ayankm wrote:123) If n is multiple of 5, and n = p^2 * q where p and q are prime, which of the following must be a multiple of 25?
a. p^2
b. q^2
c. p*q
d. p^2 * q^2
e. p^3 * q
Not getting a clue how to go about with this.
Any help or clue will be much appreciated.
Hi, since n is a multiple of 5, and since p and q are both prime, then we know that at least one of p or q must equal 5.
So, let's rephrase the question:
if either p or q = 5, which of the following MUST be a multiple of 25?
a) p^2... if q=5, p^2 could be anything... not a MUST.
b) q^2... if p=5, q^2 could be anything... not a MUST.
c) p*q... must be a multiple of 5, but doesn't have to be a multiple of 25.
d) p^2 * q^2... since either p or q = 5, either p^2 or q^2 must be 25; accordingly, p^2*q^2 = 25*(integer) which MUST be a multiple of 25... correct!
(On test day we'd stop there, but let's go into review mode and look at (e).)
e) p^3 * q... if q=5, then p^3*q must be a multiple of 5, but not of 25... not a MUST.
