Q: When 15 is divided by Y, the remainder is Y - 3. If Y must be an integer, what are all the possible values of Y?
Can anyone please explain how to solve this problem?
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Divisibility and Primes!
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--> 15 = ky + (y - 3)Ahmed MS wrote:Q: When 15 is divided by Y, the remainder is Y - 3. If Y must be an integer, what are all the possible values of Y?
--> 15 + 3 = ky + y
--> (k + 1)y = 18
Hence, y must be a factor of 18 but not of 15.
Hence, possible values of y are 2, 6, 9, and 18.
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Anurag,Anurag@Gurome wrote:--> 15 = ky + (y - 3)Ahmed MS wrote:Q: When 15 is divided by Y, the remainder is Y - 3. If Y must be an integer, what are all the possible values of Y?
--> 15 + 3 = ky + y
--> (k + 1)y = 18
Hence, y must be a factor of 18 but not of 15.
Hence, possible values of y are 2, 6, 9, and 18.
Is y=2 a correct solution coz. 15 mod 2 = 1 (and not 3)?
Please correct if my understanding is wrong
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From mathematical point of view, there is no reason to discard 2 as the value of y.msr4mba wrote:...Is y=2 a correct solution coz. 15 mod 2 = 1 (and not 3)?
If a and d are integers, with d non-zero, then a remainder is an integer r such that a = qd + r for some integer q, and with 0 ≤ |r| < |d|. Hence, the remainder can be either positive or negative. Generally we deal with positive reminders.
For example, when 15 is divided by 4, generally we say the remainder is 3 because 15 = 3*4 + 3. But 15 can also be written as 4*4 - 1, in which case -1 is the remainder.
Similarly, here for y = 2, when 15 is divided by y, the remainder is (y - 3) = (2 - 3) = -1 which is the case when 15 = 8*2 - 1
Hope that helps.
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Hi Anurag,
Since in the question it is not stated that remainder is a non-zero integer so 3 can be a possible value of Y. please explain.
Thanks,
Amit
Since in the question it is not stated that remainder is a non-zero integer so 3 can be a possible value of Y. please explain.
Thanks,
Amit