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22 May 2023, 03:30
Kudos
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D
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Difficulty:
45%
(medium)
Question Stats:
67% (02:13) correct
33%
(02:30)
wrong
based on 33
sessions
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Not Attempted Yet
If x and y are positive, is y/x + x/y > 2?
(1) x > y
(2) x > 1 > y
(1) x > y
(2) x > 1 > y
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
22 May 2023, 06:24
Kudos
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Bunuel
There can be three cases
1) x > y
2) x < y
3) x = y
For the first and the second case depending on the value of x and y either \(\frac{y}{x} \text{or} \frac{x}{y}\) will be either less than 1 or greater than 1. However the sum \(\frac{y}{x} + \frac{x}{y}\) will be greater than 2.
However, if the value of x and y are equal (i.e. x = y) the value of \(\frac{y}{x} + \frac{x}{y}\) = 2.
Hence we can translate the question as
Is y = x?
Statement 1
(1) x > y
The statements tells us that \(x \neq y\), hence we can conclude that \(\frac{y}{x} + \frac{x}{y} > 2\)
This statement is sufficient. We can eliminate B, C, and E.
Statement 2
(2) x > 1 > y
The statements tells us that \(x \neq y\), hence we can conclude that \(\frac{y}{x} + \frac{x}{y} > 2\)
This statement is sufficient.
Option D
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