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Home Aptitude Permutation and Combination See What Others Are Saying!
  • Question
  • How many number of times will the digit ?7' be written when listing the integers from 1 to 1000?


  • Options
  • A. 243
  • B. 300
  • C. 301
  • D. 290

  • Correct Answer
  • 300 

    Explanation

    7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.

     

    1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc

     

    This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7)

     

    You have 1*9*9 = 81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81 = 243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once.

     

    In each of these numbers, 7 is written once. Therefore, 243 times.

     

     

    2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77

     

    In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7).

     

    There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers.

     

    In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.

     

     

    3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it.

     

    Therefore, the total number of times the digit 7 is written between 1 and 999 is

     

    243 + 54 + 3 = 300


  • More questions

    • 1. 
      Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?

    • Options
    • A. 18 days
    • B. 21 days
    • C. 3 days
    • D. 6 days
    • Discuss
    • 2. 
      750.0003 ÷ 19.999 =?

    • Options
    • A. 49
    • B. 18
    • C. 22
    • D. 38
    • Discuss
    • 3. 
      105, 85, 60, 30, 0, - 45, - 90?

    • Options
    • A. 0
    • B. 85
    • C. -45
    • D. 60
    • Discuss
    • 4. 
      Let A = {1, 2, {3, 4}, 5}. Which of the following statements is true?

    • Options
    • A. {3, 4} ? A
    • B. {3, 4} ? A
    • C. 1 ? A
    • D. {1, 2, 5} ? A
    • Discuss
    • 5. 
      Two vessels A and B contains milk and water mixed in the ratio 5 : 3 and 2 : 3. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio ?

    • Options
    • A. 2 : 5
    • B. 3 : 5
    • C. 4 : 5
    • D. 7 : 3
    • Discuss
    • 6. 
      1, 2, 4, 8, 16, 32, 64, (...), 256?

    • Options
    • A. 148
    • B. 128
    • C. 154
    • D. 164
    • Discuss
    • 7. 
      A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole?

    • Options
    • A. 150 m
    • B. 200 m
    • C. 125 m
    • D. 115 m
    • Discuss
    • 8. 
      8% of 96 =? of 1/25

    • Options
    • A. 19.2
    • B. 7.68
    • C. 1.92
    • D. None of these
    • Discuss
    • 9. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

    • Options
    • A. Rs. 35
    • B. Rs. 245
    • C. Rs. 350
    • D. Cannot be determined
    • E. None of these
    • Discuss
    • 10. 
      If the hands of a clock coincide in every 65 minutes (true time), in 24 hours the clock will gain:

    • Options
    • A. 10 10 minutes. 143
    • B. 9 12 minutes. 143
    • C. 11 12 minutes. 143
    • D. 12 10 minutes. 143
    • Discuss


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