N is the greatest integer with distinct digits, which is a multiple of

Question

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

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TarunKumar1234 · Answer

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.

Deepakjhamb · Answer

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

Crytiocanalyst · Answer

A number multiple of 8 will have the last 3 digits divisible by 8 and in order to chose the one that maximizes the number is 987645120 
012 can be avoided for a greater number of 120 
210 doesn't produce the number divisible by 8 
240 and 320 can be avoided for mimimizing the number as 120 produces a greater number

THerefore IMO B

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=o03P7mNZYAE

Given that N is the greatest integer with distinct digits, which is a multiple of 8. What is the remainder when N is divided by 1000?

Now, we know that there are only 10 digits from 0 to 9, so N will be a 10 digit number.

Since N is a multiple of 8 => N will be divisible by 8
=> Number formed by last three digits of N should be divisible by 8 (Watch  this video  to  Learn the Divisibility Rules  for 8)

We need to find remainder of N by 1000 and we know that remainder of any number by 1000 is same as the last three digits of the number.

To have N maximum we need to write the digits in descending order from 9 onwards
=> N can be 9876543_ _ _

Now, we have 0, 1, 2 for last three digits and we need to form a number which is divisible by 8
which is 120

=> N = 987654120
=> Remainder of N by 1000 will be 120

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

KarishmaB · Answer

Greatest integer with all distinct digits will be 9876543210 But this is not divisible by 8 because its last three digits 210 do not form a number divisible by 8. So we should re-arrange the last 3 numbers to form 120 which is divisible by 8. Here is a post on divisibility rules of 2, 4, 8 etc: https://anaprep.com/number-properties-d ... wers-of-2/

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N is the greatest integer with distinct digits, which is a multiple of

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N is the greatest integer with distinct digits, which is a multiple of

Prep Toolkit

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