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Divisibility by 7

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chitrangada.maitra
 Post subject: Divisibility by 7
 Post Posted: Tue Aug 03, 2010 6:33 pm 
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Course Students


Posts: 75
This problem has been troubling me for a while.
Strategy Guide: Number Properties, page 134, #20

x has a remainder of 5 when divided by 9. y has a remainder of 7 when divided by 9. what is the remainder when x-y is divided by 9

My Approach:
X can be 5, 14, 23, 32, 41... etc
Y can be 7, 16, 25, 34, 43... etc

If X>y, the remainder of X-Y upon division by 9 is consistently 7.
However, if, X<Y, X-Y can be -2, -11, -20.... etc
These numbers upon division by 9 does NOT give one consistent answer.

The strategy guide suggests adding the divisor to a negative remainder -- that is the part that confuses me.

Can someone please suggest a simpler way to solve this.

Thanks,
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adiagr
 Post subject: Re: Divisibility by 7
 Post Posted: Wed Aug 04, 2010 10:36 am 
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Students


Posts: 89
chitrangada.maitra wrote:
This problem has been troubling me for a while.
Strategy Guide: Number Properties, page 134, #20

x has a remainder of 5 when divided by 9. y has a remainder of 7 when divided by 9. what is the remainder when x-y is divided by 9

My Approach:
X can be 5, 14, 23, 32, 41... etc
Y can be 7, 16, 25, 34, 43... etc

If X>y, the remainder of X-Y upon division by 9 is consistently 7.
However, if, X<Y, X-Y can be -2, -11, -20.... etc
These numbers upon division by 9 does NOT give one consistent answer.

The strategy guide suggests adding the divisor to a negative remainder -- that is the part that confuses me.

Can someone please suggest a simpler way to solve this.

Thanks,


Algebra wont be a bad option in this case.

x = 9 k + 5
y = 9z+5

k, z any integer.

x-y = 9(k-z)- 2

so when x-y is divided by 9, we see remainder is (-2)

add divisor to (-)2

9-2 = 7 ---> this will be the remainder.

Aditya
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tim
 Post subject: Re: Divisibility by 7
 Post Posted: Sat Sep 04, 2010 10:17 pm 
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ManhattanGMAT Staff


Posts: 1779
Location: Southwest Airlines, seat 21C
technically, -2, -11, -20 etc have a remainder of 7 when divided by 9. the only thing you have to do is, as suggested, add or subtract the divisor (in this case 9) until you get something in the range of 0 to 8. this is what you should do regardless of whether x-y is -20 or 34. if you want to avoid the hassle though, just pick your own values of x and y that make you happy.. :)

_________________
Tim Sanders
Manhattan GMAT Instructor
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dlbrownct
 Post subject: Re: Divisibility by 7
 Post Posted: Tue Dec 14, 2010 3:53 pm 
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Students


Posts: 1
OKay, I figured out the -2 part pretty quickly. Thus the actual remainder is -2/9 correct? However, I'm not 'getting' the part of adding the divisor back to the -2 to get 7.

x=9m+5
y=9n+7

x-y=9m+5-9n-7 = 9(m-n)-2
Now, (x-y)/9 has the remainder of -2, right?

Can you please clarify my misunderstanding? I know I am real close, but not close enough.
Thanks

Edit: The remainder of a division problem cannot be negative. Makes perfect sense of course. :)
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jnelson0612
 Post subject: Re: Divisibility by 7
 Post Posted: Wed Dec 15, 2010 5:44 pm 
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ManhattanGMAT Staff


Posts: 1618
dlbrown, it seems that you've got it now. Let us know if you need more guidance.

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Jamie Nelson
ManhattanGMAT Instructor
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