official quant thread for cat08

[MadMagga]

Originally Posted by naga25french

ma answers..

1) remainder is 1

2) remainder is 13...

Hey,Can you tell me how you arrived at each of these answers ?
Couldn't figure it out myself.

[ankaj]

Originally Posted by vaibhav2cool

in fact if k is -2.4 then the two equations will be inconsistent

how dumb...it is -2.4 (decimal)...i was thinking the values are -2 and 4....:bang head:

[ganesh99]

Originally Posted by naga25french

ma answers..

1) remainder is 1

2) remainder is 13...

can u pls explain how did u get that...

[shivam_01]

Originally Posted by ankit1207
try this
Quadrilateral ABCD is inscribed in a circle with diameter AD = 4, if
side AB and BC each have length 1, then find CD?
a) 5/2 b) 3 c) 7/2 d) 4 e) none of these

In a cyclic quadilateral the product of the diagonals is equal to the sum of product of opposite sides...

Now in this case the AB*CD+BC*AD=AC*BD
Now AC = sqrt(16-x^2) and BD = sqrt(15)

Now applying the above theorm we get sqrt(15*(16-x^2))=x+4
solving this we get x=7/2
I hope this is the answer

[shivam_01]

Quote:
Originally Posted by sharanr
can anybody help me in solving this question....
For what value of k the following equation will have unique solution?
3x+5y = 20 and kx-4y =16.

1. 5
2. -2/4
3. 5/3
4. 3/5
5. any value of k except -2.4


All values of k except -2.4 for which the solution is inconsistent

[naga25french]

Originally Posted by ganesh99

can u pls explain how did u get that...

@mad magga and ganesh

1) (43)^197 / 7

by fermat theorem , (43)^192 divided by 7, remainder is 1.. we r left with 43^5..

now 43^5.. remainder is (1)^5 as 43/7 leaves remainder 1..

hope its clear..

2) (21)^875/17

by fermat theorem , (21)^864 divided by 17, remainder is 1.. we r left with 21^11..

now 21^11/17

remainder is 4^11/17

(4^11/17 )= (4^8 * 4^3)/17

= (256^2 * 64)/17

= (1* 64)/17

so the final remainder is 13..

hope its clear..

[bhandari4u]

Originally Posted by shivam_01

Quote:
Originally Posted by sharanr
can anybody help me in solving this question....
For what value of k the following equation will have unique solution?
3x+5y = 20 and kx-4y =16.

1. 5
2. -2/4
3. 5/3
4. 3/5
5. any value of k except -2.4
All values of k except -2.4 for which the solution is inconsistent

for all those non-slopian (aka who don't understand what is slope). use this as a class 10th student will do:

ratio of coefficients of x = k/3
ratio of coefficients of y = -4/5

the equations will have unique solution when
k/3 != -4/5 (!= means not equal in IT industry )
implies k != -2.4

hence -2.4 will not give unique solution (answer 5)

[sidcool007]

The number of ways you can invite 3 of your friends on 5 consecutive days , exactky one friend a day , such that no friend is invited on more than two days.

PS: posting again , was lost in b/w

[shivam_01]

Originally Posted by MadMagga

Hey,Can you tell me how you arrived at each of these answers ?
Couldn't figure it out myself.

1) (43)^197 / 7

(43)^197 divided by 7 = (42+1)^197 divided by 7 remainder is 1 as on expansion all the other terms would be multiple of 42 only and that too multiple of 7 also .

2) (21)^875/17

(21)^875 divided by 17 = (17+4)^875 so we left with 4^875
which can be written as or rather left with 4^875 divided by 17.

now this can be written as 4.4^874/17 = 4.(16^437)/17
--> 4.(17-1)^437/17 so we are left with 4.16/17 and hence the final remainder is 13..

[shivam_01]

Originally Posted by naga25french

@mad magga and ganesh

1) (43)^197 / 7

by fermat theorem , (43)^192 divided by 7, remainder is 1.. we r left with 43^5..

now 43^5.. remainder is (1)^5 as 43/7 leaves remainder 1..

hope its clear..

2) (21)^875/17

by fermat theorem , (21)^864 divided by 17, remainder is 1.. we r left with 21^11..

now 21^11/17

remainder is 4^11/17

(4^11/17 )= (4^8 * 4^3)/17

= (256^2 * 64)/17

= (1* 64)/17

so the final remainder is 13..

hope its clear..

hey can u explain fermat's theorm in laymans term or rather with an example.. thanks in advance