[warrior]

Originally Posted by nebuchadnezzar

hi clsuresh/others...

help me with this one...

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles.
A possible value of the number of tiles along one edge of the floor is:

1. 10 2. 12 3. 14 4. 16

lemme tell my approach...

i take the value of the sides as n1 and n2 ..then (n1-1)(n2-1) = n1*n2 - (n1-1)(n2-1),

or, 2(n1-1)(n2-1) = n1* n2

for any of the answer options, the eqn is not giving an integer value for the other number...what is wrong with my approach..???

Vaibhav

ans nikalne ke liye back substitue kar

let the lengths be a nad b

now if b= 16 then tile son edge = 32+ 2*(a-2) = 14 *(a-2) not possibble

for 12 its 24 = 8(a-2)
a= 5 so possible

[viccy_776]

[QUOTE=nebuchadnezzar]hi clsuresh/others...

help me with this one...

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles.
A possible value of the number of tiles along one edge of the floor is:

1. 10 2. 12 3. 14 4. 16

For a m*n rectangle no.of tiles along a particular row be m while that along a particular column be n

then along the edges total number of tiles will be 2*m+2(n-2) .



Also inner tiles will be (m-2)*(n-2)

try drawing it for 4*3;5*3;5*4 matrix

2*m+2(n-2) = (m-2)*(n-2)

solve it and you get n= 2+2*m/(m-4).only m =12 satisfies among all options

[akash_b]

[quote=nagi_nov3]7...37times
=7*10^36+77*10^34+...........+77*10^4+77*10^2+77

77 mod 19 =1

10^2 mod 19 =100 mod 19 =5

so we will left with
7*5^18+5^17+..........+5^2+5^1+1
5^17+..........+5^2+5^1+1 = sum of G.p

7*5^18+ (5^18 -1 )/4

5^18 mod 19 = 6^9 = 216^3 = 7^3 = 343 = 1 mod 19

so we left 7*1+(1-1)/4 = 7

hello
i could solve the below prob till finding the summation of g.p.
bu then i dint know how to deal with the ' / 4 ' ( in bold ). here since the trm becomes zero its not a prob. but what if it did not become zero. for eg. if the remainder for 5^18 would have been 2 u would have [(2-1)/4] % 19. how do u deal with that then ??
7...37times

[nebuchadnezzar]

Originally Posted by viccy_776

hi clsuresh/others...

help me with this one...

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles.
A possible value of the number of tiles along one edge of the floor is:

1. 10 2. 12 3. 14 4. 16

For a m*n rectangle no.of tiles along a particular row be m while that along a particular column be n

then along the edges total number of tiles will be 2*m+2(n-2) .



Also inner tiles will be (m-2)*(n-2)

try drawing it for 4*3;5*3;5*4 matrix

2*m+2(n-2) = (m-2)*(n-2)

solve it and you get n= 2+2*m/(m-4).only m =12 satisfies among all options

thanks vicky/ warrior ...got it...

i was framing the eqns wrong...so bad of me...instead of (m-2) * (n-2), i was doing (m-1) * (n-1)...total tiles minus inside tiles = tiles on edges,
or,
m*n - (m-2) * (n-2) = (m-2) * (n-2)
or,
2(m-2)(n-2) = m*n

that gives the answer straightaway, unless u keep dancing around wrong equations, like me..??:.

Vaibhav

[Pragati Soni]

hello NAgi,

Plz clear my doubt...

Originally Posted by Pragati Soni

Hello navi,

Would u plz make it clear....if u r saying probability 1/8(exact)..then does it imply.....out of 8 methods we can break the stick only 1 method is their,,in which we can form the Triangle...

I am clear with the explaination that 1/2<c<1/2 but I am not clear with d probablity....

Plz tell me.

thanks

[Pragati Soni]

Hi Anupam,

M having few very simple doubts:
1) 56 mod 9 is 2 and not 1.
2) If we do both multiply n divide the fraction by 14 why we are required to multiply again?

Plz Anupam clear my doubts.I am really in need of that.

Originally Posted by anupam_khanna

breaking the denominator into least for we get

f(x)= 4 * 56^492 / 9

now 56 ^ 492 mod 9 = 1

therefore f(x) = 4 * 56^492 mod 9
=> 4

now sice we divided by 14 to make the num and den coprime we multiply this by 14 to yeild the final remainder...
therefore final rem = 4 * 14 = 56

cheers!!!

[clsuresh]

Folks, I think most of u r confused with the question breaking a stick into three parts such that the three parts form a triangle. Find the probabaility.

Here is my explanation.
Clealry if the lengths are a,b,c then a+b+c = 1
Now let's calculate the probability of not getting a triangle.
This will happen if atleast the lenght of one piece is >=1/2.
Now to cut a stick into 3 parts we need 2 cuts say P and Q.
For the piece A the length will be greater than 1/2 provided both the cuts P and Q are after the half the lenth of the stick;
Hence the probability for the cut to be after 1/2 the lenght of the stick is 1/2
and the probability of the cut Q to be after 1/2 the length of the stick is 1/2.
Hence the probability that A>=1/2 is 1/4
Similary the probabililty that B>=1/2 is 1/4 and C>=1/2 is 1/4;
So the probability of not getting a triangle is 1/4+1/4+1/4 = 3/4
Hence the probability of getting a triangle is 1/4.

I think the explanation is clear.

[clsuresh]

HEre is the next question
Remainder when (63)^165 is divided by 581.

[nagi_nov3]

Originally Posted by clsuresh

HEre is the next question
Remainder when (63)^165 is divided by 581.

i love remainder questions

63.63^164 mod 581

9.63^164 mod 83 ( we have to mutilply the answer by 7 at the end)

euler for 83 = 82

so 63^164 mod 83 =1

so we left with 9*7 = 63

[prade]

Originally Posted by clsuresh

HEre is the next question
Remainder when (63)^165 is divided by 581.

63 = 7*9
and
581 = 7 * 83
=> 63^165 mod 581= 9 * 63^164 mod 83 (later multiply by 7)

euler number for 83 is 82

=> 9* (63^82)^2 = 9 mod 83

hence the remainder is 7*9 = 63