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What is the remainder when (47)(49) is divided by 8? [#permalink]
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02 Mar 2013, 13:54
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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]
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02 Mar 2013, 15:14
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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]
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04 Mar 2013, 07:42
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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]
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03 Mar 2013, 01:12
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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 87) \(Rof (49)\)= 1 So\(Rof (47) (49)\) = 1*1 =1 Therefor 81= 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]
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02 Mar 2013, 20:40
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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. (8x61)(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]
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28 Mar 2013, 01:34
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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.  Please press KUDOS if you like my post.
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink]
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02 Mar 2013, 23:00
(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.
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink]
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03 Mar 2013, 00:30
47 x 49 = (481)(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 (81 =) 7



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Re: What is the remainder when (47)(49) is divided by 8? [#permalink]
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28 Mar 2013, 00:49
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]
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14 Jun 2017, 09:06
mun23 wrote: What is the remainder when (47)(49) is divided by 8? (A)1 (B)3 (C)4 (D)5 (E)7 \(\frac{47}{8}\) = Remainder \(7\) \(\frac{49}{8}\) = Remainder \(9\) \(\frac{63}{8}\) = Remainder \(7\) Thus, answer will be (E) Remainder \(7\)
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What is the remainder when (47)(49) is divided by 8? [#permalink]
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14 Jun 2017, 12:33
Abhishek009 wrote: mun23 wrote: What is the remainder when (47)(49) is divided by 8? (A)1 (B)3 (C)4 (D)5 (E)7 \(\frac{47}{8}\) = Remainder \(7\) \(\frac{49}{8}\) = Remainder \(9\) \(\frac{63}{8}\) = Remainder \(7\) Thus, answer will be (E) Remainder \(7\) Abhishek009, this method looks like a good one to learn. Two questions: 1. Did you choose to use 49/8 = remainder 9 instead remainder 1 so that you could get a twodigit number, 63? So that it was clearer than the single digit 7 (divided by 8, which = 0 + R7)? 2. Is it okay in problems like these to use a remainder that is bigger than the divisor?



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Re: What is the remainder when (47)(49) is divided by 8? [#permalink]
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14 Jun 2017, 12:43
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink]
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15 Jun 2017, 16:32
mun23 wrote: What is the remainder when (47)(49) is divided by 8? (A)1 (B)3 (C)4 (D)5 (E)7 To start, we can separately divide 47 by 8 and 49 by 8. 47/8 = 5 remainder 7 49/8 = 6 remainder 1 To determine the remainder of the product of 47 and 49, we can multiply the remainders together and we have 7 x 1 = 7. Alternate solution: Notice that (47)(49) = (48  1)(48 + 1) = 48^2  1^2 = 48^2  1. Now notice that the first term, 48^2, is divisible by 8 since 48 is divisible by 8. Thus, the remainder will be the second term, 1. If a number has a remainder of 1 when it’s divided by 8, the remainder is actually 1 + 8 = 7. Answer: E
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