If you can travel from Mumbai to Baroda by 6 trains, from Baroda to Jaipur by 4 trains and from Jaipur to Delhi by 3 Trains. Then in how many ways can you travel from Mumbai to Delhi?
This blog makes available plenty of questions for practice, for the Mathematics competitive exams. We also try to bring to students interesting ways of approaching the questions. If you need any assistance in questions from IPM, MTSE, SCHOLARSHIP, OLYMPIAD, CBSE , ICSE or Board test papers, you may write to us.
Sunday, October 5, 2014
Saturday, October 4, 2014
numbers
Did you know that for 76 raised to the power of n, where n is an element of Natural numbers, the last 2 digits is always 76!
761 = 76
762 = 5776
763 = 438976
764 = 33362176
765 = 2535525376 Friday, October 3, 2014
division
A three digit number is entered twice into the calculator. What will be the Remainder when the number in the calculator is divided by 91.
division
If a number is successively divided by 9,11,13 then it leaves a Remainder of 8,9 and 8 respectively.
Find the smallest number that satisfies this condition.
Find the smallest number that satisfies this condition.
factors
For the number 610 x 717 x 5527,
find
1.
The number of prime factors
2.
The number of all the factors.
tutorials -sum of factors
Sum of Factors
Another Example:
If a number N can be expressed as product of prime factors such that
N = pa x qb x rc...............................
Write the power of each of the prime factors beginning with zero and going to thee highest power of the prime number.
Record the same for each prime number.
An example will help
64= 26
Then the sum of factors (20 + 21 + 22
+ 23 + 24 + 25 + 26) = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127
Another Example:
Find the total number of factors of 222.
222 = 2 x 3 x 37
Or, 222 = 21 x 31 x 371
then the sum of factors are (20
+ 21) (30 + 31) (370 + 371) = (1+2)(1+3)(1+37) = 3 x 4 x 38 = 456
We will check the answer
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222.
Sum of factors = 456
division
When we divide 333435 by 34 the remainder is a and when we divide 333534 by 34 the remainder is b. What is the value of b – a?
tutorial on number of factors
To find the number of factors of a
number
If a number N can be expressed as product of prime factors
such that
N = pa x qb x rc...............................
Then, the total number of factors including N and 1 is given
by
(a + 1)x(b + 1)x(c + 1).................................
Example:
Find the total number of factors of 222.
222 = 2 x 3 x 37
Or, 222 = 21 x 31 x 371
So, the total number of factors = (1+1)x(1+1)x(1+1) = 2x2x2
= 8
We can check the answer as shown below.
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222.
Find the total number of factors of 64.
64 = 26
So, the total number of factors = (6+1) = 7
We can check the answer as shown below.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64.
Tuesday, September 30, 2014
Monday, September 29, 2014
JMO division
If 8n is divided by 6, then for n € N, & n is
odd, and for n € N,& n is even what is the Remainder?
Saturday, September 27, 2014
Average
There are three numbers, the average of first two numbers is 2 and the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?
JMO - DIVISION
Which is the largest number that will perfectly divide 101 100 – 1
a) 10000
b) 1000
c) 100
d) 100001
a) 10000
b) 1000
c) 100
d) 100001
JMO - numbers
How many twin prime numbers are there between 1 and 100?
Twin prime numbers are prime numbers which differ from each other by 2.
Twin prime numbers are prime numbers which differ from each other by 2.
JMO Division
When a + b is divided by 12, the Remainder is 8. When a - b is divided by 12 the Remainder is 6. If a > b, then find the Remainder when ab is divided by 6?
JMO --- numbers
We have a four-digit number that is a multiple of 9. Of the four digits, three of the consecutive digits are same. How many such numbers are possible?
JMO - Division
If S = 123456789101112................9979989991000
What will be the Remainder when S is divided by 9.
What will be the Remainder when S is divided by 9.
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