1. 7^45 = 7(7^44) = 7(2401)^11 = 7(01)^11 = 7(01) = 07. 2. 3^90 + 5^90 = 9^45 + 25^45 is always divisible by (9 + 25) = 34. So remainder is zero. 3. 4 values -...
3956
srinivas reddy
srinivasmett...
Nov 10, 2010 8:57 am
the ratio in both the buckets will progressively get closer to 50-50...
3957
kamal lohia
kamallohia
Nov 10, 2010 8:58 am
1. Phi(31) = 30. 2. 8 + 4 + 4 = 16. 3. 1050/2 = 525. 4. HCF(a, b) cannot be greater than a and b. Please confirm the answers. I am sure that there can be some...
3958
sambit pradhan
samba_east
Nov 10, 2010 10:38 am
Hii... find the next no.... 1,2,4,8,16,31,57,___ Â With Regards, Sambit Pradhan Hii... find the next no.... 1,2,4,8,16,31,57,___ With Regards, Sambit Pradhan...
3959
Uma Maheswaran
umamaheswaran_b
Nov 10, 2010 3:08 pm
answer is 99!! ... -- Thank You. Reards, Uma Maheswaran B...
3960
divakar narayan
divakar_narayan
Nov 10, 2010 3:08 pm
Ans1: If HCF is 35 then the numbers should be in the form 35k, where k is a prime number. Since it is given x+y=1085, we can write 35(a+b)=1085or a+b = 31. Now...
3961
nitin kaushik
nitin_be_32
Nov 10, 2010 3:09 pm
Dear Sambit, The next digit is 99. You just start finding the difference between digits. Finally u will find a series 1,2,3,4,5. Then do reverse. u well get to...
3962
Rajesh Balasubramanian
ascentcatprep
Nov 10, 2010 4:33 pm
Hi all, Have given below solutions to questions on LCM and HCF. Apologies for the error in the 4th question that had been posted earlier (the question has now ...
3963
divakar narayan
divakar_narayan
Nov 11, 2010 1:11 am
Hello  Rajesh BalasubramanianI wanted to know about this phi function and more about how and when to use it nuber system questions...If you can tell me a...
3964
Rajesh Balasubramanian
ascentcatprep
Nov 11, 2010 1:36 am
Hi all, Have given below three more questions on HCF and LCM on Number Theory. The questions can also be found on our blog - ...
3965
divakar narayan
divakar_narayan
Nov 11, 2010 12:20 pm
Ans 1: If we split 1080 it comes out to be 2^3X3^3X5. Since the product of a,b and HCF(a,b) has to have a cube(since it can be written as k*xk*yk=k^3*x*y. The...
3966
divakar narayan
divakar_narayan
Nov 11, 2010 12:20 pm
Sorry the LCM should be l*m*n instead of what i wrote in my previous mail. Very sorry for the blunder. Opinion is like an AssHole, everybody has one! Divakar...
3967
kamal lohia
kamallohia
Nov 11, 2010 12:20 pm
1) We need to find ordered pairs (x, y) such that xy*HCF(x, y) = 1080. Let x = ha and y = hb where h = HCF(x, y) and HCF(a, b) = 1. So h^3(ab) = 1080 =...
3968
Hemal Patel
hemalpatel55
Nov 11, 2010 12:20 pm
Hello .. i want some of the question bank which is latest with anwer please kindly send me HEMAL M PATEL Email : info@... Contact : (1) 97141...
3969
kamal lohia
kamallohia
Nov 11, 2010 12:20 pm
Bhaisaab 1) When you say how many pairs of positive integers x, y exist such that......, then there you need to find number of ordered pairs (x, y) satisfying...
3970
kamal lohia
kamallohia
Nov 11, 2010 12:20 pm
Hi Divakar a + b = 31 such that HCF(a, b) = 1. Now it is not compulsory that a and b are prime. eg. (a, b) can be (1, 30), (2, 29), (3, 28), .....(30, 1) i.e....
3971
Ravjeet Singh
rav_sr
Nov 12, 2010 3:43 am
can u calculate one ques.      6^83+8^83/49 gives remainder...???   even trying with euler number. bt logic is not buliding up ...
3972
Ravjeet Singh
rav_sr
Nov 12, 2010 3:43 am
its 3!/4Â Â u r right..its an exception ________________________________ From: Naveenan Ramachandran <6NaveenanR@...> To:...
3973
sanjay_852000
Nov 12, 2010 3:43 am
answer is 99...
3974
Rajesh Balasubramanian
ascentcatprep
Nov 12, 2010 4:04 am
I think we can think of this as (7-1)^43 + (7+1) ^43/ 7^2 Binomial expansion could give the solution. (a-1)^43 + (a+1)^43 divided by a^2 -1 and +1 will get...
3975
kamal lohia
kamallohia
Nov 12, 2010 8:34 am
Sir It is Kamal Lohia not Kohia. Please do the correction for future reference. Ravjeet Besides binomial expansion you can find the remainders of individual...
3976
sambit pradhan
samba_east
Nov 12, 2010 8:35 am
hii.... how u got it..??? Â With Regards, Sambit Pradhan ________________________________ From: sanjay_852000 <sanjay4c@...> To:...
3977
Uma Maheswaran
umamaheswaran_b
Nov 13, 2010 3:19 am
Hi Kamal Lohia amazing way to arrive at the answer (35 is correct).. never thought abt Euler's thm though... here is one more way... two basic rules... ...
3978
Rajesh Balasubramanian
ascentcatprep
Nov 13, 2010 3:24 am
Hi Kamal Lohia (correction noted. Sorry about the error) , Your solution is spot on. Sorry, I had misread the qn as 6^43 + 8^43. Neat solution. Good use of...
3979
Rajesh Balasubramanian
ascentcatprep
Nov 13, 2010 3:24 am
Hi all, Have given below the solutions to the LCM HCF questions discussed in the previous post. The solutions can also be found at our blog ...
3980
Rajesh Balasubramanian
ascentcatprep
Nov 13, 2010 4:30 am
Hi all, Have given below three more questions on Number Theory. They are also there at our blog. (These are simpler than the ones that we have seen previously....
3981
kamal lohia
kamallohia
Nov 13, 2010 1:24 pm
1. The number aabb is 7744 and a - b = 3. 2. 27 ordered triplets. 5 unordered triplets. 3. 4, 15, 26, 37, 48 ________________________________ From: Rajesh...
3982
Ravjeet Singh
rav_sr
Nov 14, 2010 4:12 pm
hi kamal g, can u plz tell me how the unordered pair u had found out ________________________________ From: kamal lohia <kamallohia@...> To:...
3983
divakar narayan
divakar_narayan
Nov 14, 2010 4:13 pm
Lohia Sir, can you give the detailed answers? It would be a great help.And I wanted to ask one thing regarding the mod question...You wrote :Â Â 6^84 = 1...
3984
Rajesh Balasubramanian
ascentcatprep
Nov 15, 2010 2:29 am
Hi all, I have given some theory on Euler's phi function. Since the theory has a few links, I am giving an extract here, kindly have a look at the blog for a ...
