Smallest possible value

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Deepthi Subbu: Master | Next Rank: 500 Posts; Posts: 298; Joined: Tue Feb 16, 2010 1:09 am; Thanked: 2 times; Followed by:1 members

Smallest possible value

by Deepthi Subbu » Wed Nov 17, 2010 8:41 pm

If x and y are positive integers and x/y has a remainder of 5 , what is the smallest possible value of xy?

Here is understand that since the remainder is 5 , the smallest possible integer (y) should be 6 . I am not able to proceed further . This problem is taken from MGMAT.

The OA is 30

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Source: Beat The GMAT — Problem Solving | Wed Nov 17, 2010 8:41 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pm; Location: Milpitas, CA; Thanked: 447 times; Followed by:88 members

by Rahul@gurome » Wed Nov 17, 2010 9:42 pm

Deepthi Subbu wrote:If x and y are positive integers and x/y has a remainder of 5 , what is the smallest possible value of xy?

Here is understand that since the remainder is 5 , the smallest possible integer (y) should be 6 . I am not able to proceed further . This problem is taken from MGMAT.

The OA is 30

You are in the right track.
To minimize xy, we have to minimize both of x and y.
Minimum value of y is 6 because if y < 6 we'll never get a remainder of 5.
Now the question is what is the minimum possible value of x for which x/6 has a remainder of 5. And we are looking at the answer! Minimum possible value of x is 5!

Thus, minimum possible value of xy is 5*6 = 30.

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