Data Sufficiency

If v = (w)^2(y)(z), how many positive factors does v have?

(1) w, y and z are integers greater than 1
(2) w, y and z are distinct prime numbers



OA B

Source: Veritas Prep

BTGmoderatorDC wrote: ↑

Mon Apr 26, 2021 3:06 pm

If v = (w)^2(y)(z), how many positive factors does v have?

(1) w, y and z are integers greater than 1
(2) w, y and z are distinct prime numbers



OA B

Source: Veritas Prep

Given: \(v = w^2 \cdot y \cdot z\)
Required: Number of positive factors of \(v\)

We can find the number of factors of \(N = x^a \cdot y^b \cdot z^c\) if \(x, y\) and \(z\) are different prime numbers.
Number of factors \(= (a+1)(b+ 1)(c+1)\)

Statement 1: \(w, y\) and \(z\) are integers greater than \(1\)
If \(w, y\) and \(z\) are prime, we can find the number of factors. If they are not, we cannot find.
INSUFFICIENT \(\Large{\color{red}\chi}\)

Statement 2: \(w, y\) and \(z\) are distinct prime numbers
This clearly tells us that \(w, y\) and \(z\) are distinct prime numbers.
Hence, we can find the number of factors.

Number of factors \(= 3\cdot 2\cdot 2 = 12\) (Not needed to calculate for the question)
SUFFICIENT \(\Large{\color{green}\checkmark}\)

Therefore, B