Find the remainder when 786786786....(657 digits) is divided by 23.
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Please tell how p^3 - 7p^2 + 16p - 12 can be written as (p - 2)(p^2 - 5p + 6)
i know it's silly question!
Any digit repeated E[n] times is divisible by n, if n is coprime to 2,3 and 5.
E[n]= N (1-1/p1)(1-1/p2)... (1-1/pn)
where N= p1^a1 x p2^a2 x ..x pn^an
Let K = aaaaaaaaa...... repeated E[n] times
K = a/9 (10E[n] -1)
Since n is coprime to 2 and 5, Rem[10E[n]/n]=1
Further, since n is coprime to 3, Rem[a/9 (10E[n] -1)] = 0Thus, K is divisible by n.
Example problem:
Find remainder when 33333333......86 times is divided by 13
Soln:E[13] = 13(1-1/13) = 12
So 3333.... repeated 12(7) = 84 times is divisible by 13.
Thus, the problem reduces to Rem[33/13] => 7
find the last two digits of 13^1642....
N=1!-2!+3!-4!+5!-6!........+47!-48!+49!, then what is unit digit of N^N ?
OPTIONS: 0,9,7,1
Four identical bags are distributed among four boys. If each boy can get any number of bags then what is probability that no boy gets more than two bags ?
18/35, 2/7, 19/35, 16/35 ?
____________________/\_______________________ MSD...Sorry for spamming...Could not resist!!
please solve it.....
The ratio of men to women in the applicants for Hyundai Motors this year is 4:3, while the ratio of men to women in the successful applicants is 5:3, and the ratio of men to women in the rejected pile is 1:1. If the number of successful applicants is 152, what is the number of applicants?
Q5
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N^2=12345678987654321 then N=
Please explain
of 128 boxes of oranges each box contain at least 120 and at most 148 Oranges . The number of boxes containing same number of Oranges is at least
1 and 8 are the first two natural numbers for which 1+2+3+..... +n = perfect square. which number is the 3rd such number?
If suppose A be a set of natural numbers and a function 'd' called as distance function defined as d(x,y)= 0 if x=y and d(x,y)= 1 if x not=y. Now Suppose Jimi, an ant from A, starts to walk from the point 1 and reach to the 'n'th point in such a manner that first it goes to point 2 from point 1 and then comes back to point 1; then it goes to point 2 and then point 3 and comes back to point 1 through point 2 and follows the pattern upto point 'n-1' and then it directly goes to point 'n' from '1'. How much distance should it have traveled if it want to reach to the point 2013?
The no of ways in which N=40500 can be resloved in two factor is
can nebody suggest how to check for divisibility by 17,23 ....and higher prime numbers
How much milk should be added to 800dl of a 15% soln to make strength of 32%..Somebody please help with soln..
One of two natural numbers A and B, one of two natural numbers C and D and one of two natural numbers E and F are multiplied together. The sum of all such possible products is equal to 105. How many distinct values are possible for A?
a)6 b)4 c) 12 d) 7This is a question of proc mock 4 . Anybody give some other solution, especially that one which can be replicated by an art student with a little maths background i.e doing quant without maths. Any other ingenious solution is also welcome.😃
There are 10 identical blocks of cuboid of dimension 2 inches × 3 inches × 5 inches. The blocks are kept one on top of the other in a random fashion to form a structure. How many structures with unique heights can be created using these blocks? (Neglect instability of the structure) NOTE: Two of the flat faces of each cube are parallel to the ground.
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0 voters
1.) Let 'xyz', 'yxz', 'yzx' and 'zyx' be four distinct three digit numbers such that (yxz – yzx) is one-fifth of (xyz – yxz). What is the number of possible values of 'xyz'?
a)64 b)56 c)72 d) 322.)In triangle ABC, D is a point on BC such that BD = DC. BE is an altitude drawn on AC. If ∠ADB = 45° and ∠ACB = 30°, what is the measure of ∠ABE?
a) 30 b)60 c)45 d) cannot be determined
These are quesions of proc mock 4 . Anybody give some other solution, especially that one which can be replicated by an art student with a little maths background i.e doing quant without maths. Any other ingenious solution is also welcome.
There exist three positive integers P, Q and R such that P is not greater than Q, Q is not greater than R and the sum of P, Q and R is not more than 10. How many distinct sets of the values of P, Q and R are possible?
a120 b43 c11 d31
solve this question by converting it into an inequality and using permutation and combination concepts.