[hansini]

Originally Posted by dharmesh.patel

has to be 3


Using Euler's theorem...3 and 101 are coprime hence we can use Euler's

Now, E=101(1-(1/101)) = 100

So we have ..Rem(3^100/101)=1

Now originally we have 3^101/101
that is 3*3^100/101

So we have to 3*1/101
so remainder =3

for prime numbers the eulers number is one less than theprime number. so here we can directly take the eulers number for 101 as 100

[dharmesh.patel]

Originally Posted by hansini

for prime numbers the eulers number is one less than theprime number. so here we can directly take the eulers number for 101 as 100

.

Great..why don't you share some more concepts and shortcuts related to this method..

[hansini]

Originally Posted by dharmesh.patel

.

Great..why don't you share some more concepts and shortcuts related to this method..

well that is it abt eulers!!!

anyways even if u wanna calculate the eulers num for prime num eg say 101 wat do u do?
u ll consider he prime factors o 101 but since 101 itself is prime so the eulers num is calc as
E(101)=101*(1-1/101) which is nothing but the value in the numerator that is 101-1!!
just try to note such details... u urself can find shortcuts!!

[Abhinav90]

Originally Posted by dharmesh.patel

.

Great..why don't you share some more concepts and shortcuts related to this method..

There is a full fledged thread consisting of all these fundaes here on PG...See the Concepts thread in this Quant section..
There you cud know everything about Euler and Inverse Euler and all...

[inava]

Hi,

I had a doubt with Qn 8 of AIMCAT1003.

A solid cube whose edges are 12 cm each, has been cut by a plane such that the plane bisects three edges meeting at a corner. Find the surface area of the remaining part of the cube after the small piece is removed.

My Approach was that, the removed part is a pyramid.

Now, Surface Area of the Pyramid = (1/2)*(Perimeter of Base)*(Slant Height)
= (1/2)*(3*6^(1/2))*(6) = = 54 * 2^(1/2)

But, the answer given has a different approach, which results in a different solution.

Could somebody please throw some light on this.

[shyam.nair]

If the number 2484x36y is divisible by 36 find the minimum value of x-y.

ans -7

[Ankurb]

Originally Posted by shyam.nair

If the number 2484x36y is divisible by 36 find the minimum value of x-y.

ans -7

x+y = 9k
y = 0,4,8
x = 0,5,1
min:-
x-y = -7

[raghav507]

Originally Posted by inava

Hi,

I had a doubt with Qn 8 of AIMCAT1003.

A solid cube whose edges are 12 cm each, has been cut by a plane such that the plane bisects three edges meeting at a corner. Find the surface area of the remaining part of the cube after the small piece is removed.

My Approach was that, the removed part is a pyramid.

Now, Surface Area of the Pyramid = (1/2)*(Perimeter of Base)*(Slant Height)
= (1/2)*(3*6^(1/2))*(6) = = 54 * 2^(1/2)

But, the answer given has a different approach, which results in a different solution.

Could somebody please throw some light on this.

hi inava,
in my view the removed part will be a tetrahedron...instead of a pyramid...
have a detailed look here...
Tetrahedron -- from Wolfram MathWorld
what is your opinion puys....?

[harshkumar1]

Originally Posted by shyam.nair

If the number 2484x36y is divisible by 36 find the minimum value of x-y.

ans -7

36 = 2^2 * 3^2
Hence for 2484x36y to be divisible by 36 it should be divisible by 4 and 9.

Divisibility by 4:
Last 2 digits should be divisible by 4
Hence (6y MOD 4) = 0
Putting y = 0, 1, 2, 3, ..... 9
Only for y = {0, 4, 8} is 6y divisible by 4

Divisibility by 9:
Sum of digits must be divible by 9
Hence (2+4+8+4+x+3+6+y) MOD 9 = 0
or, (27+x+y) MOD 9 = 0
27 is divible by 9
Therefore, (x+y) MOD 9 = 0
x = {9, 5, 1} (As y = {0, 4, 8}

For min value of x-y (x should be min while y should be max)
x = 1
y = 8
x - y = 1 - 8 = -7

Puys hope the approach is correct

[bhupi3149]

please solve

34!mod73