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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
x/w - x/y = 0 and w^2 + 4 = 4w
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25 Oct 2021, 07:50
25 Oct 2021, 07:50
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\(\frac{x}{w}-\frac{x}{y}=0\)
\(w^2 + 4 = 4w\)
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(w^2 + 4 = 4w\)
Quantity A |
Quantity B |
y |
2 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x/w - x/y = 0 and w^2 + 4 = 4w
[#permalink]
26 Oct 2021, 05:16
26 Oct 2021, 05:16
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GreenlightTestPrep wrote:
\(\frac{x}{w}-\frac{x}{y}=0\)
\(w^2 + 4 = 4w\)
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(w^2 + 4 = 4w\)
Quantity A |
Quantity B |
y |
2 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
I created this question to highlight an important consideration when comparing two equivalent fractions.
If we know that \(\frac{x}{w}=\frac{x}{y}\), we can't then conclude that \(w = y\) (even though both fractions have the same numerator), since it COULD be the case that \(x = 0\), in which case we have \(\frac{0}{w}=\frac{0}{y}\).
Notice that the equation \(\frac{0}{w}=\frac{0}{y}\) holds true for all nonzero values of \(w\) and \(y\).
So, we can't necessarily conclude that \(w = y\)
Since we now know that, when \(x=0\), the given equation (\(\frac{x}{w}=\frac{x}{y}\)) holds true for all nonzero values of \(w\) and \(y\), let's examine two possible cases:
Case a: \(w = 2\), \(x = 0\) and \(y = 2\). These values satisfy the given equation since \(\frac{0}{2}=\frac{0}{2}\)
In this case, Quantity A equals Quantity B
Case b: \(w = 2\), \(x = 0\) and \(y = 10\). These values satisfy the given equation since \(\frac{0}{2}=\frac{0}{10}\)
In this case, Quantity A > Quantity B
Answer: D
Re: x/w - x/y = 0 and w^2 + 4 = 4w
[#permalink]
29 Oct 2021, 03:15
29 Oct 2021, 03:15
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
\(\frac{x}{w}-\frac{x}{y}=0\)
\(w^2 + 4 = 4w\)
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(w^2 + 4 = 4w\)
Quantity A |
Quantity B |
y |
2 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
I created this question to highlight an important consideration when comparing two equivalent fractions.
If we know that \(\frac{x}{w}=\frac{x}{y}\), we can't then conclude that \(w = y\) (even though both fractions have the same numerator), since it COULD be the case that \(x = 0\), in which case we have \(\frac{0}{w}=\frac{0}{y}\).
Notice that the equation \(\frac{0}{w}=\frac{0}{y}\) holds true for all nonzero values of \(w\) and \(y\).
So, we can't necessarily conclude that \(w = y\)
Since we now know that, when \(x=0\), the given equation (\(\frac{x}{w}=\frac{x}{y}\)) holds true for all nonzero values of \(w\) and \(y\), let's examine two possible cases:
Case a: \(w = 2\), \(x = 0\) and \(y = 2\). These values satisfy the given equation since \(\frac{0}{2}=\frac{0}{2}\)
In this case, Quantity A equals Quantity B
Case b: \(w = 2\), \(x = 0\) and \(y = 10\). These values satisfy the given equation since \(\frac{0}{2}=\frac{0}{10}\)
In this case, Quantity A > Quantity B
Answer: D
if question didn't assign any value to variables ,then we can consider ans as D, right?
