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# Which of the following is always correct

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Manager
Joined: 07 Jun 2017
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Which of the following is always correct [#permalink]

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22 Oct 2017, 23:48
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Which of the following is always correct?

A. If $$\frac{1}{x}$$ is greater than $$x$$, $$x^2$$ is greater than $$x$$

B. If $$\frac{1}{x}$$ is greater than $$x$$, $$x$$ is greater than $$x^2$$

C. If $$x^2$$ is greater than $$x$$, $$x^3$$ is greater than $$x^2$$

D. If $$x^3$$ is greater than $$x^2$$, $$x^4$$ is greater than $$x^3$$

E. If $$x^4$$ is greater than $$x^3$$, $$x^5$$ is greater than $$x^4$$
[Reveal] Spoiler: OA

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Manager
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Re: Which of the following is always correct [#permalink]

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22 Oct 2017, 23:59
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IMO Option D is correct.
In option D x is always positive and graeter than1.
Say x=2
8 is greater than 4.So 16 is greater than 8.
Statement D is true for all values of x greater than1(even fractions).
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Re: Which of the following is always correct [#permalink]

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23 Oct 2017, 08:12
Why is the answer not A? by what is given, x must be negative, so x squared will always be larger, no?
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Re: Which of the following is always correct [#permalink]

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23 Oct 2017, 08:17
vmelgargalan wrote:
Why is the answer not A? by what is given, x must be negative, so x squared will always be larger, no?

A. If $$\frac{1}{x}$$ is greater than $$x$$, $$x^2$$ is greater than $$x$$

1/x > x holds true for x < -1 and 0 < x < 1. If x < -1, then yes, x^2 > x but if 0 < x < 1, then x^2 < x.
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Which of the following is always correct [#permalink]

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23 Oct 2017, 08:29
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nkmungila wrote:
Which of the following is always correct?

A. If $$\frac{1}{x}$$ is greater than $$x$$, $$x^2$$ is greater than $$x$$

B. If $$\frac{1}{x}$$ is greater than $$x$$, $$x$$ is greater than $$x^2$$

C. If $$x^2$$ is greater than $$x$$, $$x^3$$ is greater than $$x^2$$

D. If $$x^3$$ is greater than $$x^2$$, $$x^4$$ is greater than $$x^3$$

E. If $$x^4$$ is greater than $$x^3$$, $$x^5$$ is greater than $$x^4$$

A. 1/x > x
So, 0<x<1 (x^2<x)or x<-1(x^2>x)
NOT CORRECT

B. 1/x > x
So, 0<x<1 (x>x^2)or x<-1(x<x^2)
NOT CORRECT

C. x^2 > x
So, x>1(x^3 >X^2) or x<0 (x^3 < x^2)
NOT CORRECT

D. x^3 > x^2
So, x>1 (x^4>x^3)
CORRECT

E. x^4 > x^3 ~ x^2 > x (Same as C)
NOT CORRECT
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Last edited by shashankism on 23 Oct 2017, 08:44, edited 1 time in total.
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Which of the following is always correct [#permalink]

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23 Oct 2017, 08:36
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Which of the following is always correct?

A. If $$\frac{1}{x}$$ is greater than $$x$$, $$x^2$$ is greater than $$x$$

$$\frac{1}{x}$$ is greater than $$x$$ => Either x = fraction ( between 0 and 1) or negative (less than -1)

if x = fraction => $$\frac{1}{(1/2)}$$ > $$\frac{1}{2}$$
=> $$x^2$$ is greater than $$x$$ False

if x = negative => $$\frac{1}{(-2)}$$ > $$-2$$
=> $$x^2$$ is greater than $$x$$ True

2 different solutions. So equation not always true

B. If $$\frac{1}{x}$$ is greater than $$x$$, $$x$$ is greater than $$x^2$$

Same as above
$$\frac{1}{x}$$ is greater than $$x$$ => Either x = fraction ( between 0 and 1) or negative (less than -1)

if x = fraction => $$\frac{1}{(1/2)}$$ > $$\frac{1}{2}$$
=> $$x$$ is greater than $$x^2$$ True

if x = negative => $$\frac{1}{(-2)}$$ > $$-2$$
=>$$x$$ is greater than $$x^2$$ False

2 different solutions. So equation not always true

C. If $$x^2$$ is greater than $$x$$, $$x^3$$ is greater than $$x^2$$

$$x^2$$ is greater than $$x$$ => either x =-ve or x=+ve
if x =-ve => $$x^3$$ is greater than $$x^2$$ False
if x =+ve => $$x^3$$ is greater than $$x^2$$ True

2 different solutions. So equation not always true

D. If $$x^3$$ is greater than $$x^2$$, $$x^4$$ is greater than $$x^3$$

$$x^3$$ is greater than $$x^2$$ => For this condition to be true. x need to be +ve and greater than 1.

And for above value of x => $$x^4$$ will always be greater than $$x^3$$

1 solution. Always true condition

E. If $$x^4$$ is greater than $$x^3$$, $$x^5$$ is greater than $$x^4$$

$$x^4$$ is greater than $$x^3$$ => either x =-ve or x=+ve
if x =-ve => $$x^5$$ is greater than $$x^4$$ False
if x =+ve => $$x^5$$ is greater than $$x^4$$ True

Which of the following is always correct   [#permalink] 23 Oct 2017, 08:36
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