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Re: If x is a nonzero number, which of the three numbers x, 1/x [#permalink]
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29 Mar 2014, 09:49
2
If x is a nonzero number, which of the three numbers x, 1/x and x^2 is greatest?
(1) -1 < x < 1. If x=1/2, then x=1/2, 1/x=2, and x^2=1/4, so 1/x has the greatest value but if x is negative, then both x and 1/x are negative and x^2=positive, so x^2 has the greatest value. Not sufficient.
(2) x is negative. For negative x both x and 1/x are negative and x^2=positive, so x^2 has the greatest value. Sufficient.
I hope you have got your answer from the solution above. Just adding a few points:
1. Whenever you come across with such questions, look out for expressions which are independent of the sign of their base variables. In this question \(x^2\) is independent of the sign of \(x\). It will be always be non-negative irrespective of the sign of \(x\). Any even power of a variable will be independent of the sign of the variable whereas any odd power of a variable will be dependent on the sign of the variable
2. Do keep in mind certain ranges where numbers behave differently.
a. For example in the range \(0 < x < 1\), \(x^2 < x\) and \(x < \frac{1}{x}\).
b.Another such range is \(-1 < x < 0\) where \(x^2 > x\) but \(x^3 < x^2\) and \(x > \frac{1}{x}\)
Re: If x is a nonzero number, which of the three numbers x, 1/x [#permalink]
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27 May 2015, 11:11
1
If x is a nonzero number, which of the three numbers x, 1/x and x^2 is greatest?
(1) -1 < x < 1 We know that x is a fraction, but we don't know if it is negative or positive. If x is -1/2, then we have -1/2, -2, and 1/4 (x^2 is greatest). If x is 1/2 we have 1/2, 2, and 1/4, making (1/x greatest) (2) x is negative We can answer this knowing the sign of x (again, take -1/2 as the example) B
Re: If x is a nonzero number, which of the three numbers x, 1/x [#permalink]
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27 May 2015, 22:00
Hi sidney123,
Your approach to TEST VALUES is a good one, but you have to do the necessary work (on the pad, so you can "see" it) to make sure that you're selecting the correct answer.
Here, we're asked to consider X, 1/X and X^2.....We're asked which is GREATEST.
Fact 2 tells us that X is NEGATIVE....
Using your two examples, we'd end up with....
X = -2 1/X = -1/2 X^2 = (-2)^2 = 4 So X^2 is the greatest
X = -1/2 1/X = 1/(-1/2) = -2 X^2 = (-1/2)^2 = 1/4 So X^2 is the greatest
The two examples yield the SAME result. Based on what we're told in Fact 2, X will ALWAYS be NEGATIVE, 1/X will ALWAYS be NEGATIVE and X^2 will ALWAYS be POSITIVE, so the answer will ALWAYS be X^2. Thus, Fact 2 is SUFFICIENT.
As you continue to practice DS, whenever you think a Fact is insufficient, you should be able to quickly prove it. Doing that little bit of extra work can pick you up a LOT of points in the Quant section.
Re: If x is a nonzero number, which of the three numbers x, 1/x [#permalink]
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27 May 2015, 22:53
Thankyou for all your input guys, really appreciate the time and effort taken to explain the simple problem. For some reason, I read the Q wrong(I don't know why?), I was looking at arranging x, 1/x and x^2 from smallest to greatest, in which case we need both statements. But the Q asks for which is greatest and stmt.2 is sufficient.
Re: If x is a nonzero number, which of the three numbers x, 1/x [#permalink]
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19 Jan 2018, 11:05
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