Total 3 digit numbers = 9 x 10 x 10 = 900
Total number of 3 digit numbers without repetition = 9 x 9 x 8 = 648
So, the number of three digit numbers with at least one digit repeats = 900 - 648 = 252.
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How many numbers are divisible by 4 between 1 to 100 ?
Total number of 4 digit numbers are 9000 (between 1000 and 9999).
We find the numbers without any two in them.
So total numbers are 8 * 9 * 9 * 9 = 5832
So, numbers with number two in them = 9000 - 5832 = 3168
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In a class there are less than 500 students . when it is divided by 3 it gives a whole number. similarly when it is divided by 4,5 or 7 gives a whole number. find the no. of students in the class
Solution: Acc. to the question, the number should be such that it is completely divisible by 3,4,5,7
So check the options for their divisibility
Only 420 satisfies the criteria hence answer is 420
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Three friends divided some bullets equally. After all of them shot 4 bullets the total no.of remaining bullets is equal to that of one has after division. Find the original number divided
Lets assume no. of Bullets = x
There are 3 divided equally each have x/3 bullets.
So, 4 bullets shot By each the no of bullet shoted is 4*3=12
=> remaining bullet = the bullet of a person
x-12=x/3 => 3x-36=x => 2x=36
=> x=18
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There is a 5 digit no. 3 pairs of sum is eleven each. Last digit is 3 times the first one. 3 rd digit is 3 less than the second.4 th digit is 4 more than the second one. Find the digit.
Let the 5 digit no as "a b c d e"
Given last digit is 3 times first => e=3a
3rd digit 3 less than second => c = (b-3)
4th digit is 4 more than second => d = (4+b)
Now a,b,(b-3),(4+b),3a
Given, 3 pairs of sum is 11
so, c+d = 11 ---- (1)
=> b-3+b+4=11 => b = 5
c = 2, d = 9
so number is __529__
we have think of a number which should be added to five to get 11
5+6=11
So, last no (i.e e) = 6
a = 2
So, number is 25296
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