Bunuel wrote:

If p and q are integers greater than zero, what is the value of pq?

(1) The least common multiple of p and q is 240.

(2) The greatest common factor of p and q is 8.

Kudos for a correct solution.

St 1:

LCM of P & Q = 240,

P=60, Q=80 , or vice versa, LCM 240, PQ = 4800

P=30, Q=80 or vice versa, LCM 240, PQ = 2400

P=10, Q=240 or vice versa,LCM 240, PQ = 2400

P=8, Q=240 or vice versa, LCM 240, PQ = 1920

P=6, Q=240 or vice versa, LCM 240, PQ = 1440 ......

So many values. Not sufficient.

St 2:

GCF of P & Q = 8

P=8, Q=16 , GCF 8, PQ = 128

P=24, Q=40, GCF 8, PQ = 960

P=240, Q=8, GCF 8, PQ = 1920.....

Same here. Not sufficient.

Combine 1 & 2,

LCM of P * Q is 240, GCF is 8 only when P=240, Q=8 or vice versa

There PQ = 1920.

Ans C.