Official Quant thread for CAT 2013

MBA CAT 2024
16926
@ravi.theja said:
12,42,72,102,132,162,192...7 numbers??n/2 and n/3 case ==> multiple of 6 Now, 2n+1 has to be multiple of 5 ; at n=12 it satisfies the condition .

Now satisying both the conditions of 5 and 6..!! we obtain it at a diff of 30.

bhai 7 nahi hoga...2 hoga..
12 to 132 wale number (2n+1)/5 karne pe prime result de rae hai..which we need to take out..hence 2...
16927
@blowcat13 said:
what annual payment will discharge a debt of Rs6450 due in 4 years at 5% simple interest??a)1400rs b)1500 c)1550 d)1600
4P + P( 3*5/100 + 2*5/100 + 1*5/100 ) = 6450

4P + P( 0.15+0.10 +0.05) =6450

4.3P = 6450 ==> P = 1500
16928
@TootaHuaDil said:
How many 4 digit positive integral numbers are there in base 7 if you are counting the numbers in the same base system?
min=1000(343 in base 10)
max=6666(2400 in base 10)
So 2400-343+1=2058 numbers are there
16929
@bs0409 said:
min=1000(343 in base 10)
max=7777(2800 in base 10)
So 2800-343+1=2458 numbers are there
bhai max 7777 hoga ya fir 6666 ??
i mean base 7 mein 7777 toh exist nahi karta...fir?? or am i missing something?
16930
@TootaHuaDil said:
Bill & Clinton take the square of a certain no. in decimal system and express it in base 5 and 6 respectively. Then Bush comes and he takes the two representations and assuming that the expressions are in base 10 adds the nos. Which of the following cannot be the value of the unit's digit of the sum obtained?a) 0 b) 2 c) 8 d) 6 e) 3
@TootaHuaDil said:
If binary nos from 100 to 1000000 are written find the no of 1s in it.
@bs0409 bhai solve dis
16931

question daalo yaar bs bhai ravi bhai etc etc...

bohot boring ho gaya yahan pe :(

16932
@TootaHuaDil said:
Bill & Clinton take the square of a certain no. in decimal system and express it in base 5 and 6 respectively. Then Bush comes and he takes the two representations and assuming that the expressions are in base 10 adds the nos. Which of the following cannot be the value of the unit's digit of the sum obtained?

a) 0 b) 2 c) 8 d) 6 e) 3
In base 5, squares end in 1,4 and 0 while in base 6 squares end in 1,4,3 and 0
So 6 cannot be the product of addition of 2 squares...
16933
@Logrhythm said:
question daalo yaar bs bhai ravi bhai etc etc...bohot boring ho gaya yahan pe
ya...its so boring 😃 y no one posting questions..!!

consider a circle with unit radius. There are seven adjacent sectors, S1, S2, S3.......,S7, in the circle such that their total area is 1/16 of the are of the circle. Further, the area of jth sector is twic that of the (j-1)th sector, for j=2.....,7. What is the angle subtended by the arc of S1 at the centre of the circle (in radians).
16934
@ravi.theja said:
ya...its so boring y no one posting questions..!!

consider a circle with unit radius. There are seven adjacent sectors, S1, S2, S3.......,S7, in the circle such that their total area is 1/16 of the are of the circle. Further, the area of jth sector is twic that of the (j-1)th sector, for j=2.....,7. What is the angle subtended by the arc of S1 at the centre of the circle (in radians).

s1 + 2s1 + 2^2s1 + ... + 2^6s1 = pi/16
(2^7 -1)s1 = pi/16
127s1 = pi/16
s1 = pi/(16*127)...
16935
A circle is inscribed inside a square. In the gap between the circle and the square (at the corner) a rectangle measuring 20 X 10 cm is drawn such that the corner A of the rectangle is also a point on the circumference of the circle. what is the radius of the circle in cm?
16936

I have a doubt in the following question..


!1) Bhargavi and Shruti are twin sisters who play a game of dice. Bhargavi has a pair of distinguishable dice whereas Shruti has a pair of indistinguishable dice. Let P1 be the probability that the sum of the numbers on the dice rolled by Bhargavi is n and let P2 be the probability that the sum of the numbers on the dice rolled by Shruti is n. If 5P2b) P1

This is the explanation by one of the puys

Distinguishable Dice is like you have one dice say Yellow in color and other on Red in color. So, here you can distinguish between them when you throw them. Indistinguishable Dice is like both the dice are Yellow in color so when you throw them, you cannot distinguish between them. For Example: Suppose one shows 6 and the other shows 5, and in another throw one showed 4 and other 1. So, here you cannot tell which one previously showed 6 or 5 as the colors are same.

