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Official Quant Thread for CAT 2012 [Part 1] Quantitative

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Hi puys,
CAT 2011 season is finally over [smiley] [smiley]
Let start a new season of Quants thread for CAT 2012.. [smiley] [smiley]
Here are few links of Quants thread for CAT 2011 season...
Part-8
http://www.pagalguy.com/forum/quanti...at-2011-a.html (Official Quant Threa...

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Page 1 of 491

12:11 AM, 08 Feb '12

08 Feb '12

a train and car start at same time ...car at rear end reaches front end and come back to rear end . in the mean time train travels 1 km and speed of train is 1 km /hr ...wat is distance covered by car
:banghead:

hope for the best

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pls everyone, continue on the thread jain bhai opened (link -above). A thread needs to be closed when it has completed around 1000 pages.
Thanx.

5 5

digits 1 2 3 4 5 & 6
numbers 1 2 ( 7,8,9) (3,6,9) (31,62,93)
Ans would be 3*3*3= 27.
Correct me if i am wrong

Q) A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
ans= 27
3rd digit could be 7,8 and 9
...

2 2

my take27
third digit can take 3 values
4th digit can take 3,6,9 = 3 values
5th digit = 3 times 6th. 6th can take only 1,2,3 and corresponding three values for 5th digit

Anjali nd Sachin decided to meet at Barista sometime between 5pm to 6 pm.they decided that they would wait max of 10 min their and then leave.What is the probability that they met?
sorry for repost but i think its worthy of a shot

All the quant enthusiasts
please continue here.
http://www.pagalguy.com/forum/quantitative-questions-and-answers/78107-official-quant-thread-cat-2012-a.html#post3235962
MODS plz close this thread

sol:
-----------------------------truck (with 10 tyres)
so clearly 1st tyre will travel 9000km and so by the 2nd tyre so total distance
travelled by individual tyre
=9000*10(forward)+9000*10(backward)
=18000*10
=180000km
now when there are twelve tyres=(10*18000)/12=15000<...

Getting 15000.
18k*10/12 = 15k.
=====================
Q) A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card n...

1 1

(3/75)=(1.3/A)
=>A=32.5~33
(b)

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

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

1 1

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. I...

train___________crossing_________scooter
<---------3---------->,-------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
s...

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)

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 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...

1 1

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 < 0.04
=> A > 1.3/0.04.
So A > 32.5 kmph.

2 2

Page 2 of 491

kindly solve this question...GUY!!!

60*3 = 180 km
180/70-60 = 18 hrs
18*70 = 1260 km
1260/80 = 15.75
9:00 pm - 15 hrs 45 mins = 5:15 am = answer

1 1

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 w...

copper 25.2 kg and tin 7.2 kg previously
Approach:-
initial conc of copper=7/9 and tin=2/9
in the quantity i.e 18 kg which is added conc of copper =0%
now, final conc of copper in resulting mixture is 50% =1/2
so using alligation,
we get ratio of quantity in which the 1st alloy ...

smiyc now i got it.

My take is 5:15 am
Anil covers 180km in 3 hrs.
Ashutosh overtakes Anil in 180/10 = 18 hrs.
Ashutosh in 18 hrs covers = 18*70 = 1260 km.
=> Ajit overtakes Anil in 1260/80 = 15 3/4 hrs
So, Ajit started at 5.15 am.

1 1

initial conc of tin= 2/9 and that of copper=7/9
copper 25.2 kg ; tin =7.2 kg previously

Q) An alloy of copper and tin contains 77.78% of copper. After 18kg of tin is added, the copper content gets reduced to 50%. How much copper and tin do the new allow had respectively?
=> Copper= around 25.2 kg

wrong post..............

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....

Anjali nd Sachin decided to meet at Barista sometime between 5pm to 6 pm.they decided that they would wait max of 10 min their and then leave.What is the probability that they met?

If AB is diameter to the circle, will the circle touch CD ???
remember it touches CD.
AB will be a chord, the circle touches CD at say point P
ABP will be an equilateral triangle

Originally Posted by flanker1985
If f(x) = x^3 - 4x + p , and f(0) and f(1) are of opposite sings, then which of the following is necessarily
true
(1) -1 < p < 2 (2) 0 < p < 3 (3) -2 < p < 1 (4) -3 < p < 0
option 2

997 it will be :thumbsup:
My take is option 2.
f(0) = 0^3 - 4*0 + p = p.
f(1) = 1^2 - 4*1 + p = p - 3.
Since p and p - 3 are of opp signs then p*(p-3) < 0.
=> 0 < p < 3.
==========================
Q) An alloy of copper and tin contains 77.78% of copper. After 18kg of tin is...

f(0)=p and f(1)=p-3..now p>0 and p-3<0....therefore option 2

Originally Posted by upudit0
Let ABCD be a rectangle with AB = a, and BC = b. Suppose x is the length of the radius of the circle passing through A and B and touching CD, and y be the length of the circle passing through B and C and touching AD. If x + y = k.(a+b) for all a and b, then k ...

smiyc didn't get why x = 1/3^1/2 of ab if the circle is passing through A and B and we r assuming it to be a square then it shoul be 1/2 ab

Sol:
1001! * 1000! * 999! * 998! *997! *.....1!
basically we have to see which one among 997,991,977,973 is a prime.
starting with 997,check divisibility by all primes from
997 is not divisible by any prime less than 31.
so ans=997

If f(x) = x^3 4x + p , and f(0) and f(1) are of opposite sings, then which of the following is necessarily
true
(1) 1 < p < 2 (2) 0 < p < 3 (3) 2 < p < 1 (4) 3 < p < 0

the largest 3 digit prime number is the answer ...
1001! , 1000! and 999! : each has at least one factor of all the 3 digit numbers
hence the largest 3 digit prime number will definitely be there in the 3 factorials as a factor: it's product will be div by the cube of the prime.
I don't...

1 1