The average of a set of five distinct integers is 300.

Question

The average of a set of five distinct integers is 300. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?

A. -4,494
B. -3,997
C. -3,494
D. -3,194
E. The answer cannot be determined from the information given

wunsun · Accepted Answer

There are 5 distinct numbers that must have an average of 300
 \frac{{x_a + x_b + x_c + x_d + x_e}}{5}=300 
 x_a + x_b + x_c + x_d + x_e=1500

We want to know the sum of the two smallest values, therefore:
 x_a + x_b=1500- x_c - x_d - x_e 
The largest value,  x_e  can at most be 1999, then  x_d  is 1998 and the median  x_c  is 1997.

Therefore:
 x_a + x_b=1500-1997-1998-1999 
 x_a + x_b=-4494

Answer is A

rukna · Answer

I got confused while doing this very simple problem. The language was not very clear ( atleast to me)

Here is what I thought :-

set consists of no say A B C D E

all are distinct. Now median has to be max value ( in set , this is what I thought).

Median can be max if median is equal to all other elements ahead of set. So set should look like:

A B C C C. and C=1999.

But how is this possible, the other elements cannot be equal to median. Its stated in question that they are all distinct.

I could not understand this question

that they just want max value for other 3 elements to make median max.

BrentGMATPrepNow · Answer

Let the 5 integers be a, b, c, d and e, such that a < b < c < d < e

The average of a set of five distinct integers is 300  
So, the SUM of all 5 numbers = (5)(300) =   1500

Each number is less than 2,000 AND we want to MAXIMIZE the median (which is c)
So, let e = 1999
d = 1998 
and c = 1997

Now that we have MAXIMIZED the median, what is the sum of the two smallest numbers (i.e.,  a + b )?
Well, we know that a + b + c + d + e =   1500  
So, we can write  a + b  + 1997 + 1998 + 1999 =   1500

IMPORTANT: To make things easy calculations-wise, notice that 1997 + 1998 + 1999 is ALMOST 6000. In fact it's 6 less than 6000. 
So, we can write:  a + b  + (6000 - 6) =   1500  
Now subtract 6000 from both sides:  a + b  - 6 = -4500
Add 6 to both sides:  a + b  = -4494

Answer: A

Cheers,
Brent

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=Y9f_0QJU1ug

desaichinmay22 · Answer

The average of a set of five distinct integers is 300. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?

A. -4,494
B. -3,997
C. -3,494
D. -3,194
E. The answer cannot be determined from the information given

Kudos for the correct solution

Sum of the set = 300*5=1500 Each number is less than 2000 and median of the set is the greatest possible value.
Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.
Therefore sum of two smallest numbers= 1500-5994= -4494
Answer=A

kanigmat011 · Answer

the median of the set is the greatest possible value

Can somebody explain what is the significance of this statement mentioned in the question stem.

I personally feel it shouldn't be there as if we consider this answer turns out to be E

As median is said to be greatest possible value then that will be 1999.

SO out of 5 numbers A,B,C,D,E

C,D,E needs to be equal to 1999 as C which is median is the greatest value possible and D,E cannot exceed 2000.

But this entire situation contradicts another statement in the question that all 5 integers are distinct

So I feel this question is ambiguous and cannot be answered

Kindly let me know if my reasoning is incorrect

sagarbuss · Answer

Bunuel

Can you please clarify the ambiguity... the question stem says 
1. distinct integers.
2. median is equal to largest number, making all three digits equal contradicting #1...

since it is a prep company question, i guess the question is not badly framed...

kunal555 · Answer

In a set containing odd number of terms arranged in ascending order, the median is the middle value.
The numbers in this set can be distinct or same, positive or negative, even or odd, etc.
Maximization of median does not necessarily mean that the median has to be the biggest number in the set.
Value of median will depend upon the constraints of the question.
In this question it is given that the set contains 5 distinct integers with average of 300 or a sum of 1500.
We are also given that each number in the set is less than 2000.
So, the biggest number in the set can be 1999 followed by 1998 and 1997.
Here 1997 is our median as you need 2 numbers bigger than the median and 2 numbers less than the median.
Let a and b be the two numbers smaller than 1997.
So our set is (a,b,1997,1998,1999)
Now,
a+b+1997+1998+1999 = 1500
or a+b+5994=1500
or a+b = 1500-5994
or a+b=-4994

Answer:- A

sagarbuss · Answer

Thanks for prompt response...
So , to say in verbal terms... do you mean, 'greatest possible value' (in question stem) doesn't not refer to 'greatest number in the set', instead it points to 'greatest possible median value'?

kunal555 · Answer

Yes.
Note that the greatest number in this set cannot be the median as it would be the last number when the numbers in the set are arranged in ascending order.

guialain · Answer

I missed it beacuse the question was not clear to me.
"the median is the greatest possible value"... Hum..

guialain · Answer

I missed it beacuse the question was not clear to me.
"the median is the greatest possible value"... Hum..

JeffTargetTestPrep · Answer

We are given that the average of a set of five distinct integers is 300, and thus, the sum of the 5 integers is (5)(300) = 1,500. Since each number is less than 2,000 and we want the median to be as large as possible, the median should be 1,997, so that the two largest numbers could be 1,998 and 1,999. Therefore, the sum of the three largest numbers in the set is 1,997 + 1,998 + 1,999 = 5,994. Since the sum of the 5 numbers is 1,500, the sum of the two smallest numbers must be 1,500 - 5,994 = -4,494.

Answer: A.

ramalcha · Answer

A quick glance at the answer choices prior starting to solve shows a large difference between them, hence estimation is possible here without too much hassle with adding and subtracting difficult numbers.

Assume the 3 largest numbers, including the median, are 2000:

Therefore  \frac{Sum of all numbers}{5}=\frac{(2000 + 2000 + 2000 +2x)}{5}=300

Rearranging this gives  2x=-4500 , which is the sum of the 2 smallest integers. Closest answer is (A)

AliciaSierra · Answer

Bunuel ,

Hello  Bunuel ,
Could you please explain how "median of the set could be greatest possible value". If any term is median then it is either less than or equal to largest value of set. So if a set contains distinct integers then median will be smaller than Largest value of set.

Please help me to understand what does this line mean in above question->median of the set is the greatest possible value.

Your help is much appreciated.

Thanks,

bb · Answer

This means that the median is maxed out e.g 739. This does not mean it is greater than any of the members of the set...

Posted from my mobile device

rvgmat12 · Answer

Sum = 1500

Max out the positive numbers to get the max median possible

1997, 1998, 1999

Sum of the lowest numbers = -6000+6+1500 = -4494

A

mavelous · Answer

Just wanted to say this is a great question
I do sympathize with those members who had a difficulty deciphering the prompt. To me though, as far as GMAT language goes, the wording is spot on.
perhaps the challenge lies right there - correctly deciphering and keeping track of seemingly intimidating restraints.

TheNikunjAgarwal · Answer

This question has a big problem in its language. On one hand , question is saying that median of the set is the greatest possible value and on the other side, it is given that all integers are distinct. Clearly language is ambiguous and thus question is not at par with GMAT Standards

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.

The average of a set of five distinct integers is 300.

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 Problem Solving (PS) Questions

The average of a set of five distinct integers is 300.

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