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How many numbers are there in between 55 and 3815, which are multiples of 5 and divisible by 3?

Correct Answer: 251
For a number to be a multiple of 5 and divisible by 3, it should be divisible by 15. Between 55 and 3815, the first and last number divisible by 15 are 60 and 3810 respectively. i.e., a=5, d=15, Tn=3810 Tn = a + (n-1)d 3810 = 60 + (n-1)*15 Therefore, n=251

There are 4 consecutive odd numbers (x1, x2, x3 and x4) and three consecutive even numbers (y1, y2 and y3). The average of the odd numbers is 6 less than the average of the even numbers. If the sum of the three even numbers is 16 less than the sum of the four odd numbers, what is the average of x1, x2, x3 and x4?

Consider the following statements. I. There are finite number of rational numbers between 51 and 52. II. There are infinite number of rational numbers between 99 and 100. III. There are finite number of irrational numbers between√2 and √3. Which of the statement(s) given above is/are correct?

Two hundred multiples of seven are chosen at random. and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?

There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card?

Consider the given question and decide which of the following statements is sufficient to answer the question. All natural numbers are whole numbers?
(I) All natural numbers plus 0 are called whole numbers (II) Whole numbers are different from natural numbers

In a Class of 120 students numbered 1 to 120, all even numbered students opt for Physics , those whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subject ?

Among the 120 students of a class, numbered 1 to 120, all even numbered students opt for Bangla, whose numbers are divisible by 5 opt for English and those numbers are divisible by 7 opt for Math. How many opt for none of these three subjects?

What are the Multiples of 6 and the Common Multiples of 4 and 6?

Consider the following statements. I. To obtain prime numbers less than 256, we are to reject all the multiples of 2, 3, 5, 7, 11 and 13. II. Every composite number less than 256 is divisible by a prime number less than 16. Which of the statement(s)given above is/are correct?

Sum of consecutive multiples of 23 is 1656. Find the multiples.