Official Quant thread for CAT 2013

MBA CAT 2024
29346
@Tusharrr said:
Two points are chosen uniformly at random on the unit circle and joined to make a chord C1. This process is repeated 3 more times to get chords C2,C3,C4. The probability that no pair of chords intersect can be expressed as ab where a and b are coprime positive integers. What is the value of a+b?
Yaar. Iska solution batana agar hai to
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@falcao said:
so the solution set for p=R-{4,-4,0}
OA is D

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@heylady said:
1??
yes buddy.. silly typing mistake..
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@Marchex said:
There are five cities in a state and each of them is to be connected to exactly two other cities using telephone lines. In how many ways can this be done?(a) 12 (b) 24 (c) 36 (d) 9
First take 1 city and connect it to 2 others

number of ways of choosing 2 cities from the other 4 = 4C2 = 6

Let's say 5 has been connected to 2 and 4. cities 1 and 3 are not connected to anyone.

city 2 and 4 need one more connection. city 2 has 2 choices - city 1 or city 3. The same holds for city 4.

If 2 is connected to 3 , 4 will have to be connected to 1 and vice - versa.

If 2 is connected to 1 , 4 will have one choice.

so after selecting 2 out of 4, only 2 choices are possible, 2----->1 or 2---->3 and in each of them one 1 way is possible.

so total ways = 6x2 = 12

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@albiesriram said:
OA is D
if the OA is 0 only i.e if p=0,then the equation will have 2 soltuions and not more than 2
see,
for x>=3/2
4x=6
x=3/2
for x-3/2
2x-3+3-2x=6
so 6=6 l
now x-4x=6
x=-3/2,
so the number of solutions are 2 and not 3
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@psk.becks said:
draw the curve of the given function....value will be 6 for x( -3/2 , 3/2)after that a slope of -4 and 4 respectivelynow px+ 6= given fn...we require more than 2 solutions...so the line will only be y = 6 giving more than 2 solutions for any other slope than zero the line px + 6 will intersect in exactly 2 points.
what's wrong with my solution?
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@falcao said:
if the OA is 0 only i.e if p=0,then the equation will have 2 soltuions and not more than 2see,for x>=3/24x=6x=3/2for x-3/22x-3+3-2x=6so 6=6 lnow x-4x=6x=-3/2,so the number of solutions are 2 and not 3
draw the curve of the given function....
value will be 6 for x( -3/2 , 3/2)
after that a slope of -4 and 4 respectively
now px+ 6= given fn...
we require more than 2 solutions...
so the line will only be y = 6 giving more than 2 solutions
you are finding the solutons of the equations where the value of p will have exactly two solutions
for p>4 and p

If p lies between -4 and 4 (except 0 ) there are 2 solutions

for 0 - infiinite solutions
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@Marchex said:
Five equi-spaced points labeled 1, 2, 3, 4, 5 are marked in the same order in clockwise direction on the circumference of a circle. An ant is moving on the circumference of this circle in the clockwise direction. If the ant is at an odd numbered point it shifts one point ahead and if it is at an even numbered point it shifts two points ahead. If the ant starts from point 5, then where would it be after 2010 such movements?(a) 1 (b) 3 (c) 5 (d) None of these
5----->1---->2---->4---->1 .....

1-2-4 will keep repeating. After the 1st movement, 5-->1 , we have 2009 more movements , in which 1-2-4, which will repeat. so 2009 mod 3 = 2. so it must be at point 4.


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@Marchex said:
There are five cities in a state and each of them is to be connected to exactly two other cities using telephone lines. In how many ways can this be done?(a) 12 (b) 24 (c) 36 (d) 9
is it 12
first one can choose from other 4 cities in 4c2 ways
now other 2 cities which are connected with first 1,have 2c1 choices
and all other left has only 1 choice or else they will enter into deadlock and all 5 cities wont be completed
so 4c2*2c1=12
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@psk.becks said:
draw the curve of the given function....value will be 6 for x( -3/2 , 3/2)after that a slope of -4 and 4 respectivelynow px+ 6= given fn...we require more than 2 solutions...so the line will only be y = 6 giving more than 2 solutionsyou are finding the solutons of the equations where the value of p will have exactly two solutionsfor p>4 and pIf p lies between -4 and 4 (except 0 ) there are 2 solutions for 0 - infiinite solutions
haan theek hai dekh liya tha maine.i was looking for 2 solutions while advocating more than 2 myself
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@Marchex said:
is it 4/5??
did it without pen i guess it is more likely a logical question
as options are 0.77 0.85 1.33 0.8
now 3/4 * 17/16 this is the main numbers that are gonna make difference this amounts to 0.79 , after this its 257/256 which is 1.0003,.... till infinity it goes to 1, so it will be of form 0.79*1.0003*1.000001*1*1..... so u can say that its never gonna go above 0.79 , the number closest to 0.79 is option d so 4/5
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@Marchex said:
Rs. 4,500 was distributed among Aman, Baman and Chaman. From the amount that they received Aman, Baman and Chaman spent Rs.110, Rs.120 and Rs.140 respectively. The amounts then left with Aman and Baman were in the ratio 3 : 4 and with Baman and Chaman were in the ratio 5 : 6. What amount (in Rs.) did Baman receive?(a) 1520 (b) 1400 (c) 1600 (d) 1420
a+b+c=4500
4a-3b=80
6b-5c=20
a=1160
b=1520
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29359
@albiesriram said:
1)9
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@albiesriram said:
5)n/100-n

let x=100-n
100-x/x=100/x -1

factors of 100 are 2^2*5^2=9
9*2(both positive and negative can be taken)
18
29361
@Buck.up said:
5 letter word to be constructed from MATHEMATICS,in how many words will E occur.
M A T H (E) I C S
M A T
let their be a word e in the 5 letter word
now case1 --- all are different
7c4*5!=35*120=4200
case 2 ---- 2 same 2 different
3c1*6c2*5!/2! = 2700
case 3 ----- 2 pairs same
3c2*5!/2!2! =90
4200+2700+90 = 6990
my take
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@albiesriram said:
6)x-y=1/x -1/y =(y-x)/xy
x-y - (y-x)/xy =0
(x-y)[1 +1/xy]=0
since x!=y

1/xy=-1
xy=-1??
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@Subhashdec2 said:

18

. But why Cant n=0 be also taken ?
@Subhashdec2 said:
1)9
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@albiesriram said:
. But why Cant n=0 be also taken ?
it can be taken bhai
what cant be taken is n=100...

should have mentioned it dere...
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@albiesriram said:
for first 9
for second 100=2^2*5^2=3*3=9 so 9*2=18 values