discrete math

Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties:
(a) are divisible by 5 and by 7.


(b) have distinct digits.


(c) are not divisible by either 5 or 7.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. (a) div. by 5 and by 7 => div. by 35
    We can find out that
    35*286=10010 and 35*29=1015
    Therefore the number divisible by 35, n35
    = 286-29=257

    (b) distinct digits
    First digit has 9 choices (1-9)
    second and subsequent digits 9,8,7 choices each
    Numbers with distinct digits
    = 9*9*8*7
    = 4536

    (c) not divisible by either 5 or 7
    Divisible by 5, n5= (10000-1000)/5=1800
    Divisisble by 7, n7 = (10003-1001)/7=1286
    Divisible by 5 or 7 or both
    =n5+n7-n35
    =1800+1286-257
    =2829

    Numbers NOT divisible by either 5 or 7
    =(10000-1000)-2829
    =6171

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    2. The sum of the reciprocals of two consecutive positive integers is 17/72. Write an equation that can be used to find the two integers. What are the integers? Steve helped me yesterday and gave me the hint 8+9=17. Then I thought

  2. Algebra III

    How many positive odd integers less than 10,000 can be represented using the digits 0, 3, 6 an 9?

  3. mathematics

    Let P(x) be a nonconstant polynomial, where all the coefficients are nonnegative integers. Prove that there exist infinitely many positive integers n such that P(n) is composite. Remember that if a and b are distinct integers,

  4. Maths

    Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?

  1. Algebra

    The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. Find the integers. Must have an algebraic solution.

  2. Maths

    How many positive integers less than 1000 are there which contain at least one 4 or at least one 9 (or both)?

  3. ALGEBRA.

    The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?

  4. Math

    How many positive 3-digit integers contain only odd digits?

  1. MaTh

    Find the sum of all positive integers less than 1000 ending in 3 or 7.

  2. Integers

    The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. Find the integers.

  3. math

    Find the number of 6 -term strictly increasing geometric progressions, such that all terms are positive integers less than 1000.

  4. Math

    The product of two consecutive even positive integers is 120. Find the integers.

View more similar questions or ask a new question.