12 Days of Christmas GMAT Competition - Day 1: If the data set P

Question

12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun

If the data set P consists of 5 different prime numbers and has a median of 13, is the average (arithmetic mean) of the data set P greater than 11?

(1) The product of any three numbers of the data set P is odd.
(2) The range of the data set P is even.

Bunuel · Accepted Answer

GMAT Club Official Explanation:

If the data set P consists of 5 different prime numbers and has a median of 13, is the average (arithmetic mean) of the data set P greater than 11?

The median of a set with an odd number count, like 5, is the middle term when the numbers are arranged in order. Thus, a median of 13 implies that 13 is the middle term: {_, _, 13, _, _}.

The question asks whether the average of the data set is greater than 11, i.e., whether the sum is greater than 5*11 = 55.

Since the set consists of 5  different  prime numbers, the smallest sum for the set is 54, which occurs with the set {2, 3, 13, 17, 19}. Note that the next larger set, {3, 5, 13, 17, 19}, has a sum of 57. Thus, there would be a NO answer for the set {2, 3, 13, 17, 19}, but a YES answer for all other possible sets.

(1) The product of any three numbers of the data set P is odd.

The above implies that the set consists only of odd primes, as the inclusion of 2 would make the statement false. Consequently, our set cannot be {2, 3, 13, 17, 19}, meaning the sum is greater than 55. Sufficient.

(2) The range of the data set P is even.

The range is the difference between the largest and the smallest terms of the set. For the range to be odd, either both of those terms must be even or both of those terms must be odd. However, the first case is not possible since the largest term, being a prime greater than 13 must be odd, thus we have the second case. This means that the smallest term cannot be 2, and again our set is not {2, 3, 13, 17, 19}, and thus the sum is greater than 55. Sufficient.

Answer: D.

missionmba2025 · Answer

(1) The product of any three numbers of the data set P is odd.

The set doesn't contain two.

_ _ 13 17 19

The average will be lowest when the first two places have lowest values

3 5 13 17 19

The sum of the set is (3+5+13+17+19) = 57

As the sum is greater than 55, the average is greater than 11. The statement is sufficient.

(2) The range of the data set P is even

All prime numbers are odd, hence if the range of the prime number is even, the set doesn't contain any even prime.

The statement conveys the same information as statement 1.

If we take the lowest prime numbers 3, 5, 13, 17, and 19, the average is greater than 11.

Hence this statement is also sufficient.

IMO D

Archit3110 · Answer

given that set P has 5 different prime numbers , median is 13 
target is avg mean of P >11 ; i.e. is sum >55
#1
The product of any three numbers of the data set P is odd.
meaning that all values in set P are odd 
least value of set P ( 3,5,13,17,19) sum is 57

also for all values of set P sum will be >57
sufficient
#2
The range of the data set P is even.
meaning that all values of set P are odd
and least set value of P will be 
( 3,5,13,17,19) sum is 57 
sufficient
  option D

chetan2u · Answer

If the data set P consists of 5 different prime numbers and has a median of 13, is the average (arithmetic mean) of the data set P greater than 11?

Let us simplify and modify the question. 
  So the first two numbers could be 2, 3, 5, 7 or 11, while the larger two could be 17, 19 and greater.  
The questions asks whether the sum of the 5 prime numbers is greater than 5*11 or 55. 
The least total will be 2+3+13+17+19 or 54. 
And the next higher sum would be given by replacing 2 by 5 and the total becomes 54-2+5 or 57>55.

Finally the question has become: Is 2 in the set?

(1) The product of any three numbers of the data set P is odd.
This means all number are odd and 2 is not there. 
Sufficient

(2) The range of the data set P is even.
The largest would always be odd, so the smallest has to be odd to give range as even. 
Again, 2 is out. 
Sufficient

D

Shadyshades · Answer

If the data set P consists of 5 different prime numbers and has a median of 13, is the average (arithmetic mean) of the data set P greater than 11?

(1) The product of any three numbers of the data set P is odd.

If the products of any three numbers is odd, then the minimum number of the data can't take 2. Therefore, the minimum data set of P 3,5,13,17,19 will have an average greater than 11. 
Sufficient.

(2) The range of the data set P is even.

If the range is even, then again the minimum number of the data can't take 2. Same situation as in statement 1. Hence, it's sufficient too.

Option D.

unnati157 · Answer

Given: set of 5 numbers that are prime with median = 13 (_ , _ , 13 , _ , _)
To find: If average of numbers >11 = sum of numbers >55

The prime numbers that are less than 13 = 2,3,5,7,11

(1) The product of any three numbers of the data set P is odd.
(2) The range of the data set P is even.

Statement 1:
As the product is odd, 2 cannot be one of the prime numbers as that would result in the product being even
Assuming we use 3, 5, 17, 19 for the remaining numbers to create the smallest total, the sum would be greater than 55. 
Therefore the use of any prime numbers that are equal or greater than the above numbers will lead to an average that is greater than 11
 Statement 1 is sufficient 
Eliminate Options B, C, E

Statement 2:
Rage of set is even = largest number - smallest number
Since 2 is the only even prime number, it would have to be eliminated as only an odd number subtracted from another odd number will result in an even range
Using the same logic from above, it will lead to an average that is greater than 11
 Statement 2 is sufficient

Therefore the correct option is D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

12 Days of Christmas GMAT Competition - Day 1: If the data set P

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

12 Days of Christmas GMAT Competition - Day 1: If the data set P

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards