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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. 
      ?. x 2 ? 6x = 7
      ?. 2y 2 + 13y + 15 = 0

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 2. 
      If U = {a, b, c, d, e, f}, A = {a, b, c}, find (U ? A)?.

    • Options
    • A. U
    • B. A
    • C. ?
    • D. None of these
    • Discuss
    • 3. 
      Mukul's income is 10% more than Sunil's. How much less is Sunil's income than that of Mukul's?

    • Options
    • A. 8.09 %
    • B. 9.09 %
    • C. 7.09 %
    • D. 7.90 %
    • Discuss
    • 4. 3, 7, 15, 39, 63, 127, 255, 511

    • Options
    • A. 7
    • B. 15
    • C. 39
    • D. 63
    • E. 127
    • Discuss
    • 5. 19, 26, 33, 46, 59, 74, 91

    • Options
    • A. 26
    • B. 33
    • C. 46
    • D. 59
    • E. 74
    • Discuss
    • 6. If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:

    • Options
    • A. 2
    • B. 5
    • C. 6
    • D. 7
    • E. None of these
    • Discuss
    • 7. 6, 13, 18, 25, 30, 37, 40

    • Options
    • A. 25
    • B. 30
    • C. 37
    • D. 40
    • Discuss
    • 8. 
      The true discount on a certain bill due for nine months at 4 % simple interest is ?150. Find the amount of the bill.

    • Options
    • A. ?5150
    • B. ?5250
    • C. ?4750
    • D. ?5650
    • Discuss
    • 9. 
      The present worth of $ 220.50 due in 2 years reckoning compound interest at 5 % is :

    • Options
    • A. $ 200
    • B. $ 197.5
    • C. $ 202
    • D. $ 192.25
    • Discuss
    • 10. 
      The value of 12x2y4z3 ÷ (2xy2 × 3yz2) will be :

    • Options
    • A. 2xyz
    • B. xyz
    • C. 1 xyz
    • D. 2 xyz
    • Discuss


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