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01 Oct 2012, 05:17
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D
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Difficulty:
35%
(medium)
Question Stats:
71% (01:42) correct
29%
(01:50)
wrong
based on 4028
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If x and y are positive, is x < 10 < y?
(1) x < y and xy = 100
(2) x^2 < 100 < y^2
(1) x < y and xy = 100
(2) x^2 < 100 < y^2
01 Oct 2012, 05:18
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SOLUTION
If x and y are positive, is x < 10 < y?
(1) x < y and xy = 100. Since both \(x\) and \(y\) are positive AND \(x < y\), then in order \(xy=100\) to hold true, one multiple must be less than 10 and another greater than 10, thus \(x < 10 < y\). Sufficient.
(2) x^2 < 100 < y^2. Take the square root from all three parts: \(|x|<10<|y|\). Again, since both \(x\) and \(y\) are positive, then it transforms to \(x < 10 < y\). Sufficient.
Answer: D.
If x and y are positive, is x < 10 < y?
(1) x < y and xy = 100. Since both \(x\) and \(y\) are positive AND \(x < y\), then in order \(xy=100\) to hold true, one multiple must be less than 10 and another greater than 10, thus \(x < 10 < y\). Sufficient.
(2) x^2 < 100 < y^2. Take the square root from all three parts: \(|x|<10<|y|\). Again, since both \(x\) and \(y\) are positive, then it transforms to \(x < 10 < y\). Sufficient.
Answer: D.
01 Oct 2012, 08:19
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Bunuel
(1) If \(x=y\) and \(xy=100\), then \(x=y=10\). So, if the two positive numbers \(x\) and \(y\) are not equal, one must be smaller than \(10\) and the other one must be greater than \(10\). It is given that \(x<y\), so necessarily \(x<10<y\).
Sufficient.
(2) Since we are given that \(x\) and \(y\) are positive, we can take the square root of all the sides in the given inequality and obtain \(x<10<y\).
Sufficient.
Answer D.
