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

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Manager
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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
3
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1
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Difficulty:

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Question Stats:

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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
[Reveal] Spoiler: OA

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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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02 Mar 2013, 20:40
1
KUDOS
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]

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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.

Is it really a 700+ question??

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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 = (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]

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03 Mar 2013, 01:12
2
KUDOS
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]

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04 Mar 2013, 07:42
3
KUDOS
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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28 Mar 2013, 00:49
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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28 Mar 2013, 01:34
1
KUDOS
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]

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14 Nov 2014, 07:21
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Re: What is the remainder when (47)(49) is divided by 8? [#permalink]

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13 Jun 2017, 17:59
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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 two-digit 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.

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Re: What is the remainder when (47)(49) is divided by 8?   [#permalink] 15 Jun 2017, 16:32
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# What is the remainder when (47)(49) is divided by 8?

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