@ravi.theja said:Find the last non-zero digit in 37!
4
@ravi.theja said:crct post ur solution sir
dude! dont call me sir. lets just enjoy the camaraderie
i just have seen this question many a times to remember the ans :P
it is like this.
to find the last non-zero digit of a factorial N!
see it is of the form N=5a+b
then the last non-zero digit is the prod of last non zero digits of 2^a and a! and b!
which in this case is 8x4x2 or simply 4.
i just have seen this question many a times to remember the ans :P
it is like this.
to find the last non-zero digit of a factorial N!
see it is of the form N=5a+b
then the last non-zero digit is the prod of last non zero digits of 2^a and a! and b!
which in this case is 8x4x2 or simply 4.
@pyashraj said:@naga25french@LogrhythmN = 444(upto 50 digits) except for the nth digit(where n ranges from 1-50). If N is divisible by 13 for nth digit, then find how many value can n take ?Should Indeed be 24..n=1, N=4, Rem[N/13] = 4n=2, N=44, Rem[N/13]= 5n=3, N=444, Rem[N/13]= 2, but if N=442, Its Divisible..n=4, N=4444, Rem[N/13]=11, but if N=4446, Its Divisible..n=5, N=44444, Rem[N/13]= 10, but if N=44447, Its Divisible..n=6, N=444444, Rem[N/13]= 0..Hence N is itslf divisible..n=7, N=4444444, Rem[N/13]= 4...and the cycle gets repeated..Thus, for n= 1,2,3,4,5,6 ..there r 3 values at which this is satisfied..at n=3,4 n 5..For, n=7,8,9,10,11,12..there r 3 values at which this is satifisfied..at n= 9,10 n 11.....For n = 43, 44, 45, 46, 47, 48..There r 3 values at which this is satisfied..at n= 45, 46 n 47..For n=49 n 50..Its not satisfied..Thus, a total of 3*8 = 24 values are there of n(1-50), at which the conditions r met.. Screwd the 1st tym..
@pyashraj i am not sure if this is right.. take for example case of n=3, 442 gets divisible.. but the other 4s (47 in number) wont be divisible by 13.. so N wont be divisible by 13.. same with other cases..
@anytomdickandhary help please :(
any further leads?
@gnehagarg said:X=2^a1*3^b1Y=2^a2*3^b2Z=2^a3*3^b3a1+a2+a3=35C2=10b1+b2+b3=24C2=6ordered ways=60unordered ways=a1=a2 and b1=b2=>4 waysa2=a3 and b2=b3=>4 waysa1=a3 and b1=b3=>4 waysTotal ways =1260-12/6=8 waysUnordered ways=6+8=14
@gnehagarg please explain the unordered part.. you have taken a1=a2 and b1=b2.. similarly there would also be a1=a2 and b2=b3 and a1=a2 and b1=b3..
unko kyu nahi liya?
and heres my approach..
in a1+a2+a3=3 no of solutions such that 2 or 3 are same = 7 (for ordered) and (3 ways in unordered pair)
in b1+b2+b3=2 no of solutions such that 2 or 3 are same = 6 (for ordered) and (2 ways in unordered pair)
thus ans = 3+2+ (60-42)/6 = 8
in (60-42)/6 , i removed the 42 ordered pairs (7*6) where 2 or more terms were equal.. and divided y 3! to remove effect of ordering ...
@anytomdickandhary @naga25french inputs/second opinions please!
@vbhvgupta said:Which of the followinf is not a perfect square100856, 325137, 945729? how to find quickly?
digital sum of a perect square can be 1 4 9 and 7
so first 2 are not perfect squares :)
so first 2 are not perfect squares :)
@rayus said:ans is time between 8 am + (40*12/11) minutes and 2 pm + (40*12/11) minutes... so its 6 hours.. @pirateiim478 OA please
how 40 please explain :)
@joyjitpal Find the no of no between 200 and 300 , both incuded , which are not divisible by 2,3,4,5.
How to go for it?
@cadmium said:
Simplify:839478 * 625
simplification needs to be done.
and not multiplication.
@vbhvgupta said:@joyjitpal Find the no of no between 200 and 300 , both incuded , which are not divisible by 2,3,4,5.How to go for it?
simple set theory ques
= 101 - (51 + 26 + 20 - 17 - 11 - 7 + 4)
= total - (factors of 2 + factors of 3 + factors of 5 - factors of 2,3 - factors of 2,5 - factors of 3,5 + factors of 2,3,5)
PS.. not taken 4 as all factors of 2 will include all factors of 4
@cadmium said:@cadmium said:Simplify:839478 * 625simplification needs to be done.and not multiplication.
u can multiply it by 16 in both num. and deno. which makes you to divide it by 16 which is lot easier than multiplying by 625.
839478*10000/16 = 524673750.
839478*10000/16 = 524673750.
@joyjitpal said:how 40 please explain
min and hr hand are opposite after relative distance of 30 min.. so @ 8 am, min hand has to cover dist worth (8*5) min for it to be opposite to hr hand.. similarly @ 2 pm min hand has to cover (2*5)+30 min..
it might sound confusing.. but i got to rush now.. will write detailed soln in evening..
@rayus said:simple set theory ques= 101 - (51 + 26 + 20 - 17 - 11 - 7 + 4)= total - (factors of 2 + factors of 3 + factors of 5 - factors of 2,3 - factors of 2,5 - factors of 3,5 + factors of 2,3,5)PS.. not taken 4 as all factors of 2 will include all factors of 4
Yar ans is 26. But from here I am getting 35
@vbhvgupta said:Yar ans is 26. But from here I am getting 35
101 - (51 + 26 + 20 - 17 - 11 - 7 + 4)
26 34
101 - (51 + 34 + 20 - 17 - 11 - 7 + 4) = 26
101 - (51 + 34 + 20 - 17 - 11 - 7 + 4) = 26
@pirateiim478
Let, (x^2 - x + 1)/(x^2 + x +1) = y
=>x^2(1-y) - x(1+y) + (1-y) = 0
Now, D>=0, or, (1+y)^2 - 4(1-y)^2 >=0
=> 3y^2 -10y + 3>=0
=>y = {10 +/- [100 - 4*3*3]^(1/2)}/6
=>y = 3, 1/3
Thus, 1/3