remainder

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Jul 10, 2010 4:44 am

x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
24
21
20
17
15
how to solve this
whats the funda????

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Source: Beat The GMAT — Problem Solving | Sat Jul 10, 2010 4:44 am

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Sat Jul 10, 2010 4:48 am

If the remainder when X is divided by Y is 6, Y cannot be less than 7. This is because a number less than 7 can never yield a remainder of 6.

In short the takeaway is, the maximum remainder when dividing my N is N-1.

Thus for x/y to give remainder 6, y must be >= 7
For a/b to give a remainder 9, b must be >=10

Thus Minimum value of y + b = 7 + 10 =17

Thus 15 is not a possible value.

~Abhay

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Jul 10, 2010 6:30 am

albatross86 wrote:If the remainder when X is divided by Y is 6, Y cannot be less than 7. This is because a number less than 7 can never yield a remainder of 6.

In short the takeaway is, the maximum remainder when dividing my N is N-1.

Thus for x/y to give remainder 6, y must be >= 7
For a/b to give a remainder 9, b must be >=10

Thus Minimum value of y + b = 7 + 10 =17

Thus 15 is not a possible value.

gr8 concept
many thanks

Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working

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