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# For positive integers a and b, is (forth root)(a^b) an integer?

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Senior Manager
Joined: 18 Feb 2019
Posts: 386
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
For positive integers a and b, is (forth root)(a^b) an integer?  [#permalink]

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06 Apr 2019, 06:25
1
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:15) correct 24% (01:02) wrong based on 29 sessions

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For positive integers a and b, is $$\sqrt[4]{a^b}$$ an integer?

I. 2 is the only prime factor of b

II. a is a perfect square
Senior Manager
Joined: 25 Feb 2019
Posts: 288
Re: For positive integers a and b, is (forth root)(a^b) an integer?  [#permalink]

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06 Apr 2019, 07:13
IMO C

from statement 1

b = 2*(any other number)

insufficient

from B

a = (x^2)

alone insufficient for

x = 4 , it is integer

for x = 3 , it is not

if we combine these two we get ,

x^2(2*any other number)

means

x^4*( any other number )

so the fourth root will be an integer

IMO C

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Re: For positive integers a and b, is (forth root)(a^b) an integer?   [#permalink] 06 Apr 2019, 07:13
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