Quant by Arun Sharma

MBA CAT 2024
3617
Check up on Euler No.

Basically, for a number n, if E = k

Then for any no. p coprime to n, we can say that p^k/n leaves remainder 1

1.
E = 9(1-1/3) = 6
We need to represent 32^32^32 in form of 32^(6k+y) coz we know that 32^6k would leave remainder 1 on division with 9.

32^32Mod6 = 32 * 32^31Mod6
=> 16 * 32^31Mod3
=> 1 * -1Mod3
=>2Mod3
Multiplying back by 2, we get 32^32 = 6k+4

So 32^32^32 = 32^(6k+4)

32^(6k+4)Mod9 = 32^4Mod9 = 5^4Mod9 = 625Mod9 = 4

2.
E = 11(1-1/11) = 10

50^51^52 = 50^(10k+1)

50^(10k+1)Mod11 = 50Mod11 = 6





Hey angadbir ,


I have a doubt . I understood your method till 6k + m form .


After that if we want to express 32^32 as a multiple of 6 - we can use euler's theorem again right ?


E = 2 ; so 32 ^ 32 can be written as 32^2p so it has remainder of 1



=> 32 ^ 32 = 6k + 1



so /9 = /9 => Remainder : 5



Can you tell me y we're getting diff answers ? :shocked:
3618
Hey angadbir ,


I have a doubt . I understood your method till 6k + m form .


After that if we want to express 32^32 as a multiple of 6 - we can use euler's theorem again right ?


E = 2 ; so 32 ^ 32 can be written as 32^2p so it has remainder of 1



=> 32 ^ 32 = 6k + 1



so /9 = /9 => Remainder : 5



Can you tell me y we're getting diff answers ? :shocked:


Yes u can use euler no. again as u stated.

For the error that u made,
Check the part i've highlighted in red bolds, from my previous post below.
Check up on Euler No.

Basically, for a number n, if E = k

Then for any no. p coprime to n, we can say that p^k/n leaves remainder 1



6 and 32 are not coprime. Make them so, by cancelling out a 2 in both, and later multiplying back same after u've obtained the remainder using euler.
3619

hi I m new to this thread....

please solve this query:
how many digits in 56^22?

PS: With full explanation....

3620
Hey !


Is the answer to your question 32^4 ?? Since each apple will have an option of going to either of the 4 guys ... I'm not very sure ..please confirm ...


I don't know the answer mate! Are you sure? Anyone else?
3621
Hey !


Is the answer to your question 32^4 ?? Since each apple will have an option of going to either of the 4 guys ... I'm not very sure ..please confirm ...


And what will be the answer if it's also given that no one will get more than 10 apples?
3622
hi I m new to this thread....

please solve this query:
how many digits in 56^22?

PS: With full explanation....



guess you have taken this from TF QQD.

See the value of log 2 and log 7 is given .

Take log(56^22)
=22*log(56)
=22*
=22*
=22*
=38.4560

The number of digits = characteristic( integer part ) + 1

The number of digits = 39
3623
guess you have taken this from TF QQD.

See the value of log 2 and log 7 is given .

Take log(56^22)
=22*log(56)
=22*
=22*
=22*
=38.4560

The number of digits = characteristic( integer part ) + 1

The number of digits = 39

plz explain me dis part ( The number of digits = characteristic( integer part ) + 1 ) .
38 is the multiplication part n the question is asking 4 no. of digits after 56^22.. den hw come 39 digits?
3624

There is an equilateral triangle ABC with side =168m. A person P1 starts from A to B at 60m/hr and person P2 starts from B to C at 30m/hr.After how many hours the distance between P1 and P2 is the least??

3625
Deepakmr95 Says
There is an equilateral triangle ABC with side =168m. A person P1 starts from A to B at 60m/hr and person P2 starts from B to C at 30m/hr.After how many hours the distance between P1 and P2 is the least??

2.1 hours?
3626
plz explain me dis part ( The number of digits = characteristic( integer part ) + 1 ) .
38 is the multiplication part n the question is asking 4 no. of digits after 56^22.. den hw come 39 digits?



we have found log (56^22) = 38.4560.

So 56^22 = 10^38.4560


which would round off to next integer hence 39 digits in 56^22
3627

Arun Sharma = Thakela Book

3628

after 5.05 hours

3629
Deepakmr95 Says
There is an equilateral triangle ABC with side =168m. A person P1 starts from A to B at 60m/hr and person P2 starts from B to C at 30m/hr.After how many hours the distance between P1 and P2 is the least??


Ans :: 5.6 hr (if P1 and P2 continue their journey in the same direction after reaching B and C respectively.) _-_-_-_-_ SURE! :cheerio:

Ans :: 2.1 hr (if P1 and P2 stops their journey after reaching B and C respectively.) _-_-_-_-_ Not so SURE!
3630

Hi
How to i go about this ?

Of the adult population in Nagpur , 45 % of men and 25% of women are married. What percentage of the total population of adults is married ? (Assume no man marries more than one woman and vice versa)

Arun Sharma quant , Percentages LoD II Q 40

3631
Hi
How to i go about this ?

Of the adult population in Nagpur , 45 % of men and 25% of women are married. What percentage of the total population of adults is married ? (Assume no man marries more than one woman and vice versa)

Arun Sharma quant , Percentages LoD II Q 40


No. of adult man=x
No. of adult female=y

Now, 0.45x=0.25y => y=1.8x
Percentage of married adult= ((0.25y+0.45x)/(x+y))*100%=(0.9x/2.8x)*100%=32.14%

3632
In how many ways can you distribute 32 apples among 4 different students?

I know you'll grin seeing this question! But I really forgot the method. Please help me.


A+B+C+D = 32
so answer will be 35 c 3
3633
A+B+C+D = 32
so answer will be 35 c 3


Please explain mate.
3634

hey how is eng. book by arun sharma...

3635

you have n item which has to be distributed among n people . so in this case its possible them they few people get zero items so the distribution will be (n+r-1)C(r-1)
if in case where any of them should have atleast one item then the result will be (n-1)C(r-1)

3636
CAT_Aspirant101 Says
Please explain mate.

you have n item which has to be distributed among r people . so in this case its possible them they few people get zero items so the distribution will be (n+r-1)C(r-1)
if in case where any of them should have atleast one item then the result will be (n-1)C(r-1)