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Remainder of 5

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Remainder of 5

by joyseychow » Wed Jan 20, 2010 7:54 pm
If x and y are positive integers and x/y has a remainder of 5, what is the smallest possible value of xy?


[spoiler]This ques is from Man prep book. I don't understand why smallest value of x is 5 and not 11.[/spoiler]
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by Testluv » Wed Jan 20, 2010 9:00 pm
So, you've figured out that the minimum possible value of y is 6.

But you are forgetting to consider the cases where the numerator is smaller than the denominator. Certainly, 11 is divided by 6 once, leaving a remainder of 5, or 1R5. But 5 is divided by 6 zero times, also leaving a remainder of 5, or 0R5. So, the minimum possible value of x is 5, and the minimum possible value of xy is 30.
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by joyseychow » Thu Jan 21, 2010 12:12 am
Testluv wrote:So, you've figured out that the minimum possible value of y is 6.

But you are forgetting to consider the cases where the numerator is smaller than the denominator. Certainly, 11 is divided by 6 once, leaving a remainder of 5, or 1R5. But 5 is divided by 6 zero times, also leaving a remainder of 5, or 0R5. So, the minimum possible value of x is 5, and the minimum possible value of xy is 30.
Ahhh!! Now I see it. Thanks!! :)
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