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If p and q are positive integers, and the remainder obtained when p is
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17 Mar 2011, 00:27
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79% (01:57) correct 21% (02:07) wrong based on 226 sessions
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If p and q are positive integers, and the remainder obtained when p is divided by q is the same as the remainder obtained when q is divided by p, which of the following is a possible value of pq?
Re: If p and q are positive integers, and the remainder obtained when p is
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21 Mar 2016, 09:45
Hey Bunuel here is my approach could you help with this here => the only condition that will make the scenario possible is when the numbers are equal hence = D
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Re: If p and q are positive integers, and the remainder obtained when p is
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28 Aug 2018, 14:01
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gmatjon wrote:
If p and q are positive integers, and the remainder obtained when p is divided by q is the same as the remainder obtained when q is divided by p, which of the following is a possible value of pq?
(A) 62 (B) 55 (C) 42 (D) 36 (E) 24
The remainder obtained when p is divided by q is the same as the remainder obtained when q is divided by p This information is indirectly telling us that p = q To explain why, let's see what happens if p does NOT equal q If that's the case, then one value must be greater than the other value. Let's see what happens IF it were the case that p < q.
What is the remainder when p is divided by q? Since p < q, then p divided by q equals 0 with remainder p
IMPORTANT RULE: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
What is the remainder when q is divided by p? Based on the above rule, we know that the remainder must be a number such that 0 ≤ remainder < p
Hmmmmm. In our first calculation (p ÷ q), we found that the remainder = p In our second calculation (q ÷ p), we found that 0 ≤ remainder < p Since it's IMPOSSIBLE for the remainder to both EQUAL p and BE LESS THAN p, we can conclude that it's impossible for p to be less than q.
Using similar logic, we can see that it's also impossible for q to be less than p.
So, it MUST be the case that p = q So, pq = p² = the square of some integer
Check the answer choices . . . only D is the square of an integer.
Re: If p and q are positive integers, and the remainder obtained when p is
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20 Oct 2019, 12:46
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