Number Systems, Progressions

how many times we have to write 3 while writing numbers from 1 to 1000 ?
please tell me the solution .

number of ways by which sum of n consecutive integers comes out to be 7!

How many integer values of x and y satisfy the expression 4x + 7y =3 where IxI


@nandonachi

what is the remainder when 21^3+23^3+25^3+27^3 is divided by 96?



4 answers 1) 0



0 answers 2) 1



0 answers 3) 3



0 answers 4) 5



21^3+23^3+25^3+27^3= (21^3+27^3)+(23^3+25^3)


A. (21^3+27^3)=(21+27) (21^2-21.27+27^2)= 48 (odd number-odd number+odd number)= 48*(odd number)

B. (23^3+25^3)=(23+25) (23^2-23.25+25^2)= 48 (odd number-odd number+odd number)= 48* (odd number)


Therefore A+B= 48*(An even number)


So A+B is divisible by 48*2 or 96. Hence the remainder is zero.



Which is the smallest number which when divided by 7,8 and 9 leaves remainder 2,4 and 6 respectively?

Hi please help me in this Qs.I also want to know the procedure


Let Sm denote the sum of the squares of the first m natural numbers.for how many values of m


Ans is 24

The remainder when 2^2+22^2+222^2+......+(222...49twos)^2 is divided by 9 is


Ans 6

n is a number such that 2n has 28 factors and 3 n has 30 factors. 6n has ?

Ans is 35

It is easy to find the last-non zero digits for small factorial values like 10! to 20! but how to proceed for questions like these:-

Find the last non-zero digit in 100!.

A number of saplings are lying ready at a place side by side of a straight road. These are to be planted in a straight line at a distance interval of 10 meters between two consecutive saplings. Mithilesh, the country's best forester, can carry only one sapling at a time and has to move back to the original point to get the next sapling. In this manner he covers a total distance of 1.32 kms. How many saplings does he plant in the process if he ends at the starting point?

  • 15
  • 12
  • 13
  • 14

0 voters

solve dis..i didnt understand dis one:
(a^2*y)+(a+1^2*y-1)+(a+2^2*y-2)...for a given value of a and y...how to do this damn question!

@dheeraj73

how we fine a smallest no..when divided bu 3,7,and 11 gives remainder..2,1,2...respetevly.



i got answer bt i want a proper mathod...


3x+2=7z+1

=>3x+1=7z

number is 29

taking lcm of 7 and 3 it is 21 therefore 29 can be written as 21c+8=11z+2

21c+6=11z

c=6 and number is 134 therefore least number is 134 mg




I don't know whether its a weird question still, which are the topics than come under the heading Number Systems ? As in,how can I subdivide this topic into easy small parts?


There are “n” necklaces in a safe box (n > 1). Every necklace has the same number of diamonds. Each necklace has at least 2 diamonds. The total number of diamonds in these “n” necklaces is between 500 and 600. If this data is sufficient to find the value of n, then what is the value of “n”?


1.) 19

2.) 23

3.) 29

4.) None of these


Please explain the answer!!!

A= 12345678......upto 1852 first natural numbers written side by side. What is the remainder when 1750 digits of A are divided by 16..??

A 4 digit number"aabb" is a perfect square. What is the sum of digits of the number?

a)22
b)9
c)7
4)10

How many prime numbers less than 100 can be written as sum of 2 prime numbers?

a)3
b)8
c)4
d)6

In how many prime number less than 100 can be written as a sum of 2 prime number?

a)3
b)4
c)8
d)6

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)124
b)128
c)168
d)96

A number N has 27 factors.Let x represent the maximum number of prime factors of N and y the minimum number of prime factors N.Find the value of y-x?
a)26
b)0
c)6
d)2