Official Quant thread for CAT 2013

MBA CAT 2024
29466
@amresh_maverick said:
There are two trains - A and B, both starting from point S, with train A starting 10 seconds after train B. The length and speed for train A and train B are 100 m, 270 kmph and 200 m, 216 kmph respectively. How much time after start will train A reach train B €™s tail?
40 seconds???
26.67
29467
@amresh_maverick said:
There are two trains - A and B, both starting from point S, with train A starting 10 seconds after train B. The length and speed for train A and train B are 100 m, 270 kmph and 200 m, 216 kmph respectively. How much time after start will train A reach train B €™s tail?
26.67 sec ?
29468
@Marchex
Basically its like g(1)+g(2)+.......g(6) = 36*g(6)
g(1)+g(2)....+g(5)= 36*g(6) -g(6)= 25*g(5))
so g(6)/g(5)= 25/35, similarly g(5)/g(4)= 16(24) and so on.
so basically 25/35*16/24*9/15*4/8*1/3*5400 = g(6)=1800/7

EDIT: its 1800/7 not 240...made a silly calculation mistake earlier..
29469
What is the remainder when 90^91 is divided by 13?

(1) 0
(2) 7
(3) 12
(4) 1
29470
@Marchex said:
What is the remainder when 90^91 is divided by 13?(1) 0 (2) 7 (3) 12 (4) 1
12
29471
@Marchex said:
What is the remainder when 90^91 is divided by 13?(1) 0 (2) 7 (3) 12 (4) 1
12 ?
29472
@Marchex said:
What is the remainder when 90^91 is divided by 13?(1) 0 (2) 7 (3) 12 (4) 1
-1^91=-1=12
29473
N positive real numbers have a product of unity. Their sum must be

(1) divisible by N.
(2) equal to N + 1/N
(3) at least N.
(4) a natural number.
(5) None of these


Need Solution also
29474
@Marchex said:
N positive real numbers have a product of unity. Their sum must be(1) divisible by N. (2) equal to N + 1/N (3) at least N. (4) a natural number. (5) None of theseNeed Solution also
3??
29475
Nine boxes are numbered 1, 2, €Ś €Ś 9. Each box must be filled with a ball which is of one of the three colours white, black and yellow. Boxes which are filled with either a white ball or a black ball must have consecutive numbers. At least 6 boxes must be filled with a yellow ball. Find the number of ways in which the boxes can be filled.

(1) 83
(2) 107
(3) 93
(4) 97
(5) 103
29476
@amresh_maverick said:
There are two trains - A and B, both starting from point S, with train A starting 10 seconds after train B. The length and speed for train A and train B are 100 m, 270 kmph and 200 m, 216 kmph respectively. How much time after start will train A reach train B €™s tail?

600 m will be the distance covered by train.
adding the 100 m of the first train
we will get the required distance as 500/15=33.33 seconds
29477
@Marchex said:
N positive real numbers have a product of unity. Their sum must be(1) divisible by N. (2) equal to N + 1/N (3) at least N. (4) a natural number. (5) None of theseNeed Solution also
for solution
use
AM>=GM

[a1*a2*a3*....*a(n/2) *1/a1 *1/a2 *1/a3 *.....1/a(n/2) ]^1/n>=[a1+a2+..+a(n/2) +1/a1+1/a2+....+1/a(n/2)]/n {n/2 is the subscript}

1*n>=a1+a2+..+a(n/2) +1/a1+1/a2+....+1/a(n/2)

hence 3
29478
@Marchex said:
Nine boxes are numbered 1, 2, €Ś €Ś 9. Each box must be filled with a ball which is of one of the three colours white, black and yellow. Boxes which are filled with either a white ball or a black ball must have consecutive numbers. At least 6 boxes must be filled with a yellow ball. Find the number of ways in which the boxes can be filled.(1) 83 (2) 107 (3) 93 (4) 97 (5) 103

6Y 3 B/W
7 triplets of 3 consecutive nos
7*2^3*1=56 [each ball can be filled with either black or white]

7y 2 b/w
8 pairs of 2 consecutive nos
8*2^2=32

8Y 1b/w
9*2=18

9Y
1


56+32+18+1=107


29479
There is a water tank of capacity 1,000 L with two inlet pipes A and B that can pump in water at the rate of 50 L/hr and 25 L/hr respectively. An outlet pipe C attached to the tank can pump out water at the rate of 50.
Initially the tank is full and the outlet pipe is opened. Now when the water in the tank is (3/4)th of the maximum volume of water that it can hold, both the inlet pipes are opened until the tank becomes full after which they are closed back. This process is repeated for an infinite number of times. Find the volume of water in the tank as a fraction of the capacity of the tank after 205 hrs.
29480
@shattereddream said:
How many digits cannot be the unit €™s digit of the product of 3 three-digit numbers whose sum is 989? Options- 2,4,1,3
3?
3,8,9 are not possible
unit's digit
1*1*7=7
1*2*6=2
1*3*5=5
1*8*0=0
1*4*4=6
3*4*2=4
9*9*1=1
29481
@Marchex said:
What is the remainder when 90^91 is divided by 13?(1) 0 (2) 7 (3) 12 (4) 1
-1 or 12
29482
@amresh_maverick said:
There are two trains - A and B, both starting from point S, with train A starting 10 seconds after train B. The length and speed for train A and train B are 100 m, 270 kmph and 200 m, 216 kmph respectively. How much time after start will train A reach train B €™s tail?
OA: 26.67

A man starts from point A and walks northwards at the speed of 6 km/hr. He then turns right and walks eastwards at the speed of 4 km/hr, turns right again and walks southwards at the speed of 8 km/hr and turns left and walks eastwards at the rate of 6 km/hr. The time he walks in various directions is inversely proportional to the speed with which he walks. If the total distance that he covers is equal to 100 km then find how far he is from the starting point?
29483
@amresh_maverick said:
There is a water tank of capacity 1,000 L with two inlet pipes A and B that can pump in water at the rate of 50 L/hr and 25 L/hr respectively. An outlet pipe C attached to the tank can pump out water at the rate of 50.Initially the tank is full and the outlet pipe is opened. Now when the water in the tank is (3/4)th of the maximum volume of water that it can hold, both the inlet pipes are opened until the tank becomes full after which they are closed back. This process is repeated for an infinite number of times. Find the volume of water in the tank as a fraction of the capacity of the tank after 205 hrs.
1/4 capacity=250
250/50=5 hours

250/25=10 hours

in 15 hours tank becomes full again

205 mod 15= 10

tank empties to 3/4 in another 5

and in next 5 5*25 L are filled=125
750+125 = 875?
29484
@Marchex said:
did it in night itself
must be 1800/7
g2=g1/3
g3=g1/6
g4=g1/10
g5=g1/15
g6=g1/21 = 5400/21=1800/7
29485

plz puys.... help this !!!!


what is the digit in the unit's place of the quotient of

10^40000/(10^400+40).