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

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

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New post 05 Feb 2019, 03:19
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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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New post 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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Re: If 1/y < x < 0, then which one of the following must be true?  [#permalink]

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New post 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


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

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