BTGmoderatorDC wrote:For integers x, y, and z, x = y^2. What is the value of z?
(1) x = z!(z−1)!
(2) 12 < z < 22
OA C
Source: Veritas Prep
Let's take each statement one by one.
(1) x = z!(z−1)!
=> x = [z*(z - 1)!] / (z − 1)! = z
This is insufficient as we do not know the value of z. Insufficient.
(2) 12 < z < 22
Certainly insufficient as we do not know the unique value of z. Insufficient.
(1) and (2) together
Given the three integers are x, y and z, and x = z = y^2, the three integers are y^2, y and y^2. This implies that y^2 must be perfect square.
From Statement 2, we know that 12 < z < 22; thus, 12 < y^2 < 22 => y^2 = 16, the only perfect square number between 12 and 22.
Thus, z = y^2 = 16. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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