Two important facts:
1) since p and q are both positive, the product pq is POSITIVE
2) since p and q are both positive, AND p + q = 1, we can conclude that p and q are each less than 1

The fraction in quantity A might cause issues for us, so let's eliminate that fraction.
Since fact #1 tells us that the product pq is POSITIVE, let's multiply both quantities by pg to get:
Quantity A: 1
Quantity B: pq

Next, since p and q are each less than 1, the product pq must be less than 1.
So, we get:
Quantity A: 1
Quantity B: some number less than 1


Answer:

Cheers,
Brent
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p + q = 1

and 0<p<q.

From the given data , it's clear that both p ans q are positive fraction.

When we divide an integer by a fraction , the integer becomes much bigger. So, 1 will be greater than before.

The best answer is A.

Bump for further discussion
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I'm making this question complicated just to add another discussion point.

0<p<q
p+q = 1

So, p = 1- q

Now 0< 1-q < q (replaced p with 1-q)

0<1-q or 1-q<q
So q<1 or q>1/2

Therefore q can be 3/4 and p can be 1/4

3/4 times 1/4 = 3/16

1/(3/16) = 16/3 or 5.33 . Therefore A is greater than B

Thank you

Solution:

Rather than solving each and every case, we can solve this question in under 20 sec, if we know that if the numerator is bigger than the denominator it will yield a value greater than 1.

In the above case just because p+q=1, we know p & q are either fractions or decimal values. And when we multiply decimal values it further decreases.

IMO A

Hope this helps!

If p+q = 1 and both are bigger than 0, we could say for instance p=0.1 and q=0.9 so that 0.1+0.9=1.

Then to compute A: 1/0.1*0.9= 11.11 which is bigger than 1, so A is bigger than B.

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