Hi Paddy41,
This is a typical inequality DS question in GMAT.
It’s a YES-NO DS question.
Before moving into the statements, start understanding for what values of x, x^2 < 1/x?
Question: x^2 < 1/x?
Let’s first try with positive integers, For x = 2, 3, 4… x^2 > 1/x, here the answer to the question is NO.
For negative values, that is, x < 0, x^2 > 1/x, here the answer to the question is NO.
For “x” a proper(positive) fraction, x = ½, ¼... x^2 < 1/x, here the answer to the question is YES.
Sometimes knowing the YES and NO answer to the question helps to solve the question better.
So, NET-NET, if 0<x<1 then the answer to the question is YES.
Or else Answer to the question is NO.
Let’s move onto statements now,
Statement I is sufficient:
x^2 > x
Except for the values between, 0<x<1, x^2 > x
So, answer to the question is always NO here.
Hence sufficient.
To understand the expression, x^2 > x
We can find the roots and draw the number line.
x^2 > x
x^2-x > 0
x(x-1) > 0
So, roots (critical points) are zero and 1.
See the below number line, to understand how it works.
Just choose values from the given (in the pic below) three ranges and check which satisfy the expression x^2 > x.
Statement II is sufficient:
1 > 1/x
That is “x” has to be negative or x has to greater than 1.
You can do some plugging in here to check it.
For x is negative, 1(positive) > negative.
For x is greater than 1, 1 > 1/x. For x = 2, 3, 4… 1 > 1/x,
So, answer to the question is always NO here.
Hence sufficient.
So, the answer has to be D (Each alone sufficient).
Hope this helps.
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