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The average (arithmetic mean) of x and y
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19 May 2017, 01:18
19 May 2017, 01:18
Expert Reply
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Question Stats:
72% (00:49) correct
27% (00:53) wrong based on 233 sessions
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\(x < y\)
Quantity A |
Quantity B |
The average (arithmetic mean) of x and y |
The average (arithmetic mean) of x, y and y |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: x < y
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18 Sep 2017, 14:19
18 Sep 2017, 14:19
5
Carcass wrote:
x < y
Quantity A |
Quantity B |
The average (arithmetic mean) of x and y |
The average (arithmetic mean) of x, y and y |
We can solve the question using matching operations
First apply the formula for finding averages
Quantity A: (x + y)/2
Quantity B: (x + y + y)/3
Simplify Quantity B to get:
Quantity A: (x + y)/2
Quantity B: (x + 2y)/3
Eliminate that fractions by multiplying both quantities by 6 (the least common multiple of 2 and 3)
When we do this, we get:
Quantity A: 3(x + y)
Quantity B: 2(x + 2y)
Expand to get:
Quantity A: 3x + 3y
Quantity B: 2x + 4y
Subtract 2x from both quantities to get:
Quantity A: x + 3y
Quantity B: 4y
Subtract 3y from both quantities to get:
Quantity A: x
Quantity B: y
Since we're told that x < y, we can conclude that Quantity B is greater.
Answer:
Show: ::
B
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General Discussion
Re: x < y
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17 Sep 2017, 01:24
17 Sep 2017, 01:24
2
How could the answer be B? Without any restriction about the values of x and y, they could also be both equal to zero and then A and B would be equal. Otherwise, if for example x = 1 and y = 2, then column A would be 3/2, while column B would be 5/2, thus column B would be greater. Since there is no unique relationship, the answer should be D!
