Official Quant thread for CAT 2013

@aditi88 said:
Ramesh and Suresh are running on a circular track of length 1200m in opposite direction. everytime they meet, they exchange their speed as well as directions. what is the shortest distance btw their 13th and 23rd meeting points, if the ratio of their speeds is 1:5?a) 200mb)400mc) 800md) 1000mPlz quote me
Since ramesh and suresh are exchanging both speed and directions it could be analysed as ramesh is moving in the same direction with a speed of say x and suresh in the opposite direction with a speed of 5x.
When they will meet for the first time ramesh has covered (1200/6x)*x=200m.After covering every 200m ramesh will meet suresh.
So there will be in total 6 points on the circumference where they will be meeting.
Take any one point as the reference point
13th meeting will occur at 2nd point and 23rd will occur on 5th point, so distance between them will be 200+200=400m
@amresh_maverick said:
OA: 52In three distinct regular polygons, it is known that the measure of the internal angle of one regular polygon exceeds the measure of the internal angle of the other two regular polygons by 15째 and 27째 respectively. Furthermore, the sum of the measures of the external angles of all the three regular polygons is 177째. What is the sum of the number of sides of all these three regular polygons ?
OA:
N= 19 = 8 + 6 + 5

Sunil goes to small city in Europe on vacation, where he enjoys walking along the streets in the afternoon. He observes that there are 6 parallel roads running East - West and 5 parallel roads running North-South in the city. In order to observe the landmarks in the city, he takes different routes every time he goes out. He also observed that the distance between every consecutive pair of roads is equal. The number of shortest possible routes that Sunil can take to travel from one corner of the city to the other diagonal end is a) 130 b)124 c) 126 d) 128

Plz share ur approach as well..thanks in advance.

@Swavi91 said:
Sunil goes to small city in Europe on vacation, where he enjoys walking along the streets in the afternoon. He observes that there are 6 parallel roads running East - West and 5 parallel roads running North-South in the city. In order to observe the landmarks in the city, he takes different routes every time he goes out. He also observed that the distance between every consecutive pair of roads is equal. The number of shortest possible routes that Sunil can take to travel from one corner of the city to the other diagonal end is a) 130 b)124 c) 126 d) 128 Plz share ur approach as well..thanks in advance.
it will be 126

simply 9c5

9!/4! 5! = 126

actually see it like to travel to opposite point of a diAGnol no matter he always has to travel 5 verticals and 4 horizontals. as all vertcal paths are same and all horizontal paths are same too arranging them
9!/5! 4! = 126
@amresh_maverick said:
OA : 2Q>Three distinct numbers are randomly selected from the first 20 natural numbers. Find the probability that the selected numbers are in a geometric progression having common ratio greater than 1.
here i am getting 15/20c3
series
1 2 4
1 3 6
1 4 8
1 5 10
1 6 12
1 7 14
1 8 16
1 9 18
1 10 20
2 4 8
2 6 18
3 6 12
4 6 9
4 8 16
5 10 20


how come did u posted answer as 11/ 20c3 , is the common ratio an integer??
@amresh_maverick said:
When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present. Also, by then Sunil €™s son will be six years older than the age of Sunil at present. The sum of the ages of Sunil €™s father and Sunil is 85 years at present. What is the sum of the ages of Sunil €™s son and Sunil at present?
let age of father =x
sunil = y
sunil's son =z
x=5z --- 1)
x+y=85 ---2)
z +x-y =6+y
so z+x = 6+2y ----3)
solving 1) 2) and 3)
z = 11
y = 30
x = 55
so y+z = 41
@amresh_maverick said:
g(P) represents the product of all the digits of P, e.g. g(45) = 4 — 5.What is the value of g(67) + g(68) + g(69) + ..... + g(122) + g(123)?
1281

24*6 + 45*24 +45 + 12= 1281
@amresh_maverick said:
78 identical cubes each with 2 cm edge are joined together to form a cuboid. If the perimeter of the base of the cuboid is 64 cm, then the number of cubes along the height of the cuboid isPS: @ChirpiBird , kaun si movie dekhi aaj ?

