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If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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26 Apr 2016, 01:00
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If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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Updated on: 26 Apr 2016, 17:03
Each of the three numbers may be written as \(14p+a\), where p is an integer and a is the remainder we’re looking for. They’d look like this:
\(775 = (14p + a)\) \(778 = (14q + b)\) \(781 = (14r + c)\)
Example #1: Now, lets multiple two of them and identify the remainder of that product.
\(775 * 778\) \(= (14p + a)(14q + b)\) \(= 14^2pq + 14qa + 14pb + ab\) \(= 14 (14pq + qa + pb) + ab\)
All but one term are divisible by 14. So the remainder of that product (775*778) divided by 14 is the remainder of the product of their remainders (ab) divided by 14 only. Here, the remainder of 775/14 is 5 and the remainder of 778/14 is 8. Their product (ab) = 5*8 = 40. The remainder of 40/14 is 12. So the remainder of 775*778/14 is the same, 12.
Example #2: Similarly,
\(775 * 778 * 781\) \(= (14p + a)(14q +b)(14r + c)\) \(= 14 (14^2pqr + 14pqc + 14pbr + 14aqr + pbc + aqc + abr) + abc\)
Again all but one term are divisible by 14. In other words, it's the remainder of that product of the numbers/14 is the remainder of abc/14, only.
General rule: The remainder of the product of three large numbers divided by \(x\) is the remainder of the product of their remainders divided by \(x\).
Answer to the OP: The following are easy to determine: The remainder of 775/14 is 5 The remainder of 778/14 is 8 The remainder of 781/14 is 11
Finally, the remainder of (775 * 778 * 781)/14 is simply the remainder of the product of their remainders divided by 14:
\(abc / 14\) \(= (5 * 8 * 11)/14\) \(= 440/14\) \(= 31 + 6/14\)
The remainder is thus 6, which corresponds to A.
Originally posted by InstantMBA on 26 Apr 2016, 04:55.
Last edited by InstantMBA on 26 Apr 2016, 17:03, edited 1 time in total.




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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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26 Apr 2016, 06:10
775/14 leaves a remainder 5 778/14 leaves a remainder 8 781/14 leaves a remainder 11
5*8*11 =440 So the remainder will be the remainder of 440/14 which is 6
Ans A



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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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26 Apr 2016, 08:43
raarun wrote: 775/14 leaves a remainder 5 778/14 leaves a remainder 8 781/14 leaves a remainder 11
5*8*11 =440 So the remainder will be the remainder of 440/14 which is 6
Ans A IMHOSame approach and same answer....
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If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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26 Apr 2016, 09:10
Abhishek009 wrote: raarun wrote: 775/14 leaves a remainder 5 778/14 leaves a remainder 8 781/14 leaves a remainder 11
5*8*11 =440 So the remainder will be the remainder of 440/14 which is 6
Ans A IMHOSame approach and same answer.... Sorry i just looked at the question and wrote how i would solve it. I did not check how anyone else has solved it.



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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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26 Apr 2016, 09:13
raarun wrote: Sorry i just looked at the question and wrote how i would solve it. I did not check how anyone else has solved it. No issues bro , it doesn't matter whether a problem is solved , if you have something to share do so without any hesitation.... Abhishek
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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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11 Jul 2017, 21:01
Bunuel wrote: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
A. 6 B. 7 C. 8 D. 9 E. 10 if you divide each number by 14 then the remainder for the numbers are 5,8 & 11. i multiplied all the remainders and divided it by 14 (5x8x11/14). the remainder was 6.



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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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12 Jul 2017, 03:42
Bunuel wrote: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
A. 6 B. 7 C. 8 D. 9 E. 10 N = 775 x 778 x 781 Remainder of 775 x 778 x 781 /14 = {775 x 778 x 781 /14} = {5 x 8 x 11/14} = {5 x 4 /14} = 6 Answer A.
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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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12 Jul 2017, 03:51
Write each no. as: (14*55+5) (14*55+8) (14*55+ 11) The first no. in the bracket is divisible by 14 and thus will leave no remainder. The second nos. will leave a remainder. We will get: 5*8*11= 440 which when divided by gives 6 as remainder.
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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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22 Aug 2018, 06:42
Is it okay to apply the "last digit shortcut" here?
775*778*781
last digits multiplied together= 5*8*1= 40; here the last digit is 0
In order for the last digit of 14 to yield a 0, we have 6 as a remainder.



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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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22 Aug 2018, 06:49
Bunuel wrote: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
A. 6 B. 7 C. 8 D. 9 E. 10 20 seconds approach. Ans A Consider kudos if that helped. Attachment:
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Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14? &nbs
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