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29 Dec 2021, 05:15
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A
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Difficulty:
95%
(hard)
Question Stats:
27% (02:23) correct
73%
(02:35)
wrong
based on 49
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A certain positive number consists only of the digit '7' that repeats itself 429 times. What is the remainder when this number is divided by 1144?
(A) 777
(B) 913
(C) 1129
(D) 1492
(E) 1777
Are You Up For the Challenge: 700 Level Questions
(A) 777
(B) 913
(C) 1129
(D) 1492
(E) 1777
Are You Up For the Challenge: 700 Level Questions
05 Jan 2022, 22:20
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Bunuel
What is 1144? 1144 = 8 * 11 * 13
7777... (429 times) is too big a number to handle so let's bring it down to a number easier to handle.
7777... (429 times) = 7777... (426 times)..000 + 777
We do this because 7777... (429 times) is not divisible by 8 but 7777... (426 times)..000 is divisible by 8.
Now, the divisibility rule of 7, 11 and 13 helps us
- Split the number into 3 digits each starting from the right and add and subtract those 3 digit numbers alternatively. If the sum is divisible by 7/11/13, then the number is divisible by 7/11/13 (Based on the fact that 1001 is divisible by 7, 11 and 13)
So say we have 123456. We split it into 123,456 and calculate 456 - 123 = 333. If 333 is divisible by 7/11/13, then so is 123456.
Split 7777... (426 times)..000 into 3 digits each starting from right and add subtract to get
= 0 - 777 + 777 - 777 + 777 ... = 0 which is divisible by 11 as well as 13.
So 7777... (426 times)..000 is divisible by 8, 11 and 13 i.e it is divisible by 1144.
7777... (429 times) = Multiple of 1144 + 777
Remainder when we divide 7777... (429 times) by 1144 is 777
Answer (A)
General Discussion
05 Jan 2022, 12:25
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Hey, any idea on how to solve this?
