An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors does the number 4x have? Choose one
A) 4y	B) 3y	C) 16y	D) 5y	E) Cannot be determined
Let’s express x as a product of its prime factors:   x=2a∗3b∗5c∗…x=2a∗3b∗5c∗…   Total number of its positive divisors will be   (a+1)∗(b+1)∗(c+1)∗…=y(a+1)∗(b+1)∗(c+1)∗…=y   Now we’ll do the same for the 4x   4x=22∗2a∗3b∗5c∗…=2a+2∗3b∗5c…4x=22∗2a∗3b∗5c∗…=2a+2∗3b∗5c…   Total number of positive divisors of 4x will be   (a+3)∗(b+1)∗(c+1)…=y′(a+3)∗(b+1)∗(c+1)…=y′   For easier calculations let’s take (b+1)∗(c+1)∗…=z(b+1)∗(c+1)∗…=z   We have: (a+3)∗z=y′(a+3)∗z=y′   (a+1+2)∗z=y′(a+1+2)∗z=y′   (a+1)∗z+2∗z=y′(a+1)∗z+2∗z=y′   y+2∗z=y′y+2∗z=y′   So, as we can see, in order to find out the total # of positive divisors of 4x we need to know # of odd divisors of x, which is not given in the question.   Answer Cannot be determined.
<result>E</result>
An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors does the number 4x have?