aptitude

posted by .

The digits of a three digit number A are written in the reverse order to form another three digit number B. If B > A and B – A is perfectly divisible by 7, then which of the following is necessarily true?

1. 100 < A < 299 2. 106 < A < 305
3. 112 < A < 311 4. 118 < A < 317

  • aptitude -

    If the digits of A are abc, Then B is cba.

    100c+10b+a - 100a+10b+c = 7k

    99c-99a = 7k
    99(c-a) = 7k
    so, c-a is a multiple of 7. In fact, since c and a are both single digits, c-a=7.

    so, A must begin with 1 or 2, making c either 8 or 9

    So, of the given choices, 100<A<299

  • aptitude -

    correct answer is 2. 106 < A < 305

  • aptitude -

    Hmmm.
    Since A=101,102,103,104,105,300,301,302,303,304 all don't work,
    Both answers are true.

    Since actually 107 works and 299 works,

    107 <= A <= 299

    You are right. I should not have excluded 299 from the solution set.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    I am a 3 digit number divisible by 3. My tens digit is 3 times as great as my hundreds digit, and the sum of my digits is 15. If you reverse my digits, I am divisible by 6, as well as by 3. What number am I?
  2. 5th grade

    I am a 3-digit number divisible by three my tens digit is three times as great as my hundreds digit and the sum of my digits is 15 if you reverse my digits i am divisible by 6 as well as by three
  3. 6th grade

    i am a 3 digit number divisible by 3. my tens digit is 3 times as great as my hundreds digit and the sum of my digits is 15. if you reverse my digits i am divisible by 6 as well as 3. what number am i?
  4. math

    i am a 3 digit number divisible by 3.my tens digit is 3 times as great as my hundreds digit and the sum of my digits is 15. if you reverse my digits i am divisible by 6 and 3...... what number am i?
  5. MATH

    Need Answer to the Following Please: Using the 9 digits, 1, 2, 3, 4, 5, 6,7, 8 and 9 you can arrange four different digits to form a four-digit number that is NOT divisible by 7. The digits 1238 cannot be arranged to create a four-digit …
  6. Math

    Received answer to the following question from Jishka. (2469) Would you please explain the steps you used to get the answer 2469. I must show work. Thank you Using the 9 digits, 1, 2, 3, 4, 5, 6,7, 8 and 9 you can arrange four different …
  7. math

    Using the numbers 1 through 9 with no repeats, find a 9 number such that: the first digit is divisible by 1, the first two digits are divisible by 2, the first 3 digits are divisible by 3, and so on until we get to a 9 digit number …
  8. Math

    I am a 3digit number divisible by 3. my tens digit is three times as great as my hundreds digit and the sum of my digits is 15. if you were reverse my digits I am divisible by six, as well as by 3. what number am I?
  9. sent mary convent .sub math

    I am 4-digit number divisibleby 3.My tens digit is three times as great as my thousands digit, and sum of my digit is 15 .if you reverse my digit , I am divisible by 2 as well as by6.what am I?
  10. Maths

    I am a three-digit number. I am divisible by 6. My middle digit is a prime number. The sum of my digit is 9. I am between 400 and 500. My digits are descending order. What number am I?

More Similar Questions