@MANC-LONDON said:@Tusharrr katrina doesn't knw how to solve a problem.... illiterate hain woh..
plz don't spam in this thread.... 
DS
Information in which of the following statements is sufficient to find the unit digit of
2^(a-3)+ 3^(a-1)+ 8^(a+1)+ 7^(a+3) ...???
I. the unit digit of a is 4
II. The tens digit of a is odd.
a] Statement I only
b] Statement II only
c] Both statements I & II
d] cannot be found even by both statements.
2^(a-3)+ 3^(a-1)+ 8^(a+1)+ 7^(a+3) ...???
I. the unit digit of a is 4
II. The tens digit of a is odd.
a] Statement I only
b] Statement II only
c] Both statements I & II
d] cannot be found even by both statements.
@floamiya said:DSInformation in which of the following statements is sufficient to find the unit digit of2^(a-3)+ 3^(a-1)+ 8^(a+1)+ 7^(a+3) ...???I. the unit digit of a is 4II. The tens digit of a is odd.a] Statement I onlyb] Statement II onlyc] Both statements I & IId] cannot be found even by both statements.
C
@floamiya said:DSInformation in which of the following statements is sufficient to find the unit digit of2^(a-3)+ 3^(a-1)+ 8^(a+1)+ 7^(a+3) ...???I. the unit digit of a is 4II. The tens digit of a is odd.a] Statement I onlyb] Statement II onlyc] Both statements I & IId] cannot be found even by both statements.
a..??
@floamiya said:DSInformation in which of the following statements is sufficient to find the unit digit of2^(a-3)+ 3^(a-1)+ 8^(a+1)+ 7^(a+3) ...???I. the unit digit of a is 4II. The tens digit of a is odd.a] Statement I onlyb] Statement II onlyc] Both statements I & IId] cannot be found even by both statements.
Both are needed:)
Nice framed question around cyclicity concept:)
@Tusharrr said:@scrabbler HowAnswer IS an INteGer less than 999
Not sure I interpreted correctly btw....the probability is written as ab matlab kya? Probability should be less than 1.
regards
scrabbler
@vbhvgupta said:6 boys and 8 women finish a job in 6 days and 14 boys and 10 women finish the same job in 4 days. In how many days working together 1 boy and 1 woman can finish the work.
44.57 ??
@mani0303 said:Both are neededNice framed question around cyclicity concept
Dear thanks you tried
but one more try...!!!
but one more try...!!!
@Tusharrr said:The probability that Katarina will correctly solve a given Brilliant math problem is 1/8. The probability that Layla will solve the same problem correctly is 1/12. The probability that they will give the same incorrect numerical result is 1/1001.Suppose Katarina and Layla solve a Brilliant math problem independently and get the same result. The probability that they get the correct answer, given that they got the same result, can be written as ab, where aand b are coprime positive integers. Find a+b.
If i understand the question correctly,along with the condition that it's a/b and not ab,then
the answer could be 97?,IMO again;)
@pakkapagal said:bhai chinese remainder theorem lagayi hai...25^889/99 E(99)=60 so rem(25^60)^14/99=1left with 25^59/99applying chinese theorem here1)25^59/9 rem(25^59)/9=4 so r1=4 2)25^59/11 rem(25^59)/11=4 so r2=4and also ax+by=1 ,here a=9 b=11 so we get x=5 ,y=-4putting all these values in eq.ar2x+br1ywe get 180-176=4
could you explain the bold part?
@floamiya said:Dear thanks you triedbut one more try...!!!
Dude - I don't if you have the solution or not,but here is mine
Cyclicity of all the 4 numbers - 2,8,3 and 7 is 4
So,considering a = 4,then the unit digits of each of them in the given expression are 2,8,7 and 3 (order as taken above)
=>total sum of unit digits to get the exp's unit digit = ..0
But if you do the same considering a = 14,then the unit digit of expression would be ...8
So,you can't generalize unless given the 2nd statement...So both are needed
@vbhvgupta said:6 boys and 8 women finish a job in 6 days and 14 boys and 10 women finish the same job in 4 days. In how many days working together 1 boy and 1 woman can finish the work.
312/7 days
@mani0303 said:Dude - I don't if you have the solution or not,but here is mineCyclicity of all the 4 numbers - 2,8,3 and 7 is 4So,considering a = 4,then the unit digits of each of them in the given expression are 2,8,7 and 3 (order as taken above)=>total sum of unit digits to get the exp's unit digit = ..0But if you do the same considering a = 14,then the unit digit of expression would be ...8So,you can't generalize unless given the 2nd statement...So both are needed
Thanks Dear you asked for solution, this is my question, designed by me, any way
OA: [a]
Sol : Using statement I, we now that a is even.
And for a being a even numbers of the type 4n, the unit digit of are going to end with 2, 7, 8 and 3.
And for a being a even number of the type 4n + 2, the unit digit of are going to end with 8, 3, 2 and 7.
And these two cases take care of all even values of a. Thus, in either case, the unit digit can be found uniquely.
Statement II alone cant give you unique solution.
Please check.
@floamiya said:Thanks Dear you asked for solution, this is my question, designed by me, any wayOA: [a]Sol : Using statement I, we now that a is even.And for a being a even numbers of the type 4n, the unit digit of are going to end with 2, 7, 8 and 3.And for a being a even number of the type 4n + 2, the unit digit of are going to end with 8, 3, 2 and 7.And these two cases take care of all even values of a. Thus, in either case, the unit digit can be found uniquely.Statement II alone cant give you unique solution.Please check.
Everything seems fine except the highlighted portion - especially 8 that is unit digit of 2^11 or 2^31 or 2^51...
But actually they would have given you the unit digit 6 and NOT 8,right?
BTW,You shown have put tremendous effort in this one,Thanks:)
@floamiya said:DSInformation in which of the following statements is sufficient to find the unit digit of2^(a-3)+ 3^(a-1)+ 8^(a+1)+ 7^(a+3) ...???I. the unit digit of a is 4II. The tens digit of a is odd.a] Statement I onlyb] Statement II onlyc] Both statements I & IId] cannot be found even by both statements.
option a) imo