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w, x, y, and z are positive integers such that x > w and y < z
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13 Jul 2021, 04:35
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\(w\), \(x\), \(y\), and \(z\) are positive integers such that \( x > w\) and \(y < z\)
Quantity A
Quantity B
\(\frac{x}{y}\)
\(\frac{w}{z }\)
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.
Re: w, x, y, and z are positive integers such that x > w and y < z
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13 Jul 2021, 05:10
2
Carcass wrote:
\(w\), \(x\), \(y\), and \(z\) are positive integers such that \( x > w\) and \(y < z\)
Quantity A
Quantity B
\(\frac{x}{y}\)
\(\frac{w}{z }\)
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.
We can solve this question using matching operations (my favorite Quantitative Comparison strategy) Given: Quantity A: \(\frac{x}{y}\) Quantity B: \(\frac{w}{z }\)
Since \(y\) is POSITIVE, we can safely multiply both quantities by \(y\) to get: Quantity A: \(x\) Quantity B: \(\frac{wy}{z }\)
Since \(w\) is POSITIVE, we can safely divide both quantities by \(w\) to get: Quantity A: \(\frac{x}{w}\) Quantity B: \(\frac{y}{z }\)
If \(x\) and \(w\) are positive, and \( x > w\), then we can be certain that \(\frac{x}{w} > 1\) Likewise, if \(y\) and \(z\) are positive, and \( y < z\), then we can be certain that \(\frac{y}{z} < 1\)
So we get: Quantity A: Some number greater than 1 Quantity B: Some number less than 1
Re: w, x, y, and z are positive integers such that x > w and y < z
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19 Jul 2022, 06:57
2
The way I approached it without doing any variable manipulation or calculation:
As given in the question, w, x, y & z are positive such that x > w and y < z. This information is enough to compare the given fractions.
Among the numerators of the two fractions in both quantities, A's is greater according to the question conditions. Similarly, if we compare the denominators of the two fractions, the denominator of quantity A is smaller than that of quantity B, again as per the given conditions in the question. Therefore, A must be greater than B in this specific scenario.
Re: w, x, y, and z are positive integers such that x > w and y < z
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03 Feb 2024, 08:46
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Re: w, x, y, and z are positive integers such that x > w and y < z [#permalink]