Official Quant thread for CAT 2013

What is the probability of selecting 2 points on a straight line of length 60 cm such that the distance between the 2 does not exceed 20 cm?
Options
1) 1/4
2) 2/3
3) 4/9
4) 5/9

OA 5/9

@nick_baba said:
which post buddy..though i have edited one ...neways..try to solve it..n tell me the logic
no logic as such..just tried for some values
@krum said:
What is the probability of selecting 2 points on a straight line of length 60 cm such that the distance between the 2 does not exceed 20 cm?Options 1) 1/42) 2/33) 4/94) 5/9OA 5/9
Probability that one point is within 20 m of other = 20/60 = 1/3
Probability that one is not in the required range = 2/3
Similarly for the other point, it will be 2/3
So, probability that they are not within 20 m of each other is (2/3)*(2/3) = 4/9
Hence probability of choosing 2 points not more than 20 m apart from each other is 1 - 4/9 = 5/9


Please correct me if i am wrong.
@soumitrabengeri said:
Probability that one point is within 20 m of other = 20/60 = 1/3Probability that one is not in the required range = 2/3Similarly for the other point, it will be 2/3So, probability that they are not within 20 m of each other is (2/3)*(2/3) = 4/9Hence probability of choosing 2 points not more than 20 m apart from each other is 1 - 4/9 = 5/9Please correct me if i am wrong.
A------20m--------B------20m--------C------20m------D
say i chose B, p(other point within 20m)=2/3


here probability is not fixed but changes linearly
@soumitrabengeri said:
Probability that one point is within 20 m of other = 20/60 = 1/3Probability that one is not in the required range = 2/3Similarly for the other point, it will be 2/3So, probability that they are not within 20 m of each other is (2/3)*(2/3) = 4/9Hence probability of choosing 2 points not more than 20 m apart from each other is 1 - 4/9 = 5/9Please correct me if i am wrong.
your explanation luks right but please help me with this justification..

why we have to consider not possible cases n subtract them from 1..
why cudn't it be like prob of one being in the 20cm vicinity of the other=1/3 similarly for the other..hence why not 1/9??
@krum said:
A------20m--------B------20m--------C------20m------Dsay i chose B, p(other point within 20m)=2/3here probability is not fixed but changes linearly
bhai is thi ques of similar class to the one that was discussed in 2012 thread k wat z prob for meeting of 2 frnz within one hour if one waits for the other for not more than 15 mins???
@krum said:
What is the probability of selecting 2 points on a straight line of length 60 cm such that the distance between the 2 does not exceed 20 cm?Options 1) 1/42) 2/33) 4/94) 5/9OA 5/9

let us first consider a line on x- axis starting from coordinates (0,0) to (60,0)

let x and y be the x-coordinates of the two points we have to choose.

now according to the given condition we want |x-y| less than equal to 20

now to choose two points on the given line
no. of possible ways =61*61 ( as x,y can vary from [0,60]

now for no. of favorable outcomes,lets start making cases
for |x-y| =0, 61 cases x=y

for |x-y| =1 ,60 cases for x>y and 60 cases for x

.
.
.
.
.
for |x-y| =20 ,2*41 (41 for each)

so total favorable cases=61 + 2*(41 +42 +........60)=2081


so probability=2081/61*61=5/9

@soumitrabengeri said:
Probability that one point is within 20 m of other = 20/60 = 1/3Probability that one is not in the required range = 2/3Similarly for the other point, it will be 2/3So, probability that they are not within 20 m of each other is (2/3)*(2/3) = 4/9Hence probability of choosing 2 points not more than 20 m apart from each other is 1 - 4/9 = 5/9Please correct me if i am wrong.
@nick_baba said:
bhai is thi ques of similar class to the one that was discussed in 2012 thread k wat z prob for meeting of 2 frnz within one hour if one waits for the other for not more than 15 mins???
@busar005 said:
let us first consider a line on x- axis starting from coordinates (0,0) to (60,0)let x and y be the x-coordinates of the two points we have to choose.now according to the given condition we want |x-y| less than equal to 20now to choose two points on the given lineno. of possible ways =61*61 ( as x,y can vary from [0,60]now for no. of favorable outcomes,lets start making casesfor |x-y| =0, 61 cases x=yfor |x-y| =1 ,60 cases for x>y and 60 cases for x......for |x-y| =20 ,2*41 (41 for each)so total favorable cases=61 + 2*(41 +42 +........60)=2081so probability=2081/61*61=5/9
for the first 20cm the probability increases linearly from 1/3 to 2/3
it remains constant for next 20cm and decreases linearly from 2/3 to 1/3 for last 20cm

