no two digits are identical

As the divisibility rule states- "if the last 3 digits of a number are divisible by 8, so is the entire number",
so when the greatest integer is divided by 1000 then the remainder should be divisible by 8.
(a) 12 - not divisible by 8
(b) 21 - not divisible
(c) 102 - not divisible
(d) 120 - divisible
(e) 210 - not divisible

Hence the answer is D

niketdoshi123 wrote:As the divisibility rule states- "if the last 3 digits of a number are divisible by 8, so is the entire number",
so when the greatest integer is divided by 1000 then the remainder should be divisible by 8.
(a) 12 - not divisible by 8
(b) 21 - not divisible
(c) 102 - not divisible
(d) 120 - divisible
(e) 210 - not divisible

Hence the answer is D

Hmm..so the mistake lies in preparing the answer choices. What if it reads like below?


If Z is the greatest integer multiple of 8 in which no two digits are identical, then what is the remainder when Z is divided by 1000?
(A) 840
(B) 600
(C) 360
(D) 120
(E) 80

sanju09 wrote:

niketdoshi123 wrote:As the divisibility rule states- "if the last 3 digits of a number are divisible by 8, so is the entire number",
so when the greatest integer is divided by 1000 then the remainder should be divisible by 8.
(a) 12 - not divisible by 8
(b) 21 - not divisible
(c) 102 - not divisible
(d) 120 - divisible
(e) 210 - not divisible

Hence the answer is D

Hmm..so the mistake lies in preparing the answer choices. What if it reads like below?


If Z is the greatest integer multiple of 8 in which no two digits are identical, then what is the remainder when Z is divided by 1000?
(A) 840
(B) 600
(C) 360
(D) 120
(E) 80

If one were t disregards options, going backwards..
1000 is divisible.
992 has two numbers same
984 has all digit different. Therefore 984 is the answer

Can you post the exact question? I am failing to understand.


Thanks and Regards,
Bhaskar R

Z = greatest integer multiple of 8

remainder when Z is divided by 1000

I still believe the ans will be the same as the question stem talks about the greatest integer and none of the given option can make that integer greater than "9876543120", which gives 120 as remainder when divided by 1000.

The greatest integer with no two digits identical is the 10-digit number 9876543210, but Z cannot be this integer as this is not divisible by 8. Revisiting the divisibility rule of 8 would let us consider all permutations of the last three digits 2, 1, and 0 and we’d realize that the only order 1, 2, 0 can make it divisible by 8. Hence, the greatest such integer multiple of 8 is 9876543120, which when divided by 1000 would leave [spoiler]120 as remainder.

Hence D[/spoiler]