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

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The average of a set of five distinct integers is 300.  [#permalink]

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09 Aug 2014, 03:43
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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

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Re: The average of a set of five distinct integers is 300.  [#permalink]

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09 Aug 2014, 07:46
1
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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:
$$x_a + x_b=1500-1997-1998-1999$$
$$x_a + x_b=-4494$$

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Re: The average of a set of five distinct integers is 300.  [#permalink]

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09 Aug 2014, 08:02
1
[quote="WoundedTiger"]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
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The average of a set of five distinct integers is 300.  [#permalink]

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08 Aug 2015, 02:52
2
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.
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Re: The average of a set of five distinct integers is 300.  [#permalink]

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10 Aug 2015, 02:47
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
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Re: The average of a set of five distinct integers is 300.  [#permalink]

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27 Sep 2015, 07:43
WoundedTiger wrote:
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

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...
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Re: The average of a set of five distinct integers is 300.  [#permalink]

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27 Sep 2015, 09:38
2
sagarbuss wrote:
WoundedTiger wrote:
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

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...

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

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The average of a set of five distinct integers is 300.  [#permalink]

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27 Sep 2015, 09:55
1
kunal555 wrote:
sagarbuss wrote:
WoundedTiger wrote:
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

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...

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

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'?
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Re: The average of a set of five distinct integers is 300.  [#permalink]

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27 Sep 2015, 10:05
sagarbuss wrote:

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'?

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.
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Re: The average of a set of five distinct integers is 300.  [#permalink]

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17 Feb 2017, 05:27
I missed it beacuse the question was not clear to me.
"the median is the greatest possible value"... Hum..
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Re: The average of a set of five distinct integers is 300.  [#permalink]

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17 Feb 2017, 05:28
I missed it beacuse the question was not clear to me.
"the median is the greatest possible value"... Hum..
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Re: The average of a set of five distinct integers is 300.  [#permalink]

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23 Feb 2017, 10:27
1
WoundedTiger wrote:
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

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.

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Re: The average of a set of five distinct integers is 300.  [#permalink]

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20 Apr 2018, 15:12
Top Contributor
WoundedTiger wrote:
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

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

Cheers,
Brent

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Re: The average of a set of five distinct integers is 300. &nbs [#permalink] 20 Apr 2018, 15:12
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# The average of a set of five distinct integers is 300.

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