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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A man have many daughters, each daughter have as many sons as her sisters. The product of the number of daughters and grandsons of the man lies between 40 and 50. Find the number of daughters of the man.
Let N be the number of daughters of the man.
Then each daughter has N-1 sisters.
Given that, each daughter has as many sons as her sisters.
That is, each of them has N-1 sons.
Number of grandsons of the man = N(N-1)
And the required product = N(N-1) x N = N x N(N-1) which lies between 40 and 50.
If N = 1 then N x N(N-1) = 0.
f N = 2 then N x N(N-1) = 2 x 2(1) = 4
If N = 3 then N x N(N-1) = 3 x 3 x 2 = 18
If N = 4 then N x N(N-1) = 4 x 4 x 3 = 48
If N = 5 then N x N(N-1) = 5 x 5 x 4 = 100
Therefore the possible value of N is 4.
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(2/3) of a number is 4 more than the (1/6) of the same number?
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