Official Quant thread for CAT 2013

MBA CAT 2024
5661
@pratyush9811 said:
In a right angled triangle ABC, angle B is right angle, side AB is half of the hypotenuse. AE is parallel to median BD and CE is parallel to BA. What is the ratio of length of BC to that of EC?
root3/2
Triangle AEC is equilateral
5662
@pratyush9811 said:
The top speed of a rail engine is 80 km/hr. When pulling a train of wagons, its top speed is reduced by a quantity proportional to the square-root of the number of wagons. When the number of wagons attached to the engine is 25, its top speed is 55 km/hr. If the top speed must be more than 20 km/hr, what is the maximum number of wagons that can be attached to the engine?
143?
5663

BD is the median so BD=AD=DC=r(circumradius) so ADB is an equi triangle... so all the angles are 60.
=> so EAC is also an equi triangle=> CE=2a
BC/EC=rt3a/2a= rt3/2

5664
@19rsb sirji us work wale question ka solution!!
5665
@arumugadas said:
method pls
suppose efficiency of (as condition given in ques.)
A 168
B 120
C 100
also suppose tot work =4200 units
in 10 days A's work = 1680 units
in 15 days B's work= 1800 units
remainin work= 4200-1680-1800=720 units
req. days by C = 720/100= 7.2 days
5666
@arumugadas said:
A,B,C .......A is 40 % more efficient than B and B is 20% more efficient than C . if A starts the work and did for 10 days after B did for 15 days how long will it take C to complete the balance work
bhai isnt the number of days for any one should be given, like C completes it in N days
the answer wil then be in form of C variable, how to eliminate that
5667
@19rsb said:
suppose efficiency of (as condition given in ques.)
A 168
B 120
C 100
also suppose tot work =4200 units
in 10 days A's work = 1680 units
in 15 days B's work= 1800 units
remainin work= 4200-1680-1800=720 units
req. days by C = 720/100= 7.2 days
bhai if i chenge the work days will vary
eg instead of 4200 , i take 8400
5668
@arumugadas said:
A,B,C .......A is 40 % more efficient than B and B is 20% more efficient than C . if A starts the work and did for 10 days after B did for 15 days how long will it take C to complete the balance work
7.2?
5669
AGAIN...
A contract is to be completed in 56 days and 104 men are set to work, each working 8 hours a day. After 30 days, 2/5th of the work in finished. How many additional men may be employed so that work may be completed on time, each man now working 9 hours per day?
A. 56 men
B. 65 men
C. 46 men
D. None of the above
my last one for the day...
over to u @gs4890 , @pankaj1988
30 * 8 * 104 = 2/5 * W -- (1)
26 * 9 * (104+x) = 3/5* W -- (2)



Guys this qn was posted a few days back ...Though the answer is right ..what i did not understand is that when i tried to do this by taking W as 104 x 56 x 8 in the second eqn and tried solving it i m getting fractional value !!! can somebody explain what is wrong in my approach ??
Regards,
5670
@nick_baba said:
The number of rational points x = p/5 satisfying log(2x-3/4)/logx > 2, where p is an integer and GCD(p, 5) = 1, is/are??



log(2x-3/4)/logx > 2

clearly x>3/8 and x not equal to 1

if x>1 then
=>(2x-3/4) > x^2
=>8x -3 > 4x^2
=>4x^2 -8x +3 =>(2x-3)(2x-1) => 1 => (5)/5 => (5) so integral values of p = 6,7

if x=>(2x-3/4) =>8x -3 =>4x^2 -8x +3 > 0
=>(2x-3)(2x-1) > 0
=> 3/8 => (15/8)/5 => (15/8) so integral values of p = 2

ATDH.
5671
@techsurge said:
bhai if i chenge the work days will varyeg instead of 4200 , i take 8400
dost 4200 is nothing but the LCM of efficiency of A,B,C(as i supposed it in d abuv sol)
for 8400 their efficiencies will bcum twice
A 336
B 240
C 200
now u solve in d abuv manner u vill get d same answr
actully dis method is LCM approach of solving dese kind of ques.
u can solve dese ques by conventional(fraction) method also.....but it vill b toughr dan dis 4 sure
5672
@Shray14 said:
The difference between simple interest and compound interest on a particular amount in 2 years at 30% is Rs.360. What is the principal?1)Rs. 40002)Rs. 35003)Rs. 30004)Rs. 25005)None of these
4000
5673
@rkshtsurana said:
A fair coin is tossed n times. What is the probability that no two consecutive heads appear?
n = 1 -> P = 1 (H / T)
n = 2 -> P = 3/4 ( except HH, all)
n = 3 -> P = 5/8 ( HHH, HHT = 1 + 2 rejected)

Although, I can see the fibonacci coming up, I want to do it in another way, just for fun :/

For n,

Total cases = 2^n
Favorable = (all no heads cases (A)) + (all one head cases(B)) + (some of the cases for greater than 2 heads(C))

A = 1, B = n

For C,
2 heads => _ H _ H _

(a + b + c) = n-2 (b>=1) => n-1C2

3 heads => _ H _ H _ H _

(a + b + c + d) = n-3 ( b,c>=1) => n-2C3

So, C = n-1C2 + n-2C3 + ... 1

So, favorable cases = 1 + Sigma((n+1-r)C(r)), where r = 1 to n/2 if n is even, and r = 1 to (n+1)/2 if n is odd

So, Probability = [( 1 + Sigma((n+1-r)C(r))] / 2^n

5674
@2ndApr2011 said:
AGAIN...A contract is to be completed in 56 days and 104 men are set to work, each working 8 hours a day. After 30 days, 2/5th of the work in finished. How many additional men may be employed so that work may be completed on time, each man now working 9 hours per day?A. 56 menB. 65 menC. 46 menD. None of the abovemy last one for the day...over to u @gs4890 , @pankaj198830 * 8 * 104 = 2/5 * W -- (1)26 * 9 * (104+x) = 3/5* W -- (2)Guys this qn was posted a few days back ...Though the answer is right ..what i did not understand is that when i tried to do this by taking W as 104 x 56 x 8 in the second eqn and tried solving it i m getting fractional value !!! can somebody explain what is wrong in my approach ??Regards,
Can some 1 throw some light on this one ..plz
5675
@19rsb said:
dost 4200 is nothing but the LCM of efficiency of A,B,C(as i supposed it in d abuv sol)for 8400 their efficiencies will bcum twiceA 336B 240C 200now u solve in d abuv manner u vill get d same answractully dis method is LCM approach of solving dese kind of ques.u can solve dese ques by conventional(fraction) method also.....but it vill b toughr dan dis 4 sure
not getting you....how can you assume both the things (total work and efficiencies)

it's okay you took LCM and got 4200 but how can you say A - 336 , B - 240 , C - 200 by 8400 total units of work

I think some data is missing in this question




5676
@pratyush9811 said:
In a right angled triangle ABC, angle B is right angle, side AB is half of the hypotenuse. AE is parallel to median BD and CE is parallel to BA. What is the ratio of length of BC to that of EC?
rt(3)/4
5677
@insane.vodka its rt3:2
5678
@pratyush9811 said:
@insane.vodka its rt3:2
got mistake...it is a equilateral triangle -_-
5679

find the number of positive integer solutions of the equation 2/x +15/y=5...

share the approach 😃 Thanks in advance
5680
@pavimai said:
find the number of positive integer solutions of the equation 2/x +15/y=5...share the approach Thanks in advance
X=1,Y=5????/