Is x^7

Question

Is x^7 < 6^y ?

(1) x^3 = –125 
(2) y^2 = 36

M36-76

Bunuel · Accepted Answer

Official Solution:

Is  x^7 < 6^y  ? 
 
(1)  x^3 = –125 
 
 x = \sqrt {–125}=-5 . In this case  x^7=(-5)^7=negative , while  6^y  (a positive number in some power) is always positive. Thus,  (x^7=negative) < (6^y=positive) . Sufficient.
 
(2)  y^2 = 36 . Clearly insufficient: we know that  y  is 6 or -6 but no info about  x . Not sufficient.

Answer: A

vaigai · Answer

I think its a 
x=-5 its enough that x^7 = -ve number
if we take 6^1 0r 6^-1 the answer is still positive 
so A sufficient

BrentGMATPrepNow · Answer

KEY CONCEPTS:

#1. ODD exponents preserve the sign of the base.  
So, ( NEGATIVE )^( ODD  integer) =  NEGATIVE 
and ( POSITIVE )^( ODD  integer) =  POSITIVE

#2. An EVEN exponent always yields a positive result  (unless the base = 0)
So, ( NEGATIVE )^( EVEN  integer) =  POSITIVE 
and ( POSITIVE )^( EVEN  integer) =  POSITIVE

Target question :    Is x^7 < 6^y ?

Statement 1 : x³ = –125   
This tells us that x = -5
By Rule #1, we know that, since -5 is negative, x^7 = (-5)^7 = some  NEGATIVE  number
By Rule #2, 6^y = some  POSITIVE  number
So, it must be the case that x^7 < 6^y 
The answer to the target question is  YES, x^7 IS less than 6^y 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : y² = 36  
This tells us that EITHER y = 6 OR y = -6
There are several values of x and y that satisfy statement 2. Here are two: 
 Case a : x = -1 and y = 6. Here, x^7 = -1 and 6^y = some POSITIVE number. In this case, the answer to the target question is  YES, x^7 IS less than 6^y 
 Case b : x = 1,000,000 and y = 6. Here, x^7 = a VERY VERY big number and 6^y = a KIND OF big number. In this case, the answer to the target question is  NO, x^7 is NOT less than 6^y 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

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Is x^7 < 6^y ? (1) x^3 = 125 (2) y^2 = 36

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