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

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What is the remainder when (47)(49) is divided by 8? [#permalink] New post 02 Mar 2013, 12:54
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Question Stats:

74% (01:35) correct 26% (00:26) wrong based on 151 sessions
What is the remainder when (47)(49) is divided by 8?
(A)1
(B)3
(C)4
(D)5
(E)7
[Reveal] Spoiler: OA
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 04 Mar 2013, 06:42
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Here is how I approached this problem:

(47)(49) = (40x40)+(7x9) = 1600+63

1600 - divisible by 8
63 - a simple calculation with a remainder of 7
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 02 Mar 2013, 14:14
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Hello Mun23,

The easy way to solve such questions is to divide the numbers individually by 8 and then multiply the remainders. Confirm whether the product of the remainders can be divided by 8 again. If yes, then divide and find the remainder and that will be your answer. If not, then the product of the remainders is your answer.

Here are a few examples to show this.

Find the remainder of 15*9/4. 15/4 gives a remainder of 3 and 9/4 gives a remainder of 1. Hence, the total remainder is the product of the remainders=3 which cannot be further divided BY 4. Let us confirm this the long way. 15*9=135. Divide 135 by 4 and you get a quotient of 33 and a remainder of 3.

Similarly, try 21*9/7. 21/7 gives a remainder os 0 and 9/7 gives a remainder of 2. Hence, 0*2=0 is the total remainder. You can try this the long way.

Now, coming to the question at hand 47/8 gives a reminder of 7 and 49/8 gives a remainder of 1. 7*1=7 is the total remainder and thus, the answer is e.

Hope this helps! Let me know in case of any further questions.

mun23 wrote:
What is the remainder when (47)(49) is divided by 8?
(A)1
(B)3
(C)4
(D)5
(E)7
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 03 Mar 2013, 00:12
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mun23 wrote:
What is the remainder when (47)(49) is divided by 8?
(A)1
(B)3
(C)4
(D)5
(E)7



I have an alternate learnt here :)

\(Rof (47) (49)\) when divided by 8

Always reminder of product of two numbers divided by a divisor will be equal to product of reminders of corresponding numbers divided by same divisor


Using this rule,
\(Rof (47)\) = 7
\(Rof (49)\) = 1

So\(Rof (47) (49)\) = 7*1 =7

Other way would be
\(Rof (47)\) = -1 ( which is same as 7, but to do simpler we use -ve number 8-7)
\(Rof (49)\)= 1
So\(Rof (47) (49)\) = -1*1 =-1
Therefor 8-1= 7

I'm missed the link from which i learnt this..
I'm searching for it.. Once i get it will post it up here !!
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 02 Mar 2013, 19:40
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mun23 wrote:
What is the remainder when (47)(49) is divided by 8?
(A)1
(B)3
(C)4
(D)5
(E)7


use remainder theorem i.e. (8x6-1)(8x6+1)/8 = (-1)x(1)/8 = -1 hence remainder is 8 -1 =7
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 28 Mar 2013, 00:34
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Let N = A * B and we would like to find the remainder when N is divided by D.
A = aD + x where x is the remainder of A/D.
B = bD + y where y is the remainder of B/D.

so N = (aD + x) * (bD + y)
= abD\(^2\) + bxD + ayD + xy

So, N/D will give a remainder xy if xy < D.

Considering the above principle,

R1 = 47/8 = 7
R2 = 49/8 = 1
R = R1 * R2 = 7 * 1 = 7.
Hence option E will be the correct answer.

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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 02 Mar 2013, 22:00
(47)(49)=(8X5+7)X(8X6+1)
=(8X5)X(8X6)+(8X5)X1+(8X6)X7+7X1
all other terms have 8 as a factor except 7X1 hence remainder is 7.

Is it really a 700+ question??
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 02 Mar 2013, 23:30
47 x 49 = (48-1)(48+1)
47 x 49 = \(48^2 - 1^2\)
therefore (47 x 49)/8 = (\(48^2 - 1^2\))/8
since remainder of a number can be expressed as the sum or difference of individual fractions hence rem(\(48^2 - 1^2\))/8 = rem(\(48^2\)/8) - rem(\(1^2\)/8)
Now, Rem(48^2/8) = 0 and Rem(1^2/8) = 1
so we have rem(47)(49)/8 = -1 or (8-1 =) 7
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 27 Mar 2013, 23:49
sadovskiya wrote:
Here is how I approached this problem:

(47)(49) = (40x40)+(7x9) = 1600+63

1600 - divisible by 8
63 - a simple calculation with a remainder of 7



That's exactly how I solved it. I like this approach best. Kudos Sadovskiya!
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink] New post 14 Nov 2014, 06:21
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Re: What is the remainder when (47)(49) is divided by 8?   [#permalink] 14 Nov 2014, 06:21
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