logo

CuriousTab

CuriousTab

Discussion


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. 
      Five coins are tossed at a time. Then, the probability of obtaining at least one tail is

    • Options
    • A. 31/32
    • B. 1/32
    • C. 1/5
    • D. 5/32
    • Discuss
    • 2. 
      Find the maximum number of tree which can plant 20 m apart on the two side of straight road 1760 m long

    • Options
    • A. 174
    • B. 176
    • C. 180
    • D. 178
    • Discuss
    • 3. 
      1307 x 1307 =?

    • Options
    • A. 1601249
    • B. 1607249
    • C. 1701249
    • D. 1708249
    • Discuss
    • 4. 
      The circumferences of two concentric are 176 m and 132 m respectively. what is the difference between their radii?

    • Options
    • A. 5 meter
    • B. 7 meter
    • C. 8 meter
    • D. 44 meter
    • Discuss
    • 5. 
      (1/2 ÷ 4 + 20) / (1/2 x 4 + 20) =?

    • Options
    • A. 81 / 88
    • B. 23/11
    • C. 161 / 176
    • D. 1
    • Discuss
    • 6. 
      Find the cardinal number of the following set {x: x = 2n, n ? N, 4 ? x ? 11}

    • Options
    • A. 8
    • B. 6
    • C. 12
    • D. 4
    • Discuss
    • 7. 
      If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction, the result is 18 26/ 27. Find the fraction.

    • Options
    • A. 8/27
    • B. 11/3
    • C. 22/3
    • D. 32/3
    • Discuss
    • 8. 
      (0.04) 3 =?

    • Options
    • A. 0.064
    • B. 0.0064
    • C. 0.00064
    • D. 0.000064
    • Discuss
    • 9. 
      If a + b + c = 8, then the value of (a ? 4)3 + (b ? 3)3 + (c ? 1)3 ? 3 (a ? 4) (b ? 3) (c ? 1) is

    • Options
    • A. 2
    • B. 4
    • C. 1
    • D. 0
    • Discuss
    • 10. 
      3571 +? - 6086 = 155

    • Options
    • A. 2400
    • B. 2630
    • C. 2515
    • D. None of these
    • Discuss


    Comments

    There are no comments.

Enter a new Comment