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How many odd positives 3-digit integers are divisible by 3 but do not contain the digit 3?

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Important Questions on Number System

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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 30
Let p and q be positive integers such that 59<pq<47 and q is as small as possible. What is q-p2?
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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 31
A function f is defined recursively by f1=f2=1 and fn=fn-1-fn-2+n for all integers n≥3. What is the sum of the digits of f2018?
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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 32
Sunita has 30 thin rods, one each of every integer length from 1 cm through 30 cm. She places the rods with lengths 3 cm, 7 cm, and 15 cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 33
A five-digit palindrome is a positive integer with respective digits abcba, where a is non-zero. Let S be the sum of all five-digit palindromes. What is the sum of the digits of S? 
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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 34
The products 8888….8, where the second factor has k digits is an integer whose digits have a sum of 1000. What is the sum of digits of k?
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IOQM - PRMO and RMO
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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 35
There are total P positive integers value of n, so that n30-n is also a positive integer. What is P2?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 36
Let S be the set of positive integers n for which 1n has the repeating decimal representation 0.ab¯=0.abababab.....
with a and b different digits. The sum of the elements of S is a three-digit number abc. What is the value of abc11?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 37
Let a, b, and c be digit with a≠0. The three-digit integer abc lies one third of the way from the square of a positive integer to the square of the next larger integer. The integer acb lies two thirds of the way between the same two squares. What is a+b+c ?