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MGMAT Adv Quant - WS#5, Question 42

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by rishimaharaj » Thu Oct 13, 2011 6:22 pm
From MGMAT Advanced Quant Supplement, Chapter 9, WorkoutSet #5, page 240, #42:
What is the remainder when (47)(49) is divided by 8?
  • 1
  • 3
  • 4
  • 5
  • 7
My Solution:
(47/8)*(49)
=7 R 7 * 49
=some number R 7
So the remainder is 7.

Answer choice E.

Even thought it's the correct answer, is the logic correct? I have a feeling that I did something wrong.

Thanks,
--Rishi
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by fcabanski » Thu Oct 13, 2011 7:08 pm
47/8 is not 7 remainder 7. It's 5 remainder 7. What if the 49 had been first?

(49)(47) divided by 8. What is the remainder?

(49/8)(47) = (6 R1)(47) = some number remainder 1?

Try a simple example. Is 4 * 5 / 3 = some number remainder 1? 4/3 is 1 R 1. 20/3 = 6 remainder 2.

Why make this difficult by trying to find a short cut? It's a simple multiplication problem and then division problem that takes a few seconds.

47
x49
----
2303

2303 / 8 = 287 R 7

Or.

To find the remainder when dividing the product of two numbers by a divisor, divide each number by the divisor, then multiply the remainders to find the final remainder.

49/8 = 6 r1 47/8 = 5 r7 1*7 = 7

Try it with any pair or set of numbers.

13*14*15 divided by 3. What is the remainder?

13/3 = 4 r1 14/3 = 4 r2 15/3 = 5 r0 1*2*0=0

13*14*15=2730 and 2730/3 = 910 (no remainder).
Last edited by fcabanski on Thu Oct 13, 2011 7:45 pm, edited 1 time in total.
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by GmatMathPro » Thu Oct 13, 2011 7:34 pm
A couple of shortcuts:

1. 47/8 has a remainder of 7. 49/8 has a remainder of 1. Multiply the remainders: 7*1=7

2. (47)(49)=(48-1)(48+1)=48^2-1

This is clearly one less than a multiple of 8, so it must have a remainder of 7.
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by shankar.ashwin » Thu Oct 13, 2011 8:50 pm
Reaminders follow a constant pattern, here 2 Nos - 1 less than multiple of 8(47) and the other greater than a multiple of 8 (49).
Take the smallest such pair you can think of. (Say 7 and 9)

7*9 = 63 -> Remainder 7 when divided by 8.

Every such pair pretty much follows the same pattern.
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by fcabanski » Thu Oct 13, 2011 10:12 pm
There are a number of shortcuts or ways to remember the pattern. But the bottom line is if you spend a few seconds on this and can't think of a shortcut, quickly perform the multiplication and division.

Someone else might chime in with how many seconds to consider a shortcut before performing simple math.
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by rishimaharaj » Fri Oct 14, 2011 5:35 am
GmatMathPro wrote: 1. 47/8 has a remainder of 7. 49/8 has a remainder of 1. Multiply the remainders: 7*1=7
This is what I originally did when solving the problem the first time... even thought it looked weird, I stuck by it and chose the correct answer. But when reviewing the question later, I thought that it looked weird, since there is only one 8 in the denominator and this required dividing each by 8.

But I remembered seeing this in the MGMAT books. The solution I posted above was a "modified" version of this which I threw together after the fact when reviewing. All in all, when doing the problem, I got confused, but still ended up picking the right answer, and then moved on.

Thanks everyone for the clarifications!
--Rishi
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