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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. 
      The median for the data 2, 4, 6, 8, 10, 12, 14 is

    • Options
    • A. 6
    • B. 8
    • C. 9.5
    • D. 10
    • Discuss
    • 2. 
      The value of 47 / 10000 is?

    • Options
    • A. .0047
    • B. .0470
    • C. .00047
    • D. .000047
    • Discuss
    • 3. If 4x = 18y, then the value of ( x/y - 1) is

    • Options
    • A. 1 3
    • B. 7 2
    • C. 2 3
    • D. 3 2
    • Discuss
    • 4. 
      If the price of 23 toys is Rs. 276, then what will the price (Rs.) of 12 toys?

    • Options
    • A. 144
    • B. 158
    • C. 159
    • D. 166
    • Discuss
    • 5. 
      .02 =(......?.....)%

    • Options
    • A. 20
    • B. 2
    • C. .02
    • D. .2
    • Discuss
    • 6. 
      If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?

    • Options
    • A. 45
    • B. 55
    • C. 60
    • D. 72
    • Discuss
    • 7. 
      2?63 / 11 =233

    • Options
    • A. 4
    • B. 3
    • C. 6
    • D. 5
    • Discuss
    • 8. 
      When 121012 is divided by 12, the remainder is

    • Options
    • A. 0
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 9. 
      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
    • 10. 
      750.0003 ÷ 19.999 =?

    • Options
    • A. 49
    • B. 18
    • C. 22
    • D. 38
    • Discuss


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