Official Quant thread for CAT 2013

@sujamait said:
There are 8 poles on the same side of a straight road. Two of these poles are without flags; two ofthese have a flag of the same country and each of the rest of the four poles has a plain flag of adifferent colour. What is the probability that the first four poles from either end have two flags of thecountry and two plain colored flags?A.1/140B.6/35C.1/70D. None of these
4P2 * 4P2 *2/ (8P2 * 6P4) = 6/35 ??
@sujamait said:
Raj works part time in three different organisations €“ P, Q and R €“ everyday. Each of theseorganisations pays a fixed salary on hourly basis. On any day, Raj earned Rs. 3,850 by working for4 hrs, 5 hrs and 6 hrs respectively and on the next day, he earned Rs. 5,350 by working for 5 hrs,3 hrs and 7 hrs respectively. If the hourly salaries paid by the three organisations are in ArithmeticProgression, find the difference between the hourly salaries of the highest and the lowest payingorganisations?A. Rs. 1,000 B. Rs. 500 C. Rs. 750 D. None of these
1000

Consider for Q=> a
R=> a+d
P=> a+2d
So u get equations

15a+14d=3850
15a+17d=5350
Solving...
3d=1500 :: d=500

Diff between highest & lowest = 2d= 1000
@sujamait said:
If 'p' and 'q' are prime numbers such that p = q + 2 and 'q' is greater than 100, then which of thefollowing is always true?A. p^2 – q^2 is always divisible by 24.B. p^3 + q^3 is always divisible by 24.C. Both A and BD. None of these
Only A?
@sujamait said:
If 'p' and 'q' are prime numbers such that p = q + 2 and 'q' is greater than 100, then which of thefollowing is always true?A. p^2 – q^2 is always divisible by 24.B. p^3 + q^3 is always divisible by 24.C. Both A and BD. None of these
Only A??
p = 6k+1 and q=6k-1
A: p^2-q^2 = 24k
B: p^3+q^3 = 12k(36k^2+1)

Hence Only A is always divisible by 24
There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?
(a) 72 (b) 90 (c) 96 (d) 108 (e) 120

The THREAD is so DEAD!!

@ScareCrow28 said:
There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?(a) 72 (b) 90 (c) 96 (d) 108 (e) 120The THREAD is so DEAD!!
b) 90??
A task is assigned to a group of 11 men, not all of whom have the same capacity to work. Every day exactly 2 men out of the group work on the task, with no pair of men working together twice. Even after all the possible pairs have worked once, all the men together had to work for exactly one day more to finish the task. What is the number of days that will be required for all the men working together to finish the job.
(a) 11 (b) 21 (c) 33 (d) 12 (e) none of the foregoing
@ScareCrow28 said:
A task is assigned to a group of 11 men, not all of whom have the same capacity to work. Every day exactly 2 men out of the group work on the task, with no pair of men working together twice. Even after all the possible pairs have worked once, all the men together had to work for exactly one day more to finish the task. What is the number of days that will be required for all the men working together to finish the job.(a) 11 (b) 21 (c) 33 (d) 12 (e) none of the foregoing
11 it is..
Given a set of n rays in a plane, define a reversal as the operation of reversing precisely one ray and obtaining a new set of rays. If all the rays are reversed after 42 operations, then n can be

(a) 21 (b) 23 (c) 41 (d) 24 (e) At least two of the foregoing
a, b, c, d, e, f, g are non-negative such that a+b+c+d+e+f+g = 1. Then the minimum value of max(a+b+c, b+c+d, c+d+e, d+e+f, e+f+g) is
(a) 1/3 (b) 3/7 (c) 1 (d) 0 (e) none of the foregoing

@ScareCrow28 said:
A task is assigned to a group of 11 men, not all of whom have the same capacity to work. Every day exactly 2 men out of the group work on the task, with no pair of men working together twice. Even after all the possible pairs have worked once, all the men together had to work for exactly one day more to finish the task. What is the number of days that will be required for all the men working together to finish the job.(a) 11 (b) 21 (c) 33 (d) 12 (e) none of the foregoing
is it 11 days??
@ScareCrow28 said:
a, b, c, d, e, f, g are non-negative such that a+b+c+d+e+f+g = 1. Then the minimum value of max(a+b+c, b+c+d, c+d+e, d+e+f, e+f+g) is(a) 1/3 (b) 3/7 (c) 1 (d) 0 (e) none of the foregoing
3/7 ??
@ScareCrow28 said:
Given a set of n rays in a plane, define a reversal as the operation of reversing precisely one ray and obtaining a new set of rays. If all the rays are reversed after 42 operations, then n can be(a) 21 (b) 23 (c) 41 (d) 24 (e) At least two of the foregoing
24 i think..

remaining all are odd.
@ScareCrow28 said:
There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?(a) 72 (b) 90 (c) 96 (d) 108 (e) 120The THREAD is so DEAD!!
Within a same zone=3 (villages) * 3 (direct lines) *4 (zones)=36
Different zones=6 pairs*3 (villages of 1 zone) *3 (villages of other zone)=54
Total direct lines=36+4=90
In a triangle PQR, PQ = QR, S and T are points on PR and PQ respectively such that RQ = QS = ST = TP. Then /_ PTS (in degrees) lies in the range

(a) (75, 90) (b) (105, 120) (c) (135, 150) (d) (120, 135) (e) none of the foregoing
@ScareCrow28 said:
a, b, c, d, e, f, g are non-negative such that a+b+c+d+e+f+g = 1. Then the minimum value of max(a+b+c, b+c+d, c+d+e, d+e+f, e+f+g) is(a) 1/3 (b) 3/7 (c) 1 (d) 0 (e) none of the foregoing
3/7??
@ScareCrow28 said:
a, b, c, d, e, f, g are non-negative such that a+b+c+d+e+f+g = 1. Then the minimum value of max(a+b+c, b+c+d, c+d+e, d+e+f, e+f+g) is(a) 1/3 (b) 3/7 (c) 1 (d) 0 (e) none of the foregoing
3/7?
@pankaj1988 said:
3/7?
@adream27 said:
3/7??
@kingsleyx Nopes..It's not 3/7..
@wovfactorAPS said:
24 i think..remaining all are odd.
can u explain??
@ScareCrow28 said:
a, b, c, d, e, f, g are non-negative such that a+b+c+d+e+f+g = 1. Then the minimum value of max(a+b+c, b+c+d, c+d+e, d+e+f, e+f+g) is(a) 1/3 (b) 3/7 (c) 1 (d) 0 (e) none of the foregoing
E???getting 4/9