Question

If `p and q` are positive integers with `pq = 36,` then `p/q` cannot be.... ? A. 1/4 B. 4/9 C. 1 D. 2 E. 9

Answer 1

D `2`

Explanation:

Note that `pq=36 = 6^2` is a perfect square, so `p/q = 6^2/q^2` must be a perfect square too.

All options except D are perfect squares:

A `1/4 = (1/2)^2`

B `4/9 = (2/3)^2`

C `1 = 1^2`

E `9 = 3^2`

D `2` is not a perfect square - Its square root is irrational.

Alternatively, we can fairly quickly find:

A `1/4 = 3/12`

B `4/9 = 4/9`

C `1 = 6/6`

E `9 = 18/2`