Now, moving to the Question:

For Indistinguishable Dice: Let n = 6, Pairs possible = (1,5) (2,4) (3,3) (4,2) and (5,1) as they are different in color. Each pair can occur once out of the total 6*6 = 36 ka Sample Space. => Probability = 5/36.

For Distinguishable Dice: Again Let n = 6, Pairs possible = (1,5) (2,4) and (3,3) only as you cannot distinguish between 1,5 and 5,1 OR 2,4 and 4,2. BUT, the catch here is that the set 1,5 will actually occur twice. See, suppose you number on Yellow Dice as 1 and other as 2, Once, first will show 1 and second 5 and then the vice versa of this. But here, as we cannot distinguish so cases will be 3 but the case 1,5 and 2,4 will appear twice but won't be distinguishable. => We will have the probability of occurance of 1,5 and 2,4 twice as compared to 3,3 => 2+2+1/36 = 5/36. Hence, the Probabilities will be the same for both the cases...!!!

In the distinguishable case: wont be there two cases for (3,3) becoz of two cases in which this can occur:

1. RY
2. YR

so total cases would den become 6 nd probability will change

P.S. I might be interpreting the distinguishable case totally wrong.. so plz kindly explain

16937
@ravi.theja said:
A circle is inscribed inside a square. In the gap between the circle and the square (at the corner) a rectangle measuring 20 X 10 cm is drawn such that the corner A of the rectangle is also a point on the circumference of the circle. what is the radius of the circle in cm?
(r-10)^2 + (r-20)^2 = r^2
r = 10,50
hence, 50...
16938
A tree of height 36 m is on edge of the road, because of the wind a part of tree fall and touches the other side of the road..the road is 12 m wide then what will be the height of the broken part?
16939
@ravi.theja said:
ya...its so boring y no one posting questions..!!consider a circle with unit radius. There are seven adjacent sectors, S1, S2, S3.......,S7, in the circle such that their total area is 1/16 of the are of the circle. Further, the area of jth sector is twic that of the (j-1)th sector, for j=2.....,7. What is the angle subtended by the arc of S1 at the centre of the circle (in radians).
s1 + s2 + s3 +...........+ s7 = pi/16
s1 + 2s1 + 4s1 +..........+ 64s1 = pi/16
s1(2^7-1) = pi/16
s1 = pi/(16*127)
angle = 360/16*127 = 45/254 ?
16940
@ravi.theja said:
A tree of height 36 m is on edge of the road, because of the wind a part of tree fall and touches the other side of the road..the road is 12 m wide then what will be the height of the broken part?
20m toot gaya, 16 meter khada hai?
16941
@mailtoankit said:
s1 + s2 + s3 +...........+ s7 = pi/16s1 + 2s1 + 4s1 +..........+ 64s1 = pi/16s1(2^7-1) = pi/16s1 = pi/(16*127)angle = 360/16*127 = 45/254 ?
bhai y again 360/16*127......... s1= pi/ (16*127) here only we hav got the angle subtended by s1 at centre in radians
16942
@ravi.theja said:
bhai y again 360/16*127......... s1= pi/ (16*127) here only we hav got the angle subtended by s1 at centre in radians
bhai theta hi to batana hai......(theta)/360*pi*(1)^2 = pi/(16*127) ?
16943
@ravi.theja said:
A tree of height 36 m is on edge of the road, because of the wind a part of tree fall and touches the other side of the road..the road is 12 m wide then what will be the height of the broken part?
20m ?

x^2 + 12^2 = (36 - x)^2
x = 16
broken part = 36 - 16 = 20m
16944
@mailtoankit said:
bhai theta hi to batana hai......(theta)/360*pi*(1)^2 = pi/(16*127) ?
.(theta)/360*pi*(1)^2 ==> dis one is formula for area of sector na....here it is nt askd 😃 so jus finding s1 is enough
16945
@ravi.theja said:
A tree of height 36 m is on edge of the road, because of the wind a part of tree fall and touches the other side of the road..the road is 12 m wide then what will be the height of the broken part?

(36-k)^2 + 12^2 = k^2...