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What will be the remainder of: 12345678910/8 [#permalink]
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What will be the remainder of: 12345678910/8A. 4B. 5C. 6D. 3
PS: Apart from time consuming traditional Division method, is there any trick to attempt such type of questions?
Originally posted by jovialsarthak on 19 Jan 2014, 00:33.
Last edited by Bunuel on 19 Jan 2014, 08:37, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Remainder of the following [#permalink]
mau5 wrote:
jovialsarthak wrote:
What will be the remainder of:123........10/8a. 4b. 5c. 6d. 3
PS: Apart from time consuming traditional Division method, is there any trick to attempt such type of questions?
For any # to be divisible by 8, the last 3 digits of that # should be divisible by 8Given # --> 12345678910 --> \(10^{10}+2*10^9+.... 8000+910\)All the numbers above are divisible as they all end in 000. Thus, the remainder is what is obtained by\(\frac{910}{8} = 6\)C.
You can do the same by breaking 12345678910 only into two parts: 12345678910 = 12345678000 + 910.12345678000 is divisible by 8, because it ends with 000 and the remainder when 910 is divided by 8 is 6.Answer: C. _________________
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Re: Remainder of the following [#permalink]
jovialsarthak wrote:
What will be the remainder of:123........10/8a. 4b. 5c. 6d. 3
PS: Apart from time consuming traditional Division method, is there any trick to attempt such type of questions?
For any # to be divisible by 8, the last 3 digits of that # should be divisible by 8Given # --> 12345678910 --> \(10^{10}+2*10^9+.... 8000+910\)All the numbers above are divisible as they all end in 000. Thus, the remainder is what is obtained by\(\frac{910}{8} = 6\)C. _________________
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Re: What will be the remainder of: 12345678910/8 [#permalink]
jovialsarthak wrote:
What will be the remainder of: 12345678910/8A. 4B. 5C. 6D. 3
PS: Apart from time consuming traditional Division method, is there any trick to attempt such type of questions?
This question tests the divisibility rules:2 - The last digit should be even3 - Sum of the digits should be multiple of 34 - Last two digits should be divisible by 45 - Last digit should be 5 or 06 - Number is even and if the sum of its digits is divisible by 37 - Quiet complex and should not be used8 - Last three digits should be divisible by 8
9 - Sum should be divisible by 9
Taking the last 3 digits 12345678910 Remainder of 910/8 = 6Option C
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Re: What will be the remainder of: 12345678910/8 [#permalink]
jovialsarthak wrote:
What will be the remainder of: 12345678910/8A. 4B. 5C. 6D. 3
PS: Apart from time consuming traditional Division method, is there any trick to attempt such type of questions?
\(\frac{12345678910}{8}\) =\(\frac{12345678000}{8}\) + \(\frac{910}{8}\)\(\frac{12345678000}{8}\) + \(\frac{910}{8}\) = abcd1 +113+ \(\frac{6}{8}\)
So, Remainder is (C) 6 _________________
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Re: What will be the remainder of: 12345678910/8 [#permalink]
jovialsarthak wrote:
What will be the remainder of: 12345678910/8A. 4B. 5C. 6D. 3
PS: Apart from time consuming traditional Division method, is there any trick to attempt such type of questions?
Any number is divisible by 8 only if its last 3 digit is divisible by 8.here we will divide 910 by 8we get 6 as remainder.Hope it helps!
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Re: What will be the remainder of: 12345678910/8 [#permalink]
jovialsarthak wrote:
What will be the remainder of: 12345678910/8A. 4B. 5C. 6
D. 3
When dividing by 8, we can use the rule that if the last 3 digits of a number are divisible by 8, then that number is divisible by 8.For example, 110,440 is divisible by 8, since 440 is divisible by 8.Furthermore, the remainder when a number is divided by 8 is the same as the remainder when the last 3 digits of the number are divided by 8. So, to determine the remainder when 12345678910 is divided by 8, we simply divide 910 by 8:910/8 = 113 remainder 6Answer: C _________________
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Re: What will be the remainder of: 12345678910/8 [#permalink]
I took last three digit keeping in view "A number is divisible by 8 if its last three digits are divisible by 8"when I divide 910 got 904 so 6 is remainderOption CExpert opinion please will it satisfies all condition??
TIA
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Re: What will be the remainder of: 12345678910/8 [#permalink]
AqsaGhori wrote:
I took last three digit keeping in view "A number is divisible by 8 if its last three digits are divisible by 8"when I divide 910 got 904 so 6 is remainderOption CExpert opinion please will it satisfies all condition??
TIA
Yes. It's the same exact approach used in above solutions. _________________
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Re: What will be the remainder of: 12345678910/8 [#permalink]
jovialsarthak wrote:
What will be the remainder of: 12345678910/8A. 4B. 5C. 6D. 3
PS: Apart from time consuming traditional Division method, is there any trick to attempt such type of questions?
Any number divisible by 8 will have last 3 digit also divisible by 8.So, we should check the remainder of 910/8 = 6Answer C
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Re: What will be the remainder of: 12345678910/8 [#permalink]
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Re: What will be the remainder of: 12345678910/8 [#permalink]
31 Jul 2022, 08:28