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Remainder question

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susan.meng
 Post subject: Remainder question
 Post Posted: Mon Jul 20, 2009 9:36 pm 
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Course Students


Posts: 10
When positive integer n is divided by 3, the remainder is 2 and when positive integer t is divided by 5 the remainder is 3. What is the remainder when the product nt is divided by 15?

1. n-2 is divisible by 5
2. t is divisible by 3

Known from Q stem: n = 3k + 2; t = 5p + 3
Is this rephrasing correct? nt = 15kp + 9k + 10p + 6 --> what is 9k +10p +6?

1. n-2 = 5x --> 5x+2 = 3k+2 --> x = 3 and k = 5
what's the takeaway?

2. t=3a --> 3a = 5p+3

Could you please solve using theory?


Last edited by susan.meng on Tue Jul 21, 2009 11:04 am, edited 1 time in total.

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mxs2009
 Post subject: Re: Remainder question
 Post Posted: Tue Jul 21, 2009 1:32 am 
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Students


Posts: 16
hey Susan, you've basically done the heavy lifting and now you just need to put the puzzle pieces together.

Statement 1 tells us that:
(3k+2)-2 = an integer. (3k)/5. Thus, k must be a multiple of 5
5

Statement 2 tells us that:
5p+3 = an integer or (5/3)p +1 is an integer. Thus, p must be a multiple of 3
3

Going back to your original rephrase:
nt = 15kp + 9k + 10p + 6

rewrite as, what is the remainder of:
(15kp) + (3^2*k) + (2*5*p) + (6)
15

break down the four parts:
15kp/15 has no remainder
(3^2)*k/15 has no remainder because k is a multiple of 5
2*5*p/15 has no remainder because p is a multiple of 3
6 will always be the remainder and your answer is C

Neither A nor B is sufficient alone because we don't know if the other parts divide evenly.

hope that helps
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susan.meng
 Post subject: Re: Remainder question
 Post Posted: Tue Jul 21, 2009 11:07 am 
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Course Students


Posts: 10
fantastic, thank you
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Ben Ku
 Post subject: Re: Remainder question
 Post Posted: Thu Aug 06, 2009 4:13 pm 
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ManhattanGMAT Staff


Posts: 823
Thanks mxs2009, that's a nice way to use the theory of this problem. If you're more comfortable with the algebra, this way approach is extremely helpful. In this kind of problem, the plugging in numbers approach might be cumbersome: it's hard to find the right numbers to plug in, and you may need to try different possibilities. However, the advantage of plugging in numbers is that you can spot patterns.

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Ben Ku
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ManhattanGMAT
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