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Roots problem

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Roots problem

by Troika » Tue Mar 06, 2012 4:42 pm
If z is a positive integer, is root z an integer?

1. Root (xz) is an integer
2. x = z^3

OA: E
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Source: — Data Sufficiency |
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by krusta80 » Tue Mar 06, 2012 6:37 pm
HG10 wrote:If z is a positive integer, is root z an integer?

1. Root (xz) is an integer
2. x = z^3

OA: E
Part 1: sqrt(xz) is an integer

Examples make this easy...

x = 1 AND z = 4. sqrt(4) = 2
x = 2 and z = 2. sqrt(2) NOT an integer

INSUFFICIENT

Part 2: x = z^3

This puts no restrictions on z. INSUFFICIENT

(1) and (2)
Combining the formulas for parts 1 and 2, we get sqrt(z^4) is an integer, which again has no restriction on z, since z^2 of any integer is an integer.

INSUFFICIENT

E
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by Troika » Wed Mar 07, 2012 6:27 pm
Thanks for the solution!
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