BTGmoderatorDC wrote: ↑Sun Feb 02, 2020 7:06 pm
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)!
Certainly insufficient.
(2) 12 < z < 22
Certainly insufficient.
(1) and (2) together
=> x = y^2 = z!(z−1)! = z*[(z – 1)!]^2
=> x must be a perfect square.
Thus, y = √{z*[(z – 1)!]^2} = √z*(z – 1)
Since y is an integer, z must be a perfect square. We know that 12 < z < 22. The only perfect square value for z is 16. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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