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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Is x^7 < 6^y ? (1) x^3 = –125 (2) y^2 = 36

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Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Is x^7 < 6^y ? (1) x^3 = –125 (2) y^2 = 36  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 53% (01:11) correct 47% (01:18) wrong based on 239 sessions

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Is x^7 < 6^y ?

(1) x^3 = –125
(2) y^2 = 36

_________________
Intern  Joined: 31 Jan 2018
Posts: 1
Re: Is x^7 < 6^y ? (1) x^3 = –125 (2) y^2 = 36  [#permalink]

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2
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
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: Is x^7 < 6^y ? (1) x^3 = –125 (2) y^2 = 36  [#permalink]

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2
Top Contributor
Bunuel wrote:
Is x^7 < 6^y ?

(1) x³ = –125
(2) y² = 36

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

Cheers,
Brent
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Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: Is x^7 < 6^y ? (1) x^3 = –125 (2) y^2 = 36  [#permalink]

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Bunuel wrote:
Is x^7 < 6^y ?

(1) x^3 = –125
(2) y^2 = 36

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Non-Human User Joined: 09 Sep 2013
Posts: 13722
Re: x and y are integers. Is x^7<6^y? (1) x^3=125 (2) y^2=36  [#permalink]

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_________________ Re: x and y are integers. Is x^7<6^y? (1) x^3=125 (2) y^2=36   [#permalink] 08 Oct 2019, 09:15
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