Number Systems, Progressions

How many factors of 900 are integrals multiplies of 30?
a)30
b060
C)8
d)2

in how many ways can 576 be written as a product of two distinct factors?
a)11
b)21
c)10
d)20

@kiitsani

A rectangle has an area of 44 square units and sides of it's integers. What is the sum of perimeters of distinct rectangles?a)124b)128c)168d)96



c ?

The number of ways in which 7! can be written as sum of some consecutive natural numbers is (a) 11 (b) 7 (c) 13 (d) 9


How many non zero integral values of x, y and z are there such that z^2 = x^2 + y^2 and z^2

a. 8
b. 16

c. 2

d. 32

@kiitsani

In how many prime number less than 100 can be written as a sum of 2 prime number?a)3b)4c)8d)6



8

Remainder when 2^50 is divided by 97.
Please share your approach.

K is a 3 digit number such that the ratio of k to the sum of its digits is least. Find k.
Please explain approach.

A set S is formed by including some of the first 1000 natural numbers. S contains maximum number of numbers which:
1) No number of S is prime
2) Every number is co-prime to each other.
Number of elements in S?
Plz explain approach

How many 2-digit numbers Please explain approach

GCD of (1111.....hundred ones) and 111....sixty ones?
Please explain approach

10^n - (5 +root17)^n is divisible by 2^n+2 . Find n.
Please explain approach.

128^1000 divided by 153 gives remainder?
Please explain approach.

number of zeros in the expression:

1^1*2^2*3^3+...........*100^100

  • 1225
  • 1200
  • 1300
  • 1050

0 voters

A three digit number “xyz” is such that the number equals x! + y! + z!. Find the difference of the number formed by reversing its digits and the original number.

  • 396
  • Cannot be determined
  • 297
  • 495

0 voters

When the numbers 5, 7 and 11 divide a multiple of 17, the remainders left are 4, 6 and 10 respectively. Which multiple of 17 is the least number that satisfies the given condition ?


Please provide a detailed solution if known :)

  • 325th
  • 384th
  • 317th
  • 385th

0 voters

By adding which of the following numbers does the product of 15×16×17×18 become s a perfect square?

P is a three digit number, upon reversing P, another 3-digit number Q is obtained. Q > P and Q - P is divisible by 5. Which of the following is always true ?

  • 115 < P < 515
  • 100 < P < 499
  • 105 < P < 505
  • 110 < P < 510

0 voters

By adding which of the following numbers does the product of 15×16×17×18 become s a perfect square?

  • 2
  • 1
  • 3
  • 8

0 voters

What numbers have exactly 4 factors under 100?


Now The number will be of the form a^3 or a*b where a and b are both prime.
Does any1 has any shortcut to find how many such pairs of a*b are possible?

I don't want to go individually checking for the values.