Numbers Questions

If 49 is subtracted from the square of a number, then the result obtained is 576. What is the number?

Find a two digit number which is exactly three times the product of its digits?

The  sum  of  three  prime  numbers  is  100.  If  one  of  them  exceeds  another  by  36,  then  one  of  the numbers is

Which of the numbers given below is NOT rational?

What is the sum of the first 11 terms of an arithmetic progression if the first term is -31 and last term is 29?

A number is greater than 58 times its reciprocal by 3/4. What is the number?

Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime:

1) Both p and q may be prime numbers.

2) Both p and q may be composite numbers

3) one of p and q may be prime and the other composite.

Which of the above statements are correct?

The sum of 10 terms of the arithmetic series is 390. If the third term of the series is 19. Find the first term