The average of 5 different numbers is 14. What is the average (arithmetic mean) of the 3 largest numbers?
(1) The average (arithmetic mean) of the two smallest numbers is 5.
(2) The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.
According to me ans should be A, but the correct ans is D. Can someone explain?
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Avg of 3 largest numbers
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GMATinsight
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Suppose the numbers (in ascending order of their values) are a, b, c, d and eanurag_7 wrote:The average of 5 different numbers is 14. What is the average (arithmetic mean) of the 3 largest numbers?
(1) The average (arithmetic mean) of the two smallest numbers is 5.
(2) The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.
According to me ans should be A, but the correct ans is D. Can someone explain?
Then (Given), a+b+c+d+e = 5x14 = 70
c+d+e=?
Statement 1)The average (arithmetic mean) of the two smallest numbers is 5
a+b = 2x5 = 10
therefore c+d+e = 70-10 = 60
therefore, Average of largest three numbers = 60/3 = 20
SUFFICIENT
Statement 2)The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers
(a+b)/2 = (1/4)x{(c+d+e)/3}
i.e. (a+b) = (1/6)x(c+d+e)
therefore, a+b+c+d+e = 70 ===> [(1/6)x(c+d+e)]+(c+d+e) = 70
i.e. (7/6)x(c+d+e) = 70
i.e. (c+d+e) = 70x6/7 = 60
Average of largest three numbers = 60/3 = 20
SUFFICIENT
Answer: Option D
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Hi anurag_7,
Certain DS question can be solved with a conceptual approach, as opposed to a "math" or "tactical" one.
This prompt does NOT ask us for any of the specific numbers, it asks for the average of the 3 largest. This type of "construction" gives us some options in terms of how we can solve it.
Since your question is just about Fact 2, I'm going to focus on that piece of the question.
From the prompt, we know that the average of 5 different numbers is 14. This means that the SUM of the 5 numbers = 70.
Fact 2: The average of the two smallest numbers = (1/4)(the average of the 3 largest numbers).
Here's a way to approach Fact 2 by using 1 variable:
X = Average of the three largest numbers
Thus... (1/4)(X) = the average of the two smallest numbers
Since the sum of the 5 numbers is 70, we have....
X/4 + X/4 + X + X + X = 70
3.5X = 70
X = 20
We now know that the average of the largest three numbers is 20.
Fact 2 is SUFFICIENT
GMAT assassins aren't born, they're made,
Rich
Certain DS question can be solved with a conceptual approach, as opposed to a "math" or "tactical" one.
This prompt does NOT ask us for any of the specific numbers, it asks for the average of the 3 largest. This type of "construction" gives us some options in terms of how we can solve it.
Since your question is just about Fact 2, I'm going to focus on that piece of the question.
From the prompt, we know that the average of 5 different numbers is 14. This means that the SUM of the 5 numbers = 70.
Fact 2: The average of the two smallest numbers = (1/4)(the average of the 3 largest numbers).
Here's a way to approach Fact 2 by using 1 variable:
X = Average of the three largest numbers
Thus... (1/4)(X) = the average of the two smallest numbers
Since the sum of the 5 numbers is 70, we have....
X/4 + X/4 + X + X + X = 70
3.5X = 70
X = 20
We now know that the average of the largest three numbers is 20.
Fact 2 is SUFFICIENT
GMAT assassins aren't born, they're made,
Rich
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For average problems, remember the following:anurag_7 wrote:The average of 5 different numbers is 14. What is the average (arithmetic mean) of the 3 largest numbers?
(1) The average (arithmetic mean) of the two smallest numbers is 5.
(2) The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.
sum = (number)(average).
number = sum/average.
average = sum/number.
Let a, b, c, d, and e be the 5 values, in ascending order.
a+b+c+d+e = (number)(average) = 5*14 = 70.
Statement 1: The average (arithmetic mean) of the two smallest numbers is 5.
a+b = (number)(average) = 2*5 = 10.
c+d+e = (a+b+c+d+e) - (a+b) = 70-10 = 60.
Average of c, d, and e = sum/number = 60/3 = 20.
SUFFICIENT.
Statement 2: The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.
Statement 1 implies the following values:
Average of a and b = 5.
Average of c, d, and e = 20.
Sum of a+b+c+d+e = 70.
Notice that the two averages -- 5 and 20 -- also satisfy statement 2, since 5 is 1/4 of 20.
If these two averages both increase or both decrease, then the SUM will also increase or decrease.
Not possible, since the sum must be 70.
Implication:
Statement 2 is satisfied only by the SAME combination of values that satisfy statement 1.
Thus, the average of c, d and e = 20.
SUFFICIENT.
The correct answer is D.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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