Number System - Questions & Discussions

MBA CAT 2022
3438

@firsty how come 31^586 will end in 81?

is this a rule?
3439
@ipagal said:
@firsty how come 31^586 will end in 81?
is this a rule?
E(100) = 40

31^586 = 31^6 = 61^3 = 81

Consider it a rule if you want to 😃

Though calculating it is much more sane.
3440

A = {3, 23, 43 ………… 603} and S is a subset of A. If the sum of no two elements of S is more than 606, then what can be the maximum possible number of elements in S?

ans..16.pls EXPLAIN
3441
A number is divisible by 2, 4, 8, 16, 32,.. 2
n
when the number formed by the last one, two, three, four,
five...n digits is divisible by 2, 4, 8, 16, 32,..2
n
respectively.
Example: 1246384 is divisible by 8 because the number formed by the last three digits i.e. 384 is divisible
by 8. The number 89764 is divisible by 4 because the number formed by the last two digits, 64 is divisible
by 4.

my question is what if a number ends in 00?
3442
@PriyankaMitra : any number that ends in 00 as the last 2 digits will always be divisible by 4 and any number that ends in 000 as the last 3 digits will always be divisible by 8.
That's a universal rule!!
3443

dat means a no which ends in n zeroes is divisible by 2^n?

3444

@PriyankaMitra yes
3445

Thanks...

3446


@rahul005 The number of elements in the set A will be 31.
But the answer 16 for the elements of subset S is possible only when the sum of 2 numbers of Set A is exactly 606 and not less that that or when one of the elements is 303 always.
For sum less than or equal to 606, the number of elements of S will be 136.
Correct me if i'm mistaken.
3447
@abhijeetace Wont d remainder be 10 for 4^37+6^37 when divided by 25 as any expression of the form a^n+b^n where n is odd, the remainder will be a+b =0
3448
@Reetu107 said:
@abhijeetace Wont d remainder be 10 for 4^37+6^37 when divided by 25 as any expression of the form a^n+b^n where n is odd, the remainder will be a+b =0
Yes...the remainder wil be 10..
3449
or is it applicable only when a, b in the expression r consecuitve nos? wat wud be the remainder of 6^83 + 8^83 wen divided by 49? according to my approach ans wud be 14 but its cmng to be 35. Pls help
3450
what is the remainder when 67raised to the power of 53 is divided by 101?
(67^53 divided by 101? Smbdy pls explain
3451
Remainder when 50! is divided by 16^15.
3452

@Reetu107 said: what is the remainder when 67raised to the power of 53 is divided by 101? (67^53 divided by 101? Smbdy pls explain
Is the answer 67?
3453
@Reetu107 said:
Remainder when 50! is divided by 16^15.
What is the answer?
Highest power of 2 in 50! is 47. So that leaves us with ALL prime factors in numerator and 2^13 in denominator.. I'm not able to go further...
3454

@frostie Hey how did u get 2^13 in denominator?
3455
@Reetu107 said:
@frostie Hey how did u get 2^13 in denominator?
2^4^15 = 2^60. So, cancelled out 2^47, leaving out 2^13 in Dr.
3456

@fuzzyl0gik acn any body give the solution of these type of ques........

3457

while driving on a straight road, Jason passed a milestone with a 2 digit no. after exactly an hour , he passed a second mile stone with the same 2 digits written in reverse order. exactly 1 more hour after that , he passed a third mile stone with the same 2 digits reversed and separated by a zero.


what is the sum of the 2 digits?
1. 5
2. 6
3. 7
4. 8

smbdy plz explain.....