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N is the greatest integer with distinct digits, which is a multiple of
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04 Jan 2021, 00:09
04 Jan 2021, 00:09
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N is the greatest integer with distinct digits, which is a multiple of 8. What is the remainder when N is divided by 1000?
(A) 12
(B) 120
(C) 210
(D) 240
(E) 320
Are You Up For the Challenge: 700 Level Questions
(A) 12
(B) 120
(C) 210
(D) 240
(E) 320
Are You Up For the Challenge: 700 Level Questions
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N is the greatest integer with distinct digits, which is a multiple of
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Updated on: 04 Jan 2021, 05:38
Updated on: 04 Jan 2021, 05:38
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Divisibility rule of 8= last 3 digits must be divided by 8.
Let's say, N= ABCD.....XYZ is a multiple of 8, then XYZ must be divided by 8, distinct integers.
For max value of N, XYZ= 120. (we have to select 3 lower digits from 0,1,2 and must be divided by 8; 210 will be the largest, but won't be divided by 8, only 012 and 120 are using 3 lower digits and divisible by 8. Note- if 0,1 and 2 are not able to give number divisible by 8, then we borrow 3 to form the number)
So, I think B.
Let's say, N= ABCD.....XYZ is a multiple of 8, then XYZ must be divided by 8, distinct integers.
For max value of N, XYZ= 120. (we have to select 3 lower digits from 0,1,2 and must be divided by 8; 210 will be the largest, but won't be divided by 8, only 012 and 120 are using 3 lower digits and divisible by 8. Note- if 0,1 and 2 are not able to give number divisible by 8, then we borrow 3 to form the number)
So, I think B.
Originally posted by TarunKumar1234 on 04 Jan 2021, 01:07.
Last edited by TarunKumar1234 on 04 Jan 2021, 05:38, edited 2 times in total.
Last edited by TarunKumar1234 on 04 Jan 2021, 05:38, edited 2 times in total.
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Re: N is the greatest integer with distinct digits, which is a multiple of
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04 Jan 2021, 02:01
04 Jan 2021, 02:01
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answer should be c )
as it is asked to get the greatest integer with all distinct digits that is multiple of 8
that number will be 9876... (120 ) combination which is divisible by 8
now last 3 digits are divisible /8 so remainder cant be 12 , it can be 120 , 210 or 240 or 320
but we can rule out 240 and 320 as it will take out 3 from the thousand and 4 from the next place thus making it a smaller number
out of 120 and 210 , 210 will be bigger so that the answer
as it is asked to get the greatest integer with all distinct digits that is multiple of 8
that number will be 9876... (120 ) combination which is divisible by 8
now last 3 digits are divisible /8 so remainder cant be 12 , it can be 120 , 210 or 240 or 320
but we can rule out 240 and 320 as it will take out 3 from the thousand and 4 from the next place thus making it a smaller number
out of 120 and 210 , 210 will be bigger so that the answer
