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28 Feb 2024, 09:37
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x: 5
y: 50
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
92% (01:14) correct
8%
(01:31)
wrong
based on 1173
sessions
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A corporation uses a model of diminishing returns to make predictions about the expected returns on research investment. For this model, in order to produce an x% increase in annual profits in subsequent years, the corporation must invest y% of annual profits into research, where \(y = 2x^2\) .
Select two different numbers that are jointly compatible with the information provided and could be the values for x and for y. Make only two selections, one in each column.
Select two different numbers that are jointly compatible with the information provided and could be the values for x and for y. Make only two selections, one in each column.
ID: 700275
| x | y | |
| 1 | ||
| 3 | ||
| 5 | ||
| 20 | ||
| 50 | ||
| 80 |
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Official Answer
x: 5
y: 50
28 Feb 2024, 18:23
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A corporation uses a model of diminishing returns to make predictions about the expected returns on research investment. For this model, in order to produce an \(x%\) increase in annual profits in subsequent years, the corporation must invest \(y\)% of annual profits into research, where \(y = 2x^2\).
Select two different numbers that are jointly compatible with the information provided and could be the values for \(x\) and for \(y\). Make only two selections, one in each column.
The passage tells us that \(y = 2x^2\).
So, to find possible values of \(x\) and \(y\), we can consider each value as a possible \(x\) and square it and multiply the square by \(2\) to see whether we get one of the other values. Once one of the possible \(x\) values produces one of the other values when we put the possible \(x\) into \(2x^2\), the other value produced will be \(y\).
\(1\)
\(2(1^2) = 2\)
Not one of the other values.
Eliminate.
\(3\)
\(2(3^2) = 18\)
Not one of the other values.
Eliminate.
\(5\)
\(2(5^2) = 50\)
\(50\) is one of the other values. So, \(x = 5\), and \(y = 50\).
\(20\)
\(50\)
\(80\)
To confirm that none of the remaining three values can be \(x\), we can see that the squares of \(20\), \(50\), and \(80\) are much larger than any of the other values. So, there's no way \(20\), \(50\), or \(80\) could be \(x\), and thus also none of them squared and multiplied by \(2\) could be \(y\).
Correct answer: \(5\), \(50\)
Select two different numbers that are jointly compatible with the information provided and could be the values for \(x\) and for \(y\). Make only two selections, one in each column.
The passage tells us that \(y = 2x^2\).
So, to find possible values of \(x\) and \(y\), we can consider each value as a possible \(x\) and square it and multiply the square by \(2\) to see whether we get one of the other values. Once one of the possible \(x\) values produces one of the other values when we put the possible \(x\) into \(2x^2\), the other value produced will be \(y\).
\(1\)
\(2(1^2) = 2\)
Not one of the other values.
Eliminate.
\(3\)
\(2(3^2) = 18\)
Not one of the other values.
Eliminate.
\(5\)
\(2(5^2) = 50\)
\(50\) is one of the other values. So, \(x = 5\), and \(y = 50\).
\(20\)
\(50\)
\(80\)
To confirm that none of the remaining three values can be \(x\), we can see that the squares of \(20\), \(50\), and \(80\) are much larger than any of the other values. So, there's no way \(20\), \(50\), or \(80\) could be \(x\), and thus also none of them squared and multiplied by \(2\) could be \(y\).
Correct answer: \(5\), \(50\)
12 Mar 2024, 00:36
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Quote:
Given the relation \(y = 2x^2\)
We simply need values of x and y that satisfy this relation. Note that x will be much smaller than y so we should start trying with the smallest values for x.
If x = 1, y = 2 (not there in t able)
If x = 3, y = 2*9 = 18 (not there in table)
If x = 5, y = 2*25 = 50 (available)
Hence x = 5, y = 50 (ANSWER)
