Remainder

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Sat Feb 26, 2011 9:10 pm

When X is divided by Y what is the remainder if x=(y+2)^2? (y is integer greater than 4)

I got 4. Correct? I guess the y>4 is a give away.

x=y^2+4y+4 => x=y(y+4) +4

y= integer, is that a significant fact to determine remainder?

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Source: Beat The GMAT — Problem Solving | Sat Feb 26, 2011 9:10 pm

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sat Feb 26, 2011 9:32 pm

solution didn't suit

just plug in integer>4 to check remainder is 4

yellowho wrote:When X is divided by Y what is the remainder if x=(y+2)^2? (y is integer greater than 4)

I got 4. Correct? I guess the y>4 is a give away.

x=y^2+4y+4 => x=y(y+4) +4

y= integer, is that a significant fact to determine remainder?

Last edited by Night reader on Sat Feb 26, 2011 10:10 pm, edited 1 time in total.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Feb 26, 2011 9:47 pm

yellowho wrote:...is that a significant fact to determine remainder?

Yes, you're correct.
We can write x = y(y + 4) + 4

Now in general, when x = 2, is divided by y the remainder will be same as the remainder when 4 is divided by y. Thus, if y = 2 or 4, the remainder will be 0; if y = 3, the remainder will be 1; and if y is any integer greater than 4, then the remainder will be 4.

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HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Tue Mar 01, 2011 12:28 am

x/y = (y+2)^2 / y
= (y+2)+(4/y)

We know y is greater than 4 so (4/y) will have remainder as 4

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