Official Quant thread for CAT 2013

How many pairs of integers (x, y) exist such

that x^2+ 4y^2
1. 95
2. 90
3. 159
4. 180

Solution A contains water and milk in the ratio 7:13. Solution B contains milk and water in the ratio 3:2. These two solutions are mixed to get a solution of milk and water containing 37% water. What percentage of final mixture is the solution B?

60%

70%

30%

40%

My watch, which gains 2 min uniformly, slows down at noon on Saturday. It is 4 minutes and 48 seconds fast at 3:00 pm next Monday. When did it show the correct time?

1. Midnight Monday

2. 1 : 00 a.m Monday

3. Midnight Tuesday

4. 1:00 a.m Tuesday

5. Afternoon Monday

At what time between 4 : 15 a.m and 5.05 a.m will the angle between the hour-hand and the minute-hand of a clock be the same as the angle between the hands at 8 : 45 p.m?

1. 23 2/11 minutes past 4 o'clock

2. 22 2/11 minutes past 4 o'clock

3. 13 2/11 minutes past 4 o'clock

4. 22 2/11 minutes past 4 o'clock

5. 23 2/13 minutes past 4 o'clock

In the year 1648, if the February month has 5 Sundays, what is the day on 13th February 1750?

1. Sunday

2. Friday

3. Saturday

4. Monday

5. Friday

If 09/12/2001 happens to be a Sunday, then 09/12/1971 would have been a

1. Wednesday

2. Tuesday

3. Saturday

4. Thursday

5. Monday

Hercules goes to fight Hydra, the monster that currently has 2000 heads. However, every time Hercules kills some of Hydra's heads the remaining heads double in number. So, if Hercules kills one head right now, the number of heads will become 1999 x 2 = 3998. In order to fight the Hydra, Hercules decides to double the number of arrows he has got each time he kills Hydra's heads. Presently, he has only one arrow and a single arrow can kill only one head of Hydra. If Hercules starts attacking the Hydra once every minute and if every time he attacks he uses all the arrows that he has, after how many minutes will he be able to finish all of Hydra's heads?

Let f(x) be a polynomial in x. f(x)|x-2 = 8 & f(x)|x+2 = 4. what is f(x)|x^2-4 ?

1) X+32
2) 0
3) X+6

4) X-4

Also please share the approach !

F(x) = x^2340 + x^2335 + x^2330 + ..... + x^5 + 1

F(x) mod (x^4 + x^3 + x^2 + x + 1) = ?


Ashish, Bimal and Chatur are three friends who come to visit an amusement park. Each of the three is accompanied by his father and his grandfather to the park. In how many ways can these nine people stand in the queue at the entry gate if no father wants to stand ahead of his son in the queue?

AlwaysBeFit is a famous sports' club in the city. All the members of this club play at least of one of the following four sports – Football, Hockey, Badminton and Table Tennis. 70 members play Football and the number of players playing only Football, only Hockey, only Badminton and only Table Tennis are 13, 4, 11 and 8 respectively. Number of players playing Football, Hockey and Badminton is 10. Number of players playing Hockey, Badminton and Table Tennis is 16. Number of players playing Football, Hockey and Table Tennis is 14 and number of players playing Football, Badminton and Table Tennis is 17. Number of players playing Football and Hockey is 30 and number of players playing Badminton and Table Tennis is 35. Number of players playing exactly two games are all equal except for those who play only Football and Hockey and only Badminton and Table-tennis.


What can be the maximum number of members who play all the four games?

9

10

8

6


If a, b, c and d are positive real numbers such that a + 2b + 3c + 4d = 48, then the maximum value of a^2 b^3 c^4 d^7 is ???

Plz post approach.....

Puys!Approach!

How many integer pairs (x, y) are there such that x^3 + 3x^2 – 4x = 81y^3 – 9y^2 + 6y – 1?

a) 0

b) 1

c) 2

d) 3

When do we use the AM>=GM concept?

How many points with integer co-ordinates lie inside the triangle whose vertices are (0, 2), (–5, –3) and (5, –3)? ye kese karenge approach???


y = |x – 3|– 2 and y = 3 – |x – 2| Area enclosed.. Any aproach without graph ?


a simple qstion ..3|x-1|+x^2-7>0 ...the ans is x>-1 and x

If 3 positive real numbers x,y,z satisfy
y-x=z-y
and xyz=4
what is the minimum value possible of y.?

Given set A collection of numbers divisible by 3 in the range of [100,800] and set B collection of numbers in the rage of [100,400]. set C contains all the subsets of a and b such that a+b is even. How many elements are present in set C? OA not available