Official Quant thread for CAT 2013

@dushyantagarwal said:
I did some mistake in previous solution Here it goes:Total no's = 9 * 10^6Cases for sum of digits to be odd:1. when 1 digit is oddif it is 1st place then 5 * 6^6 and for seven places 7C1 * 5 * 6^62. when 3 digits are oddthen 7C3 * 5^3 * 6^4and so onWe have to subtract all these from total which gives me9*10^6 - (7C(7-n+1) * 5^(7-n+1) * 6^(n-1)) where n will be 7, 5, 3, 1 respectively
I think position of 0 will be tricky as it cant be in 1st place but will be count as a even digit in any other place.
@vijay_chandola said:
Q. ABCD is a quadrilateral. Now AB is extended to P such that AB = BP, BC is extended to Q such that BC = CQ, CD to R such that CD = DR and DA to S such that DA = AS. Find the area of quadrilateral PQRS if area of ABCD is 100.a) 400b) 500c) 600d) 700


100*2+100*2+100=500

@junefever said:
b)500
assuming ABCD as a square, what is the answer?
correct.
@vikky312 said:
@vijay_chandola - ha ha, yaar office mei hu, bore ho raha hai. Aur ye colleges results bhi nahi de rahe
yar bhai kahan join kar rahey ho..FMS toh already conert kar diya hai...aapne..


QUESTION..4
maximum number of points of intersection of 6 circles?
please explain the method..
QUESTION..5
MAXIMUM NUMBER WHEN POINT OF INTERSECTION OF 6 STRAIGHT LINES....

@junefever said:
b)500assuming ABCD as a square, what is the answer?
Same answer, same way 😃

P.S. Aap idhar 😲 SB ka kya hoga...

regards
scrabbler

@scrabbler said:
Same answer, same way P.S. Aap idhar SB ka kya hoga...regardsscrabbler
please, sharminda na karo, April start ho gaya, ab padhai chaalu :P

PS: sorry for spamming
@chillfactor said:
If remainder is 'r' when x is divided by y, then remainder will be 'nr' when nx is divided by nyHere 2012^2012 when divided by 2013 remainder will be 1=> 2012^2013 when divided by 2012*2013 remainder will be 2012Same way for the other partHence remainder will be 2013 + 2012 = 4025
It is already canceled in previous step naa i.e. giving remainder 1

(2012^2013)/2012*2013 => 2012^2012/2013 => rem 1
same is with other case.

Correct me if I am wrong
@vijay_chandola said:
Q. ABCD is a quadrilateral. Now AB is extended to P such that AB = BP, BC is extended to Q such that BC = CQ, CD to R such that CD = DR and DA to S such that DA = AS. Find the area of quadrilateral PQRS if area of ABCD is 100.a) 400b) 500c) 600d) 700 P.S. Bhai ab bi quant? MBA ka jake pado
500 hai kya?
@fireatwill said:
QUESTION..4maximum number of points of intersection of 6 circles? please explain the method..
ans 4: 30 => 2* 6C2 overlapping not allowed iffffffffff.
ans 5
@dushyantagarwal said:
9*10^6 - (nC(7-n+1) * 5^(7-n+1) * 6^(n-1)) where n decreases 7 to 1.

weird solution it is
I guess you need not complicate much .. just take the question as single digit and work out ..
sample space is 0,1,2,3,4,5,6,7,8,9
out of 10 single digit numbers exactly half of them has sum of digit is even . (am taking 0 as single digit number for ease of calculation)
Now coming back to the question total number of seven digit numbers is 9*10^6
so required value is 4.5*10^6
@fireatwill said:
QUESTION..5 MAXIMUM NUMBER WHEN POINT OF INTERSECTION OF 6 STRAIGHT LINES....
6C2=15
@naga25french Perfect Solution sir. Got it

@dushyantagarwal said:
It is already canceled in previous step naa i.e. giving remainder 1(2012^2013)/2012*2013 => 2012^2012/2013 => rem 1 same is with other case.Correct me if I am wrong
2 when divided by 6 remainder will be 2

2*6 when divided by 6*6 OR 12 when divided by 36 remainder will be 12 not 2

As per your method 12/36 = 2/6, so remainder will be 2 (but its incorrect)

While finding out remainders when you cancel something then you have to multiply it back to get the correct remainder

Lets take one more example:- What will be the remainder when 49 is divided by 42

Clearly answer is 7

But as you mentioned 49/42 = 7/6, so remainder 1 which is incorrect
Thats why you need to multiply back by the factor which you cancelled, hence answer will be 1*7 = 7

Solve this question:-
What will be the remainder when 2^96 is divided by 96
@chillfactor said:

Solve this question:-What will be the remainder when 2^96 is divided by 96

64? by simply applying Euler's method

remainder is 64 when 2^96 is divided by 96.

@chillfactor said:
Solve this question:-What will be the remainder when 2^96 is divided by 96
64 @chillfactor sir and @vijay_chandola ____/\____
@junefever said:
64? by simply applying Euler's method
you can't apply eulers here.
@viewpt said:
you can't apply eulers here.
*edited*
Eulers can be applied here

plz share ur aproach
@chillfactor said:

Solve this question:-What will be the remainder when 2^96 is divided by 96
2^96 mod 96
=2^5( 2^91 mod 3)
=2^5(-1 mod 3)
=2^5( 2 mod 3)
=64 mod 96