2(2a+2b)=64
a + b= 16
also abc = 78
so 13* 3* 2=78

height = 2 cm

@albiesriram said:
inclusion-exclusion:Total pool : 5+3= 8 characters are there..if it starts of with a digit:- 3* 6*5*4*5 =1800 ways( filling the fifth character is given precedence)If it starts of with a alphabet:-Similar will be the case if we create a password that start of with a albhabet and ends in a digit. ->1800 ways. Now, exclude the violating cases, we cant create p/w with 4 digits as we are having only 3 with us . so we will anyway have 2 albhabetss in the p/w Consider the cases we have created pws with 4 albhabets. 6*4*3*2* 5= 720 ways.in total 3600-720 =2880ways?
bhai i am not getting this solution , when i solved this question i got 3600 as my answer
why r u subtracting 720?
a password with 4 letters and 1 number is fairly possible
why r u subtracting that part from the rest??????
@abhishek.2011 said:
bhai i am not getting this solution , when i solved this question i got 3600 as my answerwhy r u subtracting 720?a password with 4 letters and 1 number is fairly possiblewhy r u subtracting that part from the rest??????
Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). Thats y.
@albiesriram said:
Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). Thats y.
oooooo i guess i missed the atleast 2 digit part 😞 thanks 4 making me remember it :)
@amresh_maverick said:
One day u will be awarded Noble prize for Environment (if this is ever instituted) for saving trees (paper) as u solve most of the q's orally ,P is the product of first 30 multiples of 30. N is the total number of factors of P. In how many ways N can be written as the product of two natural numbers such that the HCF of these two natural numbers is 19?
n = 19^2 * 2^x * 3^y *5^z
here let 2 numbers be 19x and 19y
now x and y has to be coprime
so 3c0+3c1 =4
my take 4
@milestogo3 said:
293768 431845725613 = INLETS
can u expain in detail.how u did it ?
A Man standing ona boat south of a light house observes his shadow to be 24 m long as measured at the sea level. on sailing 300 m eastwards , he finds his shadow as 30 m long, measured in a similar manner. the ht of the man is 6 m abve sea leavel. what is the ht of light house?
Puys dosto.....answer figure ka diagram batao

the number of integral values of x,that satisfy the inequation |x-3|+|x-4|

ans:8
@ani6 said:
the number of integral values of x,that satisfy the inequation |x-3|+|x-4|ans:8
Case 1: x
-x+3-x+4
x>=0
Values of x are 0,1,2,3

Case 2: x>3 & x
x-3-x+4
x is a Null set

Case 3: x>=4
x-3+x-4
x
Values of x are 4,5,6,7

Total values 8 (0,1,2,3,4,5,6,7)



@trip said:
A Man standing ona boat south of a light house observes his shadow to be 24 m long as measured at the sea level. on sailing 300 m eastwards , he finds his shadow as 30 m long, measured in a similar manner. the ht of the man is 6 m abve sea leavel. what is the ht of light house?Puys dosto.....answer figure ka diagram batao
Is Height of Light house 100 m ? If yes then I will attach the solution
@ani6 said:
the number of integral values of x,that satisfy the inequation |x-3|+|x-4|ans:8
x is a set of integers from 0 to 7
so 8 values

critical points are 3 and 4
before three equation is increasing so is after four
for lhs it gives 7 on 0 for rhs it gives 7 on 7
so 0 to 7 all values
@trip said:
A Man standing ona boat south of a light house observes his shadow to be 24 m long as measured at the sea level. on sailing 300 m eastwards , he finds his shadow as 30 m long, measured in a similar manner. the ht of the man is 6 m abve sea leavel. what is the ht of light house?Puys dosto.....answer figure ka diagram

my take 100 m
h/6 = y/24
y = 4h

similarly h/6 = x/30
x =5h
now y^2 + 300^2 =x^2
300 = 3h
h=100m

@ani6 said:
the number of integral values of x,that satisfy the inequation |x-3|+|x-4|ans:8
u can either do it the conventional way

or see it like this...

max value this expression can take is 7, so we see that when x = 7 then |7-3|+|7-4| = 4+3 = 7
so max(x) = 7
now find the min value...
put a negative value, |-1-3|+|-1-4| = 4+5 = 9 (does not satisfy)
put 0, |-3|+|-4| = 3+4 = 7

hence, 0 to 7 -> 8 values satisfy this expression