Official Quant thread for CAT 2013

If f(x) is a quadratic polynomial such that f(5)=35 , and f(-5) =15 , and f(p)=f(q) =0 , then find p+q

A point P (a, b) lies on the line 3x = 2y, where a and b are integers. What is the value of a2 + b2 + ab

if the distance between P and another point Q (7, 5) is minimum possible?

(a) 0 (b) 171 (c) 76 (d) 19

Please refer me some good material for understanding probability concepts.....I kinda suck in it:(

Consider families with 4 children. What is the probability of having(i) two boys and two girls

Remainder when 402^12 is divided by 1000

A certain number of trucks required to transport 60 tons of steel from TISCO to Jamshedpur
However it is found that since each truck could take 0.5 tons of cargo less. Another 4 trucks were needed. How many trucks initially planned to use ?

10

15
20
25


==========================
n = no of truck
t = capacity of each truck to carry
n*( t + 0.5) = 60 ---- (1)
(n+4) * t = 60 ---- (2)

solving the equation

n = 8t
putting in equation

8t^2 + 4t -15 = 0
t = 5, -6

Thus
n = 40 : but OA = 20 :banghead:



In a parallelogram ABCD, let M be the midpoint of the side AB and N the midpoint of BC. Let P be the intersection point of the lines MC and ND

Find the ratio of area of ▲s APB : BPC : CPD : DPA. (a) 3:1:2:4 (b) 3:2:1:4 (c) 2:1:3:4 (d) 1:2:3:4


OA-a

Find the smallest number that has exactly 18 factors.

288

768

180

None of the above


Please explain in detail😐

First 100 natural numbers in the decimal system are converted to base 6 and their product is found. Find the number of consecutive zeros at the end of the product as counted in the base 6 system.


a 124

b 130

c 140

d 120

e 136

x + y + z = 20 . Find number of integral values of xyz such that x >= y >=z

How to apply allegation in these questions !????
Solvable through another method but since the question was posted in allegation section Allegation must work.

Q1. A mixture of 125 gallon of wine and water contains 20% water, how much water added to the mixture in order to increase the percentage of water to 25% of the new mixture

OA = 8.33 Gallon

Q1. A bartender stole the champagne from a bottle that contained 50% spirit and replaced it with 20% spirit solution. The bottle then contained 25% spirit solution. How much did he steal ?

OA - 83.33%

Q2. A man possessing Rs 6800, Lent a part of it at 10% simple interest and remaining at 7.5% SI. His total income after 3.5 years 1904. Finds the sum lent at a 10 % rate ?


OA - 1360


@anandmadhav @trial.verison @Dexian

please post the approach !

please post the approach !

Two Astronauts, Vaibhav and Kanishk land on a spherical shaped meteor of diameter 7 km, which is rotating about its own central axis at 2.5 km/sec. Equator is the maximum circumference possible on the spherical shaped meteor. Vaibhav starts running along the equator at 20% of the speed of the meteor in a direction opposite to the direction of the rotation of meteor. Kanishk standing at the point from Vaibhav started, records the time taken by Vaibhav to reach the starting point once again. Calculate the time recorded by Kanishk.

a 44 sec

b 12 sec

c 48 sec

d 11 sec

e 22 sec

Post the method please, it continues to elude me :(


A train moves at a constant speed of 120km/h for one kilometer and at 40km/h for next one kilometer. What is the average speed of the train?

  • 60kmph
  • None of these
  • 80kmph
  • 50kmph
  • 48kmph

0 voters

f(x) = [ 3^ (1+ log x) ] / [ x^log 3] , find f (1994) is ?

In how many ways a 7 digit number can be formed such that at least one digit is repeated

Find the number of numbers till 50000(less than 50k) whose sum of digits is 13.

guys are u aware f the new snap selection process?? wont der be any gd/pi ???

In the library ,there are 8 books bys stephen covey and 1 book by vinay sing in shelf A.At the same time,there are 5 books by stephen covey in shelf B.one book is moved from shelf A to shelf B.A student picks up a book from shelf B.Find the probability that book by Vinay Singh
is in shelf B
a)3/54
b)4/54
c)5/54
d)6/57
steps please