Official Quant thread for CAT 2013

solve and explain

solve

Two containers A and B, with 30 litres and 50 litres capacity respectively, are filled to the brim. The concentration of milk in container B is 40% and that in container A is less than 20%. If the contents of the two containers are emptied into a large container, the concentration of milk in the final solution cannot be

1 less than 32.5%

2 greater than 32.5 %

3 less than 25.7 percent

4 none of these


solve

If S1 = {1, 2, 3, 4, ... , 23} and S2 = {207, 208, 209, 210, 211, ... , 691}, how many elements of the set S2 are divisible by at least four distinct prime numbers that are elements of the set S1?

The degree of each term of a polynomial P(x) is odd. When P(x) is divided by (x – 3), the remainder is 6. What is the remainder when P(x) is divided by (x^2 – 9)?

a) 2x

b) -36

c) 0

d) Cannot be determined


Puys share your approach please jugad if any

Find remainder when

189189189189....189(1000 times ) is divided by 13.

During one of the shows in 'Jemini' circus, four hats are picked randomly from a trunk that contains 3 red hats, 5 black hats, 4 blue hats and 6 yellow hats, and are given to four dwarfs such that each dwarf gets exactly one hat. All the dwarfs throw their hats in the air simultaneously. Then each dwarf comes under exactly one of the hats, not necessarily the one thrown by him, such that the hat fits snugly on his head. What is the probability that at least two dwarfs are wearing the hats of same colour now and no dwarf has the same hat on his head that he had thrown in the air?

  • 45/136
  • none of these
  • 83/272
  • 91/136

0 voters

A watch gains uniformly is 5 min slow at 8:00 am on sunday and is 5 min 48 sec fast at 8:00 pm on the following sunday. Whwn did it show the correct time?

  • 7:20 am Wednesday
  • 7:20 am Thu
  • 7:20 pm Wed
  • 7:20 pm Thursday

0 voters



If x is an integer, what is the value of x?

a 2

b 1

c Either (a) or (b)

d Cannot be determined


In a class of 200 students who play cricket and hockey, the number of students who play neither of the games is 16 less than those who play both. The number of students who do not play cricket is 24 more than those who do not play hockey. Find the number of students who play hockey

a) 120

b) 80

c) 104

d) 96
Approach?

solve and explain :banghead:

Ques #52 solution??

Abhinav starts in a car from Hyderabad to Chennai at a constant speed planning to reach Chennai at a scheduled time. After some time he realizes that he had miscalculated and with this speed he will cover only 5/7th of the distance in the planned time. And will take 4 hours more to teach China. HE then triples the speed immediately and reached Chennai on the planned time. Find the time after which he has planned to change the speed.


Can it be solved with this method, or comparing the times is mandatory ??

Let original time be t + 4 hours (without increased speed)
where t = planned time.

Nw when speed is 3 times, time reduces 3times, ie. 1-2/3
if 2/3 speed is 4 then actual time is = 6 hours.
so t = 2 hours...

@Akrosh007 @Dexian @sagarcat @jasneetdua


In a company in Delhi, there are three Tamilians and three others who know Hindi. Each of them has a message that he wants to share with all the others on the telephone. Only one Tamilian knows Hindi and none of the others who know Hindi knows Tamil. Find the minimum number of phone calls which would be required for the purpose above.

options: a) 10 b) 8 c)11 d) 9.

kindly explain the approach for this ques.

@ankurkhanna14 bhai refer to ques 87 & 88...wo rectangle wale ques ka solution hai...from CAT '99

Suppose 20 books are aligned in a bookcase. How many ways can we choose 3 books so that no adjacent books are chosen?

  • 18C3
  • 19C3

0 voters

Question: There are 13 equidistant bus stops on a straight road. A bus running at 60 km/hr is some distance away from the 1st stop from where it will move towards the 13th stop. Two cars start running from the 6th stop in opposite directions with the same speed. If the bus meets one of the cars at the 1st stop and the other at the 13th stop, then find the speed of the cars. (A) 10 km/hr(B) 20 km/hr(C) 30 km/hr(D) Cannot be determined

Shortcut to find last two digits of 12 raised to any power ??

How many zeros at the end of 27!^27!