Number System - Questions & Discussions

MBA CAT 2022
2396
Asfakul Says
find the sum up to 20 th term of the series 2+4+7+11+...


first term=s1+1
2nd term=s2+1




20th term=s20+1
sum=(s1+s2+s3....S20)+20=1540+20=1560
2397
first term=s1+1
2nd term=s2+1




20th term=s20+1
sum=(s1+s2+s3....S20)+20=1540+20=1560


2nd term =s2+1 or s2+2?
2398

I have one concern though..
I did the following ..
S=2+4+7+11+.....+T20
S= 2+4+7.........+T19+T20
---------------------------------------
0=2+(2+3+4+......20)-T20 // 20 as inner series has term =n+1
getting 20th term as 211.


now average of the series (2+211)/2

Sum of the series =20*213/2
2130

WHICH TURNS OUT TO BE WRONG

Guys please point the error in it..
Thanks !

2399
bbwi Says
2nd term =s2+1 or s2+2?


2nd term=4=(1+2)+1=s2+1
2400

answer1237

2401

wat is E(17) ...???

2402
prathi s Says
wat is E(17) ...???


E(17) = 16

E of any prime number = number - 1

if the number is not a prime then express it is as product of prime number and den use the formula
if N = a^p*b^q.....
E(n) = N*(1-1/a)*(1-1/b)....

for e.g.
E(25) = 20
how??
25 = 5^2
E(25) = 25*(1-1/5) = 25*4/5 = 20

hope it helps u
2403

i dint understand.. could any one pls explain it elaborately???
find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13

2404

find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13

2405
find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13


Is the remainder 1?

I'll explain if I'm right.
2406
find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13


It should be 1.
Euler's number for 17 = 16.
So, any number if it is co-prime to 17, raised to power 16 will leave remainder as 1.
Now, (38^16!)^1777 = 38^(16! * 1777) = 38^16k => Remainder to be 0.
2407
find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13


Hi
I have created a video tutorial for providing solution to this question. Check out: Pattern Recognition - 4 - YouTube
Hope this will help you.
2408
find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13


The ans should be 16
2409
bbCAT005 Says
The ans should be 16


I think answer should be 1. Kindly see my previous post with link to video solution. Still if think that is wrong, kindly post your reasoning for answer to be 16.
2410
i dint understand.. could any one pls explain it elaborately???
find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13


answer is 1.. it was asked in one of the AIMCATS as well..

since the divider 17 is prime number we can apply FERMENT's law(dnt wry if u do not knw)
E(17) = 16
now 38^16 when divided by 17 will give u a remainder of 1...
so we have 16! = 16*15*..*2*1
so when 38^16! gives remainder 1
so 1^1777777777777777777777 (whatver it is) = 1


Hope u understand....
2411

puys i have a doubt, please help
supposing we are asked to find the remainder when divided by a composite number (say 100)
lets assume that we have to find it using euler's method
i have noticed in various forums that two ways of finding E(100) is used

---1st method---
100=2^2 * 5^2
E(100)= 100 * (1-1/2) * (1-1/5)
= 40

---2nd method---
100=25 * 4
E(25)= 20
E(4)= 2
so E(100)= LCM(20,2)
= 20

what i want to know is that when do we use which method ???

2412

double post

2413

Answer is 1

2414
answer is 1.. it was asked in one of the AIMCATS as well..

since the divider 17 is prime number we can apply FERMENT's law(dnt wry if u do not knw)
E(17) = 16
now 38^16 when divided by 17 will give u a remainder of 1...
so we have 16! = 16*15*..*2*1
so when 38^16! gives remainder 1
so 1^1777777777777777777777 (whatver it is) = 1


Hope u understand....


One can go this way too-:
38 gives 4 as remainder when divided by 17
thus the question reduces to finding the remainder when (4^16!)^1777 is divided by 17. Now we can write (4^16!)^1777 as (16^(15!*8 )^1777......(im converting the 4 into 16 taking a 2 from 16! hope you get it) which can be further written as ((17-1)^(15!*8 )^1777.
Now Since the power of (17-1) is even (that can be inferred from either the 15! or 8 therefore we have +1 as the remainder when divided by 17
2415
puys i have a doubt, please help
supposing we are asked to find the remainder when divided by a composite number (say 100)
lets assume that we have to find it using euler's method
i have noticed in various forums that two ways of finding E(100) is used

---1st method---
100=2^2 * 5^2
E(100)= 100 * (1-1/2) * (1-1/5)
= 40

---2nd method---
100=25 * 4
E(25)= 20
E(4)= 2
so E(100)= LCM(20,2)
= 20

what i want to know is that when do we use which method ???


you use the first one ..

the second one doesnt make sense ....