If P and Q are two distinct positive integers, what is the remainder

(1) P is the product of a prime number and its reciprocal.

Any number (prime or not) multiplied by its reciprocal = 1

So p = 1

Q can't be 1 as stem says 'distinct positive integers'....So (1/any number) will yield reminder = 1

1/2, 1/4, 1/1000, 1/345.....etc

Insufficient

(2) Q is a prime number.

Q could be 2,3,5,11,13....etc

P can take any other number

Let P=10, Q =2......R=0

Let P=10, Q =3......R=1

Insufficient


Answer: A

Gemelo90

We are asked the remainder not the value

Mo2men
You are misleading the concept of remainder
1/2--> 1=q*2+r where q is the quotient and r is the remainder, in this case q=0 r=1
1/3--> 1=q*3+r where q is the quotient and r is the remainder, in this case q=0 r=1

You are right. It seems it is sleeping time now

But actually there is trick. The answer is neither C nor E.

From statement 1: we concluded that p= 1........If you divide 1/any number that reminder will always by 1. You may argue that Q could equal 1 but take care of question stem 'Distinct positive numbers'. So Q can't be 1

1/2 & 1/100 & 1/50 ........So answer is A

Damn so true, "Distinct positive Integer" means that if P=1 Q cant be 1
I underestimated the trickiness of the question

Statement 1:
Essentially this means that P=1, take any prime number and multiply it by its reciprocal and you will get 1.

ex : 2*\(\frac{1}{2}\)=1, or 3*\(\frac{1}{3}\)=1

Now if you don't pay attention to the wording in the prompt you end up picking a trap answer: "If P and Q are two distinct positive integers"

Because the two integers are positive and have different values and you know that P=1 you get : 0 < P < Q
The rule about remainders: If you divide a smaller integer by a larger integer, the quotient is always zero and the remainder is always the dividend.

Because Q is greater than P the remainder will always be 1 (Because P=1).
Sufficient


Statement 2:
If Q=2 and P=3 then the remainder is 1
If Q=3 and P=2 then the remainder is 2
Not sufficient