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 OA is D.
I got confused here. I need an explanation. Experts, help.
If p and q are positive integers. . . . . . .
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Hi Vincen,
This question is built around the concept of 'remainders.' For example, 7/2 = 3 remainder 1. In this prompt, we're told that 2 calculations would have the SAME remainder:
P/Q
Q/P
The 'easiest' remainder is 0. That occurs when the denominator divides evenly into the numerator. For BOTH of those calculations to have a remainder of 0, the two values would need to be EQUAL to one another... meaning that (P)(Q) would be a PERFECT SQUARE. There's only one answer that fits...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question is built around the concept of 'remainders.' For example, 7/2 = 3 remainder 1. In this prompt, we're told that 2 calculations would have the SAME remainder:
P/Q
Q/P
The 'easiest' remainder is 0. That occurs when the denominator divides evenly into the numerator. For BOTH of those calculations to have a remainder of 0, the two values would need to be EQUAL to one another... meaning that (P)(Q) would be a PERFECT SQUARE. There's only one answer that fits...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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The remainder obtained when p is divided by q is the same as the remainder obtained when q is divided by pVincen 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
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.
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Since we've already seen in the above posts that pq COULD equal 36, let's find some actual values that satisfy the given information.Vincen 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
Notice that, if p = 6 and q = 6, then p divided by q leaves remainder 0, AND q divided by p also leaves remainder 0
Here, pq = (6)(6) = 36
Cheers,
Brent
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Hi Vincen,Vincen 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 OA is D.
I got confused here. I need an explanation. Experts, help.
Let's take a look at your question.
Remember that when p and q are two positive integers, there is only one case for the remainder to be the same either p is divided by q or q is divided by p.
And that is when p and q are exactly the same numbers, then remainder = 0, either we divide p by q or q by p.
For example for p = 2 and q = 2
Either we divided p by q or q by p, remainder is always equal to zero.
The question asks to find the possible value of pq for this case.
Since p = q , then the product pq will be a perfect square.
i.e. pq = p(p) = p^2
It means we have to look for a perfect square in the options given i.e. 36.
Therefore, Option D is the correct answer.
I am available if you'd like any follow up.
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If p = 6 and q = 6, the remainder is the same for p/q and q/p.Vincen wrote: ↑Sun Oct 08, 2017 11:13 amIf 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 OA is D.
I got confused here. I need an explanation. Experts, help.
Answer: D
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