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# Official Quant Thread for CAT 2012 [Part 1]

Hi puys, CAT 2011 season is finally over :: :: Let start a new season of Quants thread for CAT 2012.. :: :: Here are few links of Quants thread for CAT 2011 season... Part-8 http://www.pagalguy.com/forum/quanti...at-...
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anujgupta21 Says
kindly solve this question...GUY!!!

bhai d ans is x-8
(kx-6)(x^2+2x-
=x^3-ax^2-bx+48
comparing a=4
putting a in d exp.
x^2-4x-32.
div by x-8
xat (2013) 97.43:cat (2012) 95.03: calls:xlri(bm/hr)
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A truck having ten tyres travels from P to Q and then back to P. If there are 2 additional spare tyres and the distance between P and Q is 9000 kilometres (km), then the maximum distance travelled (in km) by any tyre is at least?
(1) 12000 (2) 18000 (3) 9000 (4) 16000 (5) 15000

my take15000

total distance travelled ( sum of distance travelled by individual tyres) = 18000*10
we have used 12 tyres for this so per tyre it come sot 18000*10/12 = 15000
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why did you take 25 instead of 50 on the LHS and RHS mei why did you multiply by 2/5

f(1000) = 999
f(1000)*f(f(1000))= 1
or, 999*f(999) = 1
or, f(999) = 1/999

as f(x) is continuous, there must be a real value 'c' in the range (999,1000)
for which,

f(c) = 891

now,
f(c) * f(f(c)) = 1
or, 891 * f(891) = 1
or, f(891) = 1/891

Please revert back, in case you have doubt/queries with the solution

I am also getting the same answer with the same method .I think ans would be 1/891
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A 250 m long train is approaching an unmanned railway crossing. The train is
running at a uniform speed of 75 km/h and is 3 km away from the crossing. At the same instant, a scooter is also approaching the crossing and is 1300 m away from it. The scooter is moving at a uniform speed of A. In which of the following ranges, A exists such that the scooter would pass the crossing by just escaping the collision?
(1) 24km/h to 28 km/h
(2) 29km/h to 33km/h
(3) 35km/h to 40km/h
(4) 41km/h to 45km/h
(5) 45 km/h to 50km/h

Any speed> 32.5k/hr so ans is option 2

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why did you take 25 instead of 50 on the LHS and RHS mei why did you multiply by 2/5

Because Work is inversly proportional to the Men and days.
I have taken 25 because additional men are not required till the 25th day and after that they require another men ( assume x) so total ( 105 + x) men.

But they have to finish the work in 50 days but only 25 days are left ( to complete 3/5th work ) so both side 25 days

I hope you are clear now .

Correct me if i am wrong
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A 250 m long train is approaching an unmanned railway crossing. The train is
running at a uniform speed of 75 km/h and is 3 km away from the crossing. At the same instant, a scooter is also approaching the crossing and is 1300 m away from it. The scooter is moving at a uniform speed of A. In which of the following ranges, A exists such that the scooter would pass the crossing by just escaping the collision?
(1) 24km/h to 28 km/h
(2) 29km/h to 33km/h
(3) 35km/h to 40km/h
(4) 41km/h to 45km/h
(5) 45 km/h to 50km/h

train___________crossing_________scooter

,-------1.3------------>

total distance between scooter and train=4.3km

time to collide t= 4.3/75+A................1

also t*A=1.3km....................2

using 1&2 we get A=32.5kmph in order to just avoid collision

so A should be in the range 29
J.P Morgan | Media Cell | IIM Kozhikode 2014-16 | CAT 13 99.43 | XAT 97.21 |
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A 250 m long train is approaching an unmanned railway crossing. The train is running at a uniform speed of 75 km/h and is 3 km away from the crossing. At the same instant, a scooter is also approaching the crossing and is 1300 m away from it. The scooter is moving at a uniform speed of A. In which of the following ranges, A exists such that the scooter would pass the crossing by just escaping the collision?
(1) 24km/h to 28 km/h
(2) 29km/h to 33km/h
(3) 35km/h to 40km/h
(4) 41km/h to 45km/h
(5) 45 km/h to 50km/h

sol:
time taken by train =3/75 hr
and time taken by scooter=1.3/A
they will collide if 3/75=1.3/A
A=32.5 km/hr
now for escaping collison A>32.5
option 2)
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A truck having ten tyres travels from P to Q and then back to P. If there are 2 additional spare tyres and the distance between P and Q is 9000 kilometres (km), then the maximum distance travelled (in km) by any tyre is at least?
(1) 12000 (2) 18000 (3) 9000 (4) 16000 (5) 15000

"You are the creator of your own Destiny."
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Ajit, Ashutosh and Anil started from the same place and travelled in the same direction at the speeds of 80, 70 and 60 kmph respectively. Ashutosh started 3 hours after Anil and both Ajit and Ashutosh overtook Anil at 9.00 p.m. of the same day. Find the time at which Ajit started?
(1) 5:15 a.m. (2) 5:30 a.m.
(3) 6:00 a.m. (4) 5:45 a.m.

my take5:15 a.m.
in 3 hours anil would have travelled 180 kms.
effective speed of ashu and anil = 10 kmph

it would take 18 hours for them to cover 180kms gap. so 9:00 p.m. - 18 hours = 3 a.m. was when ashu started and 00:00 was the time when anil started.
so anil travelled for 21 hrs before he met ajit. In 21 hrs anil was 60*21 = 1260kms away from the starting point. Ajit would take 1260/80*60 = 945 minutes before they meet.

945 minutes = 15 hours 45 minutes.
so 9:00 p.m - 15 hours 45 minutes = 5:15 a.m.
• 1 Like
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A 250 m long train is approaching an unmanned railway crossing. The train is
running at a uniform speed of 75 km/h and is 3 km away from the crossing. At the same instant, a scooter is also approaching the crossing and is 1300 m away from it. The scooter is moving at a uniform speed of A. In which of the following ranges, A exists such that the scooter would pass the crossing by just escaping the collision?
(1) 24km/h to 28 km/h
(2) 29km/h to 33km/h
(3) 35km/h to 40km/h
(4) 41km/h to 45km/h
(5) 45 km/h to 50km/h

Getting option 2.

The train will cover this 3km in 0.04 hrs.
The scooter needs to cover 1.3 km in less than 0.04 hrs.
=> Speed of scooter = A = 1.3/Time.
=> 1.3/A => A > 1.3/0.04.
So A > 32.5 kmph.
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