What is the median of the list above?

Question

GMAT CLUB TESTS' FRESH QUESTION:

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

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

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

M36-120

Bunuel · Accepted Answer

Official Solution:

\{a, b, c, d\}  
 
 What is the median of the list above?  
 
(1) The product of no two elements of the list is negative
 
The above means that the product of numbers in all two-number groups possible from the list is 0 or positive:  ab \geq 0 ,  ac \geq 0 ,  ad \geq 0 ,  bc \geq 0 , ...
 
Notice that the list cannot contain both positive and negative numbers because in this case positive*negative will give negative result.
 
We can have the following nine cases:
 
 \{negative, \ negative, \ negative, \ negative \} 
 
 \{negative, \ negative, \ negative, \ 0 \} 
 
 \{negative, \ negative, \ 0, \ 0 \} 
 
 \{negative, \ 0, \ 0, \ 0 \} 
 
 \{0, \ 0, \ 0, \ 0 \} 
 
 \{0, \ 0, \ 0, \ positive \} 
 
 \{0, \ 0, \ positive , \ positive \} 
 
 \{0, \ positive , \ positive , \ positive \} 
 
 \{positive , \ positive , \ positive , \ positive \} 
 
The median can be some negative number (for the first three cases), 0 (for the next three cases) or some positive number (for the last three cases). Not sufficient.
 
(2) The sum of the elements of the list is 0
 
The median of  \{0, \ 0, \ 0, \ 0 \}  is 0;
 
The median of  \{-10, \ -1, \ 5, \ 6 \}  is 2.
 
Not sufficient.
 
(1)+(2) From (1) we got that the list cannot contain both positive and negative numbers and from (2) we know that the sum of the numbers is 0, so all numbers must be 0, making the median also equal to 0. Sufficient.
 
OR just check which case from (1) gives the sum of 0. Only  \{0, \ 0, \ 0, \ 0 \} ! Sufficient.

Answer: C

Leo8 · Answer

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

(1) The product of no two elements of the list is negative ->   or   NS

(2) The sum of the elements of the list is 0 ->     : NS

1 & 2 -> C
  Median = 0

sudarshan22 · Answer

+1 for   C  .

(1) The product of no two elements of the list is negative
The elements could be positive, zero, non-integer.
  Insufficient

(2) The sum of the elements of the list is 0
The elements could be zero or mix of both positive and negative.
  Insufficient

Combining both :
All the elements have to be zero in order to fit the condition.
Therefore, Median = 0
  Sufficient

Hence,   C  .

Izzyjolly · Answer

Here is my approach.
(1) The product of no two elements of the list is negative --> all the elements of the list have the same sign. The list could be (-1,-1,-1,-1) or (1,1,1,1) --> Not sufficient.
(2) The sum of the elements of the list is 0 --> The list could be (0,0,0,0) or (-1,-1,-1,3) --> Not sufficient.
(1)+(2) : only (0,0,0,0) satisfies --> median = 0 --> Sufficient.
Answer C.

Archit3110 · Answer

#1: (1,1,1,1) , ( 1,2,3,4).. in sufficiet

#2: sum of list is 0 : ( 0,0,0,0) , ( -2,-1,1,2). in sufficient

from 1 & 2:
(0,0,0,0)

IMOC

Bunuel · Answer

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

GMATin · Answer

Median of the set will be average of the middle two values when all elements are arranged in ascending or descending order.

Statement 1: If product of no two elements of the list is negative, then either all numbers are positive (resulting in product of any two numbers becoming positive) or at least three of those numbers are 0 (resulting in the product of any two numbers becoming 0)

Thus, either median a positive number or 0. Thus,  this statement is insufficient

Statement 2: If sum of the elements is 0, either all the elements are 0 or some elements are positive, while other are negative. Let's take examples of the latter case:
Example 1: {-14, 2, 5, 7}
Example 2: {-2, -1, 1, 2}
Since, median in both cases will be different, we cannot come with a unique value.

Hence,  this statement is insufficient

Combining 1 & 2: The only way to satisfy both equations is if all elements were 0, resulting in median of 0.

Hence, correct answer is C

merajul · Answer

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

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

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

From Option 1, {a,b,c,d} = (-a,-b,-c,-d) or (a,b,c,d) or (0,0,0,0). Hence  Not Sufficient.

From Option 2, {a,b,c,d} = like (-2,-1,1,2) or like (0,0,0,0). Hence  Not Sufficient.

From (1) + (2), only suffices {a,b,c,d} = {0,0,0,0}

Correct answer is C

What is the median of the list above?

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What is the median of the list above?

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