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# If 1/y < x < 0, then which one of the following must be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 52911
If 1/y < x < 0, then which one of the following must be true?  [#permalink]

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05 Feb 2019, 03:19
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Difficulty:

(N/A)

Question Stats:

14% (00:18) correct 86% (01:48) wrong based on 7 sessions

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If $$\frac{1}{y}< x < 0$$, then which one of the following must be true?

A. $$1 < x^2$$

B. $$x^2 < x$$

C. $$−1 < x^3 < 0$$

D. $$\frac{1}{x} > -1$$

E. $$x^3 < x$$

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Re: If 1/y < x < 0, then which one of the following must be true?  [#permalink]

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05 Feb 2019, 05:14
Bunuel wrote:
If $$\frac{1}{y}< x < 0$$, then which one of the following must be true?

A. $$1 < x^2$$

B. $$x^2 < x$$

C. $$−1 < x^3 < 0$$

D. $$\frac{1}{x} > -1$$

E. $$x^3 < x$$

good question :
I am not sure of my soln.. given
$$\frac{1}{y}< x < 0$$
we can say
1/xy<1<0 --- ( a)
or 1<xy<0---( b)
or we can say that from (a) xy is -ve and from (b) xy lies between 1 & 0 and is +ve
only option which I think satisfies these two parameters is option B
IMO B
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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If 1/y < x < 0, then which one of the following must be true?  [#permalink]

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05 Feb 2019, 05:32
1
Bunuel wrote:
If $$\frac{1}{y}< x < 0$$, then which one of the following must be true?

A. $$1 < x^2$$

B. $$x^2 < x$$

C. $$−1 < x^3 < 0$$

D. $$\frac{1}{x} > -1$$

E. $$x^3 < x$$

A. $$1 < x^2......x^2-1>0.....(x-1)(x+1)>0$$ Now, x-1<0 since x<0, therefore, x+1<0 or x<-1.. But x could be anything <0. say y is -2, so x>-1/2

B. $$x^2 < x......$$ This means x>0.. Never true, as x<0

C. $$−1 < x^3 < 0......-1<x<0$$.... Say y = -1/8, so x>1/(-1/8) or x>-8.. Thus x could be -7, -3 and so on.

D. $$\frac{1}{x} > -1.........\frac{x+1}{x} > 0$$...... x<0, so x+1<0 or x<-1.. We have seen in A, need not be true

E. $$x^3 < x$$ this is same as $$x^2>1$$, multiply it by negative x $$x^3<x$$.. same as A.. need not be true.
or (x^3-x)<0......x(x^2-1)<0... x<0, so x^2-1>0, that is x^2>1 or x<-1...

None seems to be true. May be there is some restriction on variables x and y. Bunuel
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Re: If 1/y < x < 0, then which one of the following must be true?   [#permalink] 05 Feb 2019, 05:32
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