# @sweetcutehimani

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###### CATQuant by Arun Sharma

A set of consecutive natural numbers beginning with 1 is written on the board. A student came along and wrote one of these numbers one more time and found the average of the numbers written on the board as 40 20/27.What was the number that was written twice on the board?

27

53

26

60

###### CATQuant by Arun Sharma

Find the remainder when 37^(1257) *28^3512 is divided by 5.

2
6
8
4

###### CATQuant by Arun Sharma
2222^7777 + 7777^2222
=(2222^7)^1111 + (7777^2)^1111
The number has to be divisible by 2222^7 + 7777^2( a^n+b^n is divisible by a+b if n is odd)

2222^7 + 7777^2
=1111^2( 2^7*1111^5 + 7^2 )

If we check for 88 and get it right then 44 should also be right, hence 88 cannot be the answer.
We are left with 44, 77 and 99. .

11 divides 1111^2.
So the remaining term should be divisible by either 7,4 or 9
2^3 = -1(mod 9) => 2^7 = 2(mod 9)
1111 = 4(mod 9) => 1111^5 = 4^5(mod 9) = 2^10(mod 9) = -1*2
= -2(mod 9)

2^7*1111^5 = -4(mod 9) and 7^2 = +4( mod 9 )
9 divides ( 2^7*1111^5 + 7^2 )
Hence,99 divides the given number

Let me know if you have any problem

did not get this step.
###### CATQuant by Arun Sharma

plz rahulmn.............

###### CATQuant by Arun Sharma
My take
2) 99

it's ryt. bt cn u xplain it 4 me?

options are
1)999
2)99
3)88
4)77
5)44

###### CATQuant by Arun Sharma

2222's power 7777 + 7777's 2222
is divisible by
?

Lajwanti D'Souza @laj
_Pic from the FMS website_ Another MBA entrance exam is expected to bite the dust soon. Faculty of Management Studies (FMS) is in all probability going to shelve its 40-year old entrance exams in favour of the Comm
@sweetcutehimani

whts d prob wid FMS??????????