Official Quant thread for CAT 2013

MBA CAT 2024
26728
@Asfakul said:
Xavier and Haneef are competing with each other in a swimming competition in a pool of 50m length for 1000m Race . xavier crosses 50m length in 2 min's and haneef cross it in 3min 15secs . How many times they cross/meet each other ?please share the detailed explanation .Also had it been 5 min for crossing 50m in case of Haneef , what would have been the ans ? Please explain in detail .

LCM(180,195) = 1560 secs = 26 mins
in 26 mins , no. of 50m rounds = 13 = 650 m
in 650 m no. of crossings + meeting = (650-50)/50 = 12 (-50 bcoz , in first round they wont meet or cross)
in next 350 m , they ll cross each other for 7 times
OA = 12 + 7 = 19 ?
26729
@Koushik98 said:
sir, yeah 3/5 and 5/3 ratio kon sa interval pe a raha hain??
@bodhi_vriksha said: Nishant, I have drawn and attached the graph. Hope that helps.Team BV - Vineet

Exactly this was my doubt too...
26730
@rnishant231 said:
@bodhi_vriksha said: Nishant, I have drawn and attached the graph. Hope that helps.Team BV - VineetExactly this was my doubt too...
did u get those 2 ratios??i am not getting it....
26731
@Koushik98 said:
did u get those 2 ratios??i am not getting it....


No , i too did'nt get..
@bodhi_vriksha sir , pl. comment.
26732
a certain city has a circular wall around it with four gates north,south,west and east.A house stands outside the city ,3 km north of the north gate,and it can just be
seen from a point 9 km east of the south gate.What is the diameter of the wall that surrounds the city ?
26733
@nole said:
a certain city has a circular wall around it with four gates north,south,west and east.A house stands outside the city ,3 km north of the north gate,and it can just be seen from a point 9 km east of the south gate.What is the diameter of the wall that surrounds the city ?
9 ?
26734
@Narci m getting 18,can u share the solution ?
26735
@nole said:
a certain city has a circular wall around it with four gates north,south,west and east.A house stands outside the city ,3 km north of the north gate,and it can just be seen from a point 9 km east of the south gate.What is the diameter of the wall that surrounds the city ?
Is it 9*sqrt 3 - 3 ?
26736
@ankittripathi OA is 9
26737
@nole said:
@Narci m getting 18,can u share the solution ?
it will be a right angled triangle.. will share the diagram in my next post..
26738


Happy quanting !

26739
@albiesriram said:
Happy quanting !
7c4 for choosing 4 letters
a+b+c+d=3
6!/3!3!=20
when a=2
b+c+d=1
3 sol
when a=3
1 sol
same for b
4*2=8
when c=3
1 sol
20-8-1=11
7c4 *11=385*7!=1940400
second part=1940400/2!2! = 485100


where m i gng wrong @albiesriram
26740
@Narci said:
it will be a right angled triangle.. will share the diagram in my next post..
i got 2r^3 - 3r^2 - 243 = 0
r = 4.5 satisfies it... hence d = 9
but how did u solve it exactly ?
26741
@Koushik98 said:
sir, yeah 3/5 and 5/3 ratio kon sa interval pe a raha hain??
@rnishant231 said:
No , i too did'nt get..@bodhi_vriksha sir , pl. comment.
For k = 2.4 and r = 4, k/r = 0.6 =3/5

For k = 10/3 and r = 2, k/r = 5/3 :)

Team BV - Vineet
26742
The word ''chemika'' has 7 different letters.
So we need to select 7 square boxes for these 7 different letters to be placed. Selection of 7 square boxes can be done in the following ways:

Case 1: 1 from first row, 1 from second row, 1 from third row and 4 from the fourth row 2C1 × 2C1 × 3C1 × 4C4 = 2 × 2 × 3 × 1 = 12 ways

Case 2: 1 from first row, 1 from second row, 2 from third row and 3 from the fourth row 2C1 × 2C1 × 3C2 × 4C3 = 2 × 2 × 3 × 4 = 48 ways

Case 3: 1 from first row, 1 from second row, 3 from third row and 2 from the fourth row 2C1 × 2C1 × 3C3 × 4C2 = 2 × 2 × 1 × 6 = 24 ways

Case 4: 1 from first row, 2 from second row, 1 from third row and 3 from the fourth row 2C1 × 2C2 × 3C1 × 4C3 = 2 × 1 × 3 × 4 = 24 ways

Case 5: 1 from first row, 2 from second row, 2 from third row and 2 from the fourth row 2C1 × 2C2 × 3C2 × 4C2 = 2 × 1 × 3 × 6 = 36 ways

Case 6: 1 from first row, 2 from second row, 3 from third row and 1 from the fourth row 2C1 × 2C2 × 3C3 × 4C1 = 2 × 1 × 1 × 4 = 8 ways

Case 7: 2 from first row, 1 from second row, 1 from third row and 3 from the fourth row 2C2 × 2C1 × 3C1 × 4C3 = 1 × 2 × 3 × 4 = 24 ways

Case 8: 2 from first row, 1 from second row, 2 from third row and 2 from the fourth row 2C2 × 2C1 × 3C2 × 4C2 = 1 × 2 × 3 × 6 = 36 ways

Case 9: 2 from first row, 1 from second row, 3 from third row and 1 from the fourth row 2C2 × 2C1 × 3C3 × 4C1 = 1 × 2 × 1 × 4 = 8 ways

Case 10: 2 from first row, 2 from second row, 1 from third row and 2 from the fourth row 2C2 × 2C2 × 3C1 × 4C2 = 1 × 1 × 3 × 6 = 18 ways

Case 11: 2 from first row, 2 from second row, 2 from third row and 1 from the fourth row 2C2 × 2C2 × 3C2 × 4C1 = 1 × 1 × 3 × 4 = 12 ways

Total number of ways of selection of 7 square boxes = 12 + 48 + 24 + 24 + 36 + 8 + 24 + 36 + 8 + 18 + 12 = 250

For each selection of 7 square boxes, the number of arrangements of 7 different letters = 7! = 5040

Hence , Total number of arrangements = 5040 × 250 = 1260000 = > official solution


26743
@albiesriram said:
Happy quanting !
1) Option 4-> 1260000
2) Option 2) -> 315000


Total boxes 2 2 3 4
Total cases are -> 1 1 3 2
1 1 2 3
1 1 1 4
2 1 3 1
2 1 2 2
2 1 1 3
1 2 3 1
1 2 2 2
1 2 1 3
2 2 2 1
2 2 1 2

Calculate the all combination and add them and multiply them with 7!

2)Same as above but at last multiply them with 7!/2!2!

26744
@iLoveTorres nahi yaar . it is 19
26745
@rnishant231 said:
i increased the side to 10 and got total area as 1100...so area as per question may be 11.. not sure .. .need to do + 1/2 for other triangle(opposite half of square) - 23/2 ?
And that's the right one :). Well done!

Team BV - Vineet
26746
@nole said:
a certain city has a circular wall around it with four gates north,south,west and east.A house stands outside the city ,3 km north of the north gate,and it can just be seen from a point 9 km east of the south gate.What is the diameter of the wall that surrounds the city ?
d=9??
26747

Ok ...here goes the next one...


The sum of all the possible values of integral k such that (k^2-2k) ^ (k^2+47) = (k^2-2k) ^ (16k-16) is

(a) 16 (b) 17 (c) 18 (d) 19 (e) none of these

Team BV - Vineet