All natural numbers that give remainders 1 a...

### Related Test All natural numbers that give remainders 1 and 2 when divided by 6 and 5, respectively, are written in ascending order, side by side from left to right. What is the 99th digit from the left?
• a)
2
• b)
7
• c)
1
• d)
0 Kunaal Satija Natural numbers which when divided by 5 give a remainder 2 are given by 5K + 2 [‘k’ is a whole number].
Natural numbers which when divided by 6 give a remainder 1 are given by 6m +1 [‘m’ is a whole number].
5k + 2 = 6m + 1 or 6m - 5k = 1.
All such natural numbers are 7, 37, 67, 97,127
Numbers when written one beside the other
7, 37, 67, 97, 127, 157, 187, 217, 247, 277, 307, 337.......so on.
Observe the series.
The first 4 numbers give first 7 digits. After these 4 numbers, 3 digit numbers follow. The 3 digit numbers from an A.P. with common difference 30.
First three digit number = 127
The 30th 3-digit number is = 127 + (30 -1) × 30
= 997
=> The first 34 numbers (= 4 + 30) give 97 digits (= 7 + 3 × 30)
The next number in this A.P is 997 + 30 = 1027
=> the 99th digit is 0.
Hence answer is an option (d). View courses related to this question Explore CAT courses
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