so p=1/3*(1/3+2/3)/2+1/3*2/3+1/3*(1/3+2/3)/2
=>1/6+2/9+1/6
=>(3+4+3)/18
=>10/18
=>5/9
Let p1, p2, p3 and p4 be distinct prime numbers satisfying :
2p1 + 3p2 + 5p3 + 7p4 = 162
11p1 + 7p2 + 5p3 + 4p4 = 162
If p1p2p3p4 = k find the number of possible values of k?
a) 0
b) 1
c) 2
d) 3
@krum said:
for the first 20cm the probability increases linearly from 1/3 to 2/3it remains constant for next 20cm and decreases linearly from 2/3 to 1/3 for last 20cmso p=1/3*(1/3+2/3)/2+1/3*2/3+1/3*(1/3+2/3)/2=>1/6+2/9+1/6=>(3+4+3)/18=>10/18=>5/9
thanks for the explanation..did not realize the fact that the prob changes linearly and is not fixed.
@nick_baba said:
an easy one...For how many primes p is p^2 + 3p ˆ' 1 also prime?a) 0 b) 1 c) 2 d) 3 koi mast sa general sol batao..option dekh ke mat karna..
(p+1)(p-1)+3p this number is always divisible by 3 so ans is zero

@HeCtEr said:
(p+1)(p-1)+3p this number is always divisible by 3 so ans is zero
nai dost...ans is b
@krum said:
for the first 20cm the probability increases linearly from 1/3 to 2/3it remains constant for next 20cm and decreases linearly from 2/3 to 1/3 for last 20cmso p=1/3*(1/3+2/3)/2+1/3*2/3+1/3*(1/3+2/3)/2=>1/6+2/9+1/6=>(3+4+3)/18=>10/18=>5/9


can you plzz explain me sir how the the probability is increasing in first 20 cm and it is 2/3 in next...??
by the way,great method..
@krum said:
for the first 20cm the probability increases linearly from 1/3 to 2/3it remains constant for next 20cm and decreases linearly from 2/3 to 1/3 for last 20cmso p=1/3*(1/3+2/3)/2+1/3*2/3+1/3*(1/3+2/3)/2=>1/6+2/9+1/6=>(3+4+3)/18=>10/18=>5/9
whooosshhhh.......sar ke upar se gaya .. guruji thoda vistar se(ho sake to diagram )..jaise ATDH sir smjhate hai..
@nick_baba said:
nai dost...ans is b
smjha nhi y b?
@HeCtEr said:
smjha nhi y b?
http://pagalguy.com/forums/quantitative-ability-and-di/official-quant-thread-c-t-88456/p-3611604/r-4027641?page=42

find the post#825 by krum..its self explanatory...plus if u put p=3..u'll get a prime number .i.e. 17
There are two ants on opposite corners of a cube. On each move,
they can travel along an edge to an adjacent vertex. If the probability that
they both return to their starting position after 4 moves is m/n , where m and

n are relatively prime integers, find m+n. (NOTE:They do not stop if they
collide.)

a) 17
b) 65
c) 73
d) 85
@nick_baba said:
pagalguy.com/forums/quantitati...find the post#825 by krum..its self explanatory...plus if u put p=3..u'll get a prime number .i.e. 17
got it . p=3 will be the only value though.
@HeCtEr said:
got it . p=3 will be the only value though.
yep..

@nick_baba said:
Let p1, p2, p3 and p4 be distinct prime numbers satisfying :2p1 + 3p2 + 5p3 + 7p4 = 16211p1 + 7p2 + 5p3 + 4p4 = 162If p1p2p3p4 = k find the number of possible values of k?a) 0 b) 1 c) 2 d) 3
0?