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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
Correct answer is option 'D'. Can you explain this answer?

Answers

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).

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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)2b)7c)1d)0Correct answer is option 'D'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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)2b)7c)1d)0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)2b)7c)1d)0Correct answer is option 'D'. Can you explain this answer?.
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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, 97,127Numbers when written one beside the other7, 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 = 127The 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).