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If P and Q are two distinct positive integers, what is the remainder
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02 Jul 2018, 10:15
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If P and Q are two distinct positive integers, what is the remainder when P is divided by Q? (1) P is the product of a prime number and its reciprocal. (2) Q is a prime number.
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If P and Q are two distinct positive integers, what is the remainder
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Updated on: 02 Jul 2018, 12:33
1 statement tells us that P=1 nothing about Q insuff 2 statement tells us that Q is a prime, nothing about P insuff
together P=1 Q=Prime (minimum prime is 2) 1/2 gives 1 as a remainder. sufficient
In My Opinion Ans: C



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Re: If P and Q are two distinct positive integers, what is the remainder
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02 Jul 2018, 11:43
E for me.
A implies that 1 is the only solution. No details about Q. B basically says that Q is 2,3,5,7,11 etc.
Together we get different solutions if 1/2, 1/3 etc.



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If P and Q are two distinct positive integers, what is the remainder
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Updated on: 02 Jul 2018, 12:39
amanvermagmat wrote: If P and Q are two distinct positive integers, what is the remainder when P is divided by Q?
(1) P is the product of a prime number and its reciprocal.
(2) Q is a prime number. (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
Originally posted by Mo2men on 02 Jul 2018, 11:52.
Last edited by Mo2men on 02 Jul 2018, 12:39, edited 2 times in total.



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Re: If P and Q are two distinct positive integers, what is the remainder
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02 Jul 2018, 12:01
Gemelo90 We are asked the remainder not the value Mo2menYou 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



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If P and Q are two distinct positive integers, what is the remainder
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02 Jul 2018, 12:26
LevanKhukhunashvili wrote: Gemelo90 We are asked the remainder not the value Mo2menYou 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



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Re: If P and Q are two distinct positive integers, what is the remainder
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02 Jul 2018, 12:31
Mo2men wrote: LevanKhukhunashvili wrote: Gemelo90 We are asked the remainder not the value Mo2menYou 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



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Re: If P and Q are two distinct positive integers, what is the remainder
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03 Jul 2018, 18:11
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




Re: If P and Q are two distinct positive integers, what is the remainder &nbs
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03 Jul 2018, 18:11






