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The average of a set of five distinct integers is 300. If each number
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13 Aug 2021, 09:52
13 Aug 2021, 09:52
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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
A. -4,494
B. -3,997
C. -3,494
D. -3,194
E. The answer cannot be determined from the information given
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Re: The average of a set of five distinct integers is 300. If each number
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13 Aug 2021, 09:57
13 Aug 2021, 09:57
2
Carcass 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
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
Answer: A
Cheers,
Brent
RELATED VIDEO
Re: The average of a set of five distinct integers is 300. If each number
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15 Aug 2021, 19:58
15 Aug 2021, 19:58
1
GreenlightTestPrep wrote:
Carcass 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
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
Answer: A
Cheers,
Brent
RELATED VIDEO
Thank you for the explanation. I might have also solved pretty much the same way if I had not read this confusing statement "median of the set is the greatest possible value". I thought on the same lines a<b<c<d<e but that statement contradicted my method.
