Official Quant thread for CAT 2013

Here comes the tournament question. I would like to invite most of the gods here and guys enlighten me with ur awesome approaches :sneaky: @scrabbler @Dazed-Confused @rubikmath @Akrosh007 @vipin011 @Ankurk14 @nikhil.kulkarni @placiddisciple @plant.waters @ahsish9virgo @jasneetdua @Shubh.i and all the puys :thumbup: I ll be posting the question in 3 parts, do find them n plz crack them :banghead:

Sameer and Sumer started running from the same point in opposite directions on a circular track of length 120 m. Their speeds are 20 m/s and 40 m/s respectively. After every second, Sameer increases his speed by 2 m/s whereas Sumer decreases his speed by 2 m/s. How many times would they have met on the track by the time Sumer comes to rest?


a 2

b 5

c 10

d None of these


part2 tournament que

and part 3 mg

What is the conjugate of the surd √5 - 2 ? With reason ? And what is the rationailizing factor of 6 + 3√5?


Whether there is any difference bw conjugate and rationailizing factor?

A, B, C can do a certain work in 20, 30, 40 days respectively. If on each day two man do the work, and the amount of total work done by them is same, find in how many days work would be finished ?


between two junction stations X and Y there are 12 intermediate stations.the number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is.
a) 70
b)126
c)210
d) none of these


Given that 2^x^y + x^2^y = 3. What is the total number of integral solutions for the given equation?

a. 0

b. 2

c. 1

d. 3

e. More than 3

10. Consider a set P = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. We define another set Q,such that it contains no more than one out of any three consecutive natural numbers.How many subsets Q of P including the empty set exist?

(1) 114 (2) 117(3) 129 (4) 136



post the approach plz 😁

A number is such that its square is exactly divisible by its factorial. How many such numbers are there?

1. 1

2. 2

3. 3

4. No such number exists

Set A has m elements, set B has n elements.

m=7
n=5

A) What are the total number of functions from A to B

B) what are the total number of injective functions from A to B
C) what are the total number of surjective functions from A to B
D) what are the total number of bijective functions from A to B

Detailed approach welcome 😃


@Shubh.i @anandmadhav @jasneetdua @sagarcat @happy3475 @sanu8080 @ralins @vipin011
@jaffa @Dante_ftw1

Two persons P & Q run in same direction on a circular track. Their speeds are in the ratio 9:1. How many times will they both be diagonally opposite each other by the time the slower one completes one round?
a) 7 b) 8 c) 9 d) Cannot be determined

(P.S. I know the answer and the formula for it, but i'm not able to grasp how we arrive at that formula. Any explanation would be welcome. 😃 )

1)Find the value of q given that [log(base 3) p]^2 = log(base 3) p^2 and log(base 3)(p+q) = log(base 3) p + log(base 3) q?

Please post with the solution.

All Possible pairs are formed from the divisors of 21600.How many pairs have hcf of 45?

O.A is 49 😁

splat

if a^2 - b^2 = 105, how many pairs of (a,b) are possible, approach pls puyslookround

Any quick method to check any no, whether it is prime or not?
any 2,3,4 digit no.😁😁

Any link to finding out 'number of bijective/surjective and all such blah..' functions possible from Set A to Set B?

Ignore.

3x + y + z