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Difficulty:
95%
(hard)
Question Stats:
32% (02:10) correct
68%
(01:59)
wrong
based on 118
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Is x < 10 < y?
(1) x < y and xy = 100
(2) x^2 < 100 < y^2
M36-81
(1) x < y and xy = 100
(2) x^2 < 100 < y^2
M36-81
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10 Nov 2021, 03:25
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Bunuel
Is x < 10 < y?
(1) x < y and xy = 100
(2) x^2 < 100 < y^2
M36-81
(1) x < y and xy = 100
(2) x^2 < 100 < y^2
M36-81
Official Solution:
Is \(x < 10 < y\)?
(1) \(x < y\) and \(xy = 100\)
If \(x=-20\) and \(y=-5\), then the answer is NO but if \(x=5\) and \(y=20\), then the answer is YES. Not sufficient.
Notice that from \(xy = 100\) we can deduce that x and y have the same sign.
(2) \(x^2 < 100 < y^2\)
The above gives: \(-10 < x < 10\) and \(|y|>10\). So, \(y\) can be more than 10 as well as less than -10. Not sufficient.
(1)+(2) Since given that \(x < y\) and \(-10 < x < 10\), then \(y < -10\) is not possible, thus \(y > 10\). So, we have that \(x < 10 < y\). Sufficient.
Answer: C
General Discussion
grassbird
Joined: 08 Oct 2020
Last visit: 07 Dec 2021
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08 Feb 2021, 09:15
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This question, from first glance, is asking the positivity or negativity of X and Y.
(1) alone is not sufficient, take x=-20, y=-5, it works; take x=5,y=20, also works. Therefore, not sufficient.
(2) alone is not sufficient neither, take x=-5, y=-20, it works; take x=5. y=20, it also works. multiple suitable cases means its not sufficient.
Combine (1) and (2) together, X <Y and XY=100 AND X^2 <100 < Y^2. This confirms that X and Y must be >0, while X must be smaller than 10 and Y is bigger than 10. Which means yes its sufficient to determine the statement (The statement is true, but we don't really need that, we just want to know if the info given is enough to DETERMINE the statement)
So C, both statements together are sufficient, but neither statement alone is sufficient.
(1) alone is not sufficient, take x=-20, y=-5, it works; take x=5,y=20, also works. Therefore, not sufficient.
(2) alone is not sufficient neither, take x=-5, y=-20, it works; take x=5. y=20, it also works. multiple suitable cases means its not sufficient.
Combine (1) and (2) together, X <Y and XY=100 AND X^2 <100 < Y^2. This confirms that X and Y must be >0, while X must be smaller than 10 and Y is bigger than 10. Which means yes its sufficient to determine the statement (The statement is true, but we don't really need that, we just want to know if the info given is enough to DETERMINE the statement)
So C, both statements together are sufficient, but neither statement alone is sufficient.
