Is x^7 x^6? (1) x + x^3 0 (2) x - 1/x 0

Question

Is x^7 > x^6 ? (1) x+x^3 > 0 (2) x - \frac{1}{x} > 0 Source : https://www.GMATinsight.com

Babineaux · Answer

Please refer to the pic uploaded.

And let me know whether I'm missing anything.

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dimri10 · Answer

I'll try: 
It is actually is X>1( divide by x^6)
1. Only (+ fractions) and (+ numbers) satisfy the statement. So not sufficient. Fractions are less than 1, positive numbers are more than one
2. Only (- fractions) and (+ numbers) satisfy.
Both
Only + numbers is common to both statements. 
So I hope it is C and I was not trapped somehow

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ArunSharma12 · Answer

x^7 > x^6 x^6(x-1) > 0 x^6 will be non- negative number. is x > 1? statement 1: x+x^3 > 0 x(1+x^2) > 0 1 + x^2 > 0 for all values of x, so x > 0. not sufficient statement 2: x - \frac{1}{x} > 0 \frac{x^2 - 1}{x} > 0 following cases are possible (x^2 - 1) > 0 & x > 0: (x+1)(x-1)> 0; or x > 1 as x < -1 is not a valid value (x^2 - 1)<0 & x < 0: (x+1)(x-1)< 0; or -1< x < 0 not sufficient combining both statements, x > 0, only possible range remains x >1 Ans: C

Archit3110 · Answer

target find x^7>x^6

target x^7>x^6 
 #1 x+x^3>0 
which can be possible at x +ve integer and +ve fraction (1/2, 3/2) insufficient 
 
#2 x-1/x>0 possible at x+ integer or -ve integer ( -1/2) or + fraction >1 (3/2) insufficient

from 1 &2 we see that for any value x>1 satisfies both conditions so x^7>x^6 ; sufficient 
OPTION C

Kinshook · Answer

Asked: Is x^7 > x^6 ? (1) x+x^3 > 0 x (1 + x^2) >0 x > 0 NOT SUFFICIENT (2) x - \frac{1}{x} > 0 (x^2 - 1)/x > 0 (x+1)(x-1)/x >0 x > 1 or -1 0 x (1 + x^2) >0 x > 0 (2) x - \frac{1}{x} > 0 (x^2 - 1)/x > 0 (x+1)(x-1)/x >0 x > 1 or -1 1 x^7 > x^6 SUFFICIENT IMO C

GMATGuruNY · Answer

Since x ^7 > x^6 is valid only if x is NONZERO, we can safely divide both sides by x^6 , which must be a positive value: \frac{x^7}{x^6} > \frac{x^6}{x^6} x > 1 Question stem, rephrased: Is x > 1? Statement 1: x+x^3 > 0 Here, x can be any positive value. If x=1, the answer to the question stem is NO. If x=2, the answer to the question stem is YES. INSUFFICIENT. Statement 2: x - \frac{1}{x} > 0 x > \frac{1}{x} Since 1/x is valid only if x is NONZERO, we can safely multiply both sides by x^2 , which must be a positive value: x * x^2 > \frac{1}{x }* x^2 x^3 > x The resulting inequality is valid if x>1 (in which case the answer to the question stem is YES) or if -11 also satisfies Statement 1. Since both statements are satisfied only by x>1, the answer to the question stem is YES. SUFFICIENT. C

Is x^7 > x^6? (1) x + x^3 > 0 (2) x - 1/x > 0

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