

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