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UShukla
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If x is a non-zero number, is x^5 < x^7? Updated on: 23 Apr 2020, 12:29
Originally posted by UShukla on 23 Apr 2020, 12:27.
Last edited by Bunuel on 23 Apr 2020, 12:29, edited 1 time in total.
Renamed the topic and edited the question.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

58% (02:02) correct 42% (02:22) wrong based on 132 sessions

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If x is a non-zero number, is x^5 < x^7?

(1) x < x^2

(2) 1/x >1/x^2

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This is a question from e-gmat and i am not convinced with the way they have solved this question.
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B
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If x is a non-zero number, is x^5 < x^7? 23 Apr 2020, 13:07
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\(x^5 < x^7\) is true in the ranges \(-1<x<0\) and \(x>1\)

So we must find out if \(x\) lies in one of these two ranges

(1) \(x < x^2\)

\(x(x-1)>0\)

If \(x>0\), we have \(x-1>0\) or \(x>1\) (in this case \(x^5<x^7\))

If \(x<0\), we have \(x-1<0\) or \(x<1\) so \(x\) may or may not be in the range \(-1<x<0\)

1 is not sufficient

(2) \(\frac{1}{x} >\frac{1}{x^2}\)

Since \(x\) is non zero, \(x^2\) must be positive so we can multiply both sides by \(x^2\) and keep the same inequality

\(\frac{x^2}{x}>\frac{x^2}{x^2}\)

\(x>1\) so yes, \(x^5<x^7\)

2 is Sufficient

Answer is (B)

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If x is a non-zero number, is x^5 < x^7? 23 Apr 2020, 14:45
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UShukla
If x is a non-zero number, is x^5 < x^7?

(1) x < x^2

(2) 1/x >1/x^2

Show Spoiler
This is a question from e-gmat and i am not convinced with the way they have solved this question.

1) x can lie anywhere in the number line except 0< x< 1. Depending on the sign of x, x^5 could be greater or lower than x^7. for x =-2, x^5 =- -32, x^7 =-128, so x^5 > x^7. But for positive sigh, the opposite happens. not sufficient
2) 1/x > 1/x^2, or, x < x^2. Same info as 1. Not sufficient
E is the answer.
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If x is a non-zero number, is x^5 < x^7? 23 Apr 2020, 23:18
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UShukla
If x is a non-zero number, is x^5 < x^7?

(1) x < x^2

(2) 1/x >1/x^2

Show Spoiler
This is a question from e-gmat and i am not convinced with the way they have solved this question.

for x^5 < x^7
x > 1 or -1 < x < 0

1) x < x^2
so x > 1 or x < 0
insufficient

2) 1/x >1/x^2
x^2/x > 1
x > 1

sufficient
IMO B
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If x is a non-zero number, is x^5 < x^7? 24 Apr 2020, 00:19
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UShukla
If x is a non-zero number, is x^5 < x^7?

(1) x < x^2

(2) 1/x >1/x^2

Show Spoiler
This is a question from e-gmat and i am not convinced with the way they have solved this question.

1) x can lie anywhere in the number line except 0< x< 1. Depending on the sign of x, x^5 could be greater or lower than x^7. for x =-2, x^5 =- -32, x^7 =-128, so x^5 > x^7. But for positive sigh, the opposite happens. not sufficient
2) 1/x > 1/x^2, or, x < x^2. Same info as 1. Not sufficient
E is the answer.

You cannot cross multiply in inequalities until you know x is definitely positive or negative.

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If x is a non-zero number, is x^5 < x^7? 24 Apr 2020, 00:56
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UShukla
If x is a non-zero number, is x^5 < x^7?

(1) x < x^2

(2) 1/x >1/x^2

Show Spoiler
This is a question from e-gmat and i am not convinced with the way they have solved this question.

Simplify the inequality


x^5 < x^7.......x^7-x^5>0......x^5(x^2-1)>0

So we are asked..
1) if x>0, then x^2>1 or {x<-1 and x>1}
2) If x<0, then x^2<1 or {-1<x<1}
3) If x=0, then answer is straight No

(1) x < x^2..
\(x^2>x.......x(x-1)>0\)
Two cases
If x>0, x>1....x>1......MAtches with (1)
If x<0, x<1....x<0.......Does not match with (2)
Insuff

(2) 1/x >1/x^2
\(\frac{1}{x} >\frac{1}{x^2}..........\frac{x^2}{x}>1............\frac{x^2-x}{x}>0\)
Two cases
If x>0, then \(x^2-x>0.....x>\)1..Matches with (1)
If x<0, then \(x^2-x<0.....x^2<x\).....that is \(x>x^2>0\).....Not possible as x<0
So, x>1...Sufficient

B
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If x is a non-zero number, is x^5 < x^7? 25 Apr 2020, 15:34
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UShukla
If x is a non-zero number, is x^5 < x^7?

(1) x < x^2

(2) 1/x >1/x^2

Show Spoiler
This is a question from e-gmat and i am not convinced with the way they have solved this question.

Solution:

Since x ≠ 0, we know that x^4 > 0. x^5 < x^7 is equivalent to x < x^3 (when the former inequality is divided by x^4). In order for x < x^3, x is either a positive number greater than 1 or a negative number between 0 and -1.

Statement One Alone:

x < x^2

Since x is less than x^2, either x is a positive number greater than 1 or x is any negative number. If x > 1, then x^5 < x^7. However, if x < -1, then x^5 is not less than x^7.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

1/x >1/x^2

Since 1/x is greater than 1/x^2, then x must be a number greater than 1. Since x > 1, x^5 will be less than x^7.

Statement two alone is sufficient to answer the question.

Answer: B
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If x is a non-zero number, is x^5 < x^7? 03 Sep 2023, 09:15
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