Official Quant thread for CAT 2013

@abhishek.2011 said:
no actuually u can see that difference between 36-8 and 64-36 is same as graph of this function is nothing but between 8 and 64 it must be symetrical between the two.had the difference between the roots not be same nothing could be said but here it must be symetrical
Symmetrical between 8 and 64 yes but not between 8 and 36....

It is (x-8)(x-36)(x-36)(x-64) ka root...

Check this link....also look at my solution on page 1477...reply 29525

http://www.wolframalpha.com/input/?i=max{root+[+%28x^2%E2%88%9244x%2B288%29+%C3%97+%28%E2%88%92x2%2B100x%E2%88%922304%29+]}

regards
scrabbler

@Buck.up @Logrhythm said:hahahah....i remember i did that in an interview when i asked "what is your fav subject" i replied "math" and uske baad it was a colossal fiasco.....pata nahi usko laga meine math bola toh mein Aryabhatt hunok, no spammingq) what is the highest power of 12 that divides (5^36 - 1)1,2,3,4
2?
can u plz explain??
@abhishek.2011 said:
graph has roots at 8,36,64domain is 8,64maximum occurs at x=22 and x=50value = _/(14^3*42) = 196_/3
bhai there will be no maxima at x = 22. (Even if ur considering individual quadratic polynomial.)


@simplydevesh said:
@Buck.up@Logrhythm said:hahahah....i remember i did that in an interview when i asked "what is your fav subject" i replied "math" and uske baad it was a colossal fiasco.....pata nahi usko laga meine math bola toh mein Aryabhatt hunok, no spammingq) what is the highest power of 12 that divides (5^36 - 1)1,2,3,42?can u plz explain??
is this correct ?
12 is a factor of (5^36-1)
so, (5^36-1)=12^k
5^36=12^k+1
last digit of 5^36=5
so last digit of 12^k has to be 4 which is possible with k=2 (from options)


@simplydevesh said:
@Buck.up@Logrhythm said:hahahah....i remember i did that in an interview when i asked "what is your fav subject" i replied "math" and uske baad it was a colossal fiasco.....pata nahi usko laga meine math bola toh mein Aryabhatt hunok, no spammingq) what is the highest power of 12 that divides (5^36 - 1)1,2,3,42?can u plz explain??
5^36-1
625^9-1
(625^3-1)(625^6+625^3+1)
(625-1)(625^2+625+1)(625^6+625^3+1)
624(625^2+625+1)(625^6+625^3+1)
624 is divisible by 12 and leave a quo is 52
now if we again devide 52 by 12 rem will be 4
rem for (625^2+625+1) by 12 is 3
(625^6+625^3+1) by 12 is 3 also
so now 4*3*3
again divisible by 12
so max power 12^2
@Buck.up said:
is this correct ?12 is a factor of (5^36-1)so, (5^36-1)=12^k5^36=12^k+1last digit of 5^36=5so last digit of 12^k has to be 4 which is possible with k=2 (from options)
great
@Buck.up said:
is this correct ?12 is a factor of (5^36-1)so, (5^36-1)=12^k5^36=12^k+1last digit of 5^36=5so last digit of 12^k has to be 4 which is possible with k=2 (from options)
but only one ques how 5^36-1 =12^k ?????
it must be 12^k* x ( x can be any digit )
@Buck.up got it.....
@chillfactor @Tusharrr said:Suppose there are 10 coins laid out in front of you. All of the coins are fair (i.e. have an equal chance of heads or tails) except one, which flips to heads every time. You draw one coin at random and flip it 5 times. If each of the 5 flips results in heads, then the probability that this coin is fair can be written as a/b, where a and bare coprime positive integers. What is the value of a+b?
probability of getting 5 heads = (1/10)(9*1/32 + 1) = 41/320
Probability that a fair coin is selected and we get 5 heads = (1/10){9*(1/32)} = 9/320
required prob = (9/320)/(41/320) = 9/41


cud u plz explain it???
@Buck.up said:
is this correct ?12 is a factor of (5^36-1)so, (5^36-1)=12^k5^36=12^k+1last digit of 5^36=5so last digit of 12^k has to be 4 which is possible with k=2 (from options)
awesome, well played with the options....should have thrown in a 0 😛

meine saare bracket ko open kar kar kara, but your method dekh kar mazza aa gaya
@AsihekAdhvaryu said:
but only one ques how 5^36-1 =12^k ????? it must be 12^k* x ( x can be any digit )
Happy birthday Bhai. Today is your bday na.
I know this is not a reliable. Thats why I was nt sure of my ans. but it seems (5^36-1) is a factor of 12 only
@AsihekAdhvaryu said:
but only one ques how 5^36-1 =12^k ????? it must be 12^k* x ( x can be any digit )
i gave the question, what is the highest power of 12 that divides 5^36 - 1
and the options i gave were 1,2,3,4 (made these up actually)
so it was implied that at least 12^1 definitely divides 5^36 - 1
he exploited that, and exploited it well :D

@Buck.up said:
Happy birthday Bhai. Today is your bday na.I know this is not a reliable. Thats why I was nt sure of my ans. but it seems (5^36-1) is a factor of 12 only
Ty and nice attempted Kudos
@Tusharrr said:
Determine the number of subsets of A={1,2, €Ś,10} whose sum of elements are greater than or equal to 28.
is it 512?
max sum 55 total sets 1024
sets for sum 28 1024/2=512
@Buck.up said:
In a locality there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are adjacent to each other.
a+b+c+d=5
solutions 8c3 = 56
@abhishek.2011 said:
is it 512?max sum 55 total sets 1024sets for sum 28 1024/2=512
Maine bhi similar logic lagaya and got 512...but he has not posted any OAs...bus question daalke chod raha hai...:(

regards
scrabbler

@simplydevesh said:
@Buck.up@Logrhythm said:hahahah....i remember i did that in an interview when i asked "what is your fav subject" i replied "math" and uske baad it was a colossal fiasco.....pata nahi usko laga meine math bola toh mein Aryabhatt hunok, no spammingq) what is the highest power of 12 that divides (5^36 - 1)1,2,3,42?can u plz explain??
5^36 - 1 = 25^18 - 1

= (24 + 1) ^18 - 1

C0 + C1(24) + C2(24)^2 + .......C18(24)^18 - 1

= C1(24) + C2(24)^2 + .......C18(24)^18

= 144[ 6 + C2 + C3(24) + ......]

so highest power of 12 will be 2


@Buck.up said:
There are 25 points on a plane of which 7 are collinear , how many quadrilaterals can be formed from these points?a)5206b)2603c)13015d)none of these
18c4 + 7c1*18c3 + 7c2*18c2

Plz solve :

@Logrhythm said:
hahahah....i remember i did that in an interview when i asked "what is your fav subject" i replied "math" and uske baad it was a colossal fiasco.....pata nahi usko laga meine math bola toh mein Aryabhatt hun ok, no spammingq) what is the highest power of 12 that divides (5^36 - 1) 1,2,3,4
must be 2
5^36mod12=1
5^36 mod 144 =1
5^36 mod 12^3 =/1
so 12^2