Official Quant thread for CAT 2013

@19rsb said:
A train, an hour after starting, meets with anaccident which detains it for a half hour, afterwhich it proceeds at 3/4 of its former rate andarrives 3(1/2) hours late. Had the accidenthappened 90 kilometers farther along the line, itwould have arrived only 3 hour late.What was the length ofthe trip in kilometers?......Dont hav the OA so post answer with your approach
let speed = 4x
and distance = D

D/4x + 3.5 = 1.5 + (D - 4x)/3x
D/4x + 3 = 1.5 + 90/4x + (D - 4x - 90)/3x

(1) - (2)
=> x = 15

speed will be = 60 and distance = 600 km
@19rsb said:
A train, an hour after starting, meets with anaccident which detains it for a half hour, afterwhich it proceeds at 3/4 of its former rate andarrives 3(1/2) hours late. Had the accidenthappened 90 kilometers farther along the line, itwould have arrived only 3 hour late.What was the length ofthe trip in kilometers?......Dont hav the OA so post answer with your approach

4/3t=3
t=9/4
also,
90*2=s
D=180*9/4 = 405
405 + 180 = 585
@sujamait said:
how wud i knoe what are here respective terminuses ? i cud assume both to be A also ..
Sir 'terminuses' diya hua tha. So, I assumed both to be different.

Waise even if we assume both to be A, answer would be same. :D

7/(x-7)=(x-3)/(x+3)
=> x=17
@sujamait said:
Ram, a farmer, managed to grow shapedwatermelons inside glass cases of differentshapes. The shapes he used were: a perfect cube, hemi-spherical, cuboid, cylindrical along with the normal spherical shaped watermelons. Thickness of the skin was same for all the shapes. Each of the glass cases was so designed that the total volume and the weight of the all the watermelons would be equal irrespective of the shape. A customer wants to but water-melons for making juice, for which the skin of the watermelon has to be peeled off, and therefore is a waste. Which shape should the customer buy? (1 mark)(1) Cube (2) Hemi-sphere(3) Cuboid (4) Cylinder(5) Normal spherical
Should be spherical I guess. Sphere has the least surface area. So, customer would buy the product in which he has to peel off the least.
@sujamait said:
han yar yeh sitters exam mein rah jate hein..pata nhn chal pata...Ram, a farmer, managed to grow shapedwatermelonsinside glass cases of differentshapes. The shapes he used were: a perfect cube,hemi-spherical, cuboid, cylindrical along with thenormal spherical shaped watermelons. Thicknessof the skin was same for all the shapes. Each ofthe glass cases was so designed that the totalvolume and the weight of the all the watermelonswould be equal irrespective of the shape.A customer wants to but water-melons formaking juice, for which the skin of the watermelonhas to be peeled off, and therefore is awaste. Which shape should the customer buy? (1mark)(1) Cube (2) Hemi-sphere(3) Cuboid (4) Cylinder(5) Normal spherical
5) Normal spherical?
@19rsb said:
A train, an hour after starting, meets with anaccident which detains it for a half hour, afterwhich it proceeds at 3/4 of its former rate andarrives 3(1/2) hours late. Had the accidenthappened 90 kilometers farther along the line, itwould have arrived only 3 hour late.What was the length ofthe trip in kilometers?......Dont hav the OA so post answer with your approach
600 km?

x/S + 0.5 + 4(d-x)/3S = d/S + 3.5
(x + 90)/S + 0.5 + 4(d-x-90)/3S = d/S + 3

90/S + 4(-90)/3S = -0.5
-30/S = -0.5
S = 60kmph

x/60 = 1
x = 60
1.5 + 4(d - 60)/180 = d/60 + 3.5
(4d - 240 - 3d)/180 = 2
d - 240 = 360
d = 600km

PS: I'm sure there is a shorter method :)
@sujamait said:
Suresh, who runs a bakery, uses a conical shapedequipment to write decorative labels (e.g., HappyBirthday etc.) using cream. The height of thisequipment is 7 cm and the diameter of the base is5 mm. A full charge of the equipment will write330 words on an average. How many words canbe written using three fifth of a litre of cream?(1.5 marks)(1) 45090 (2) 45100(3) 46000 (4) 43200(5) None of the above..........................................................OA 25
Is it 144000 words?

h = 70
r = 2.5
V = 1/3 * 22/7 * 2.5 * 2.5 * 70 = 1375/3

1375/3 cubic mm writes 330 words
3/5 * 10^6 cubic mm writes
330 * 3/5 * 10^6 *3 / 1375
= 144000 words
A quick search revealed that ticket from Jamshedpur
to Delhi is available in two trains. Trains 12801 and
12443 depart from Jamshedpur station at 06:45 hrs
and 15.55 hrs and reach Delhi next day at 04:50 hrs
and 10:35 hrs respectively. Trains 12444 and 12802
start from Delhi at 17:20 hrs and 22:20 hrs and reach
Jamshedpur next day at 10:35 hrs and 20:05 hrs
respectively.
Another option is to reach Ranchi by a three hour
road trip and take a flight to Delhi from Ranchi. The
distance between Ranchi and Delhi is covered in 105
minutes both-ways by any of the scheduled flights.
Air India operates two flights, AI 9810 and AI 810,
which depart Ranchi at 8:00 hrs and 15:25 hrs
respectively. Flight number IT-3348 operated by
Kingfisher Airlines departs Ranchi at 19:20 hrs.
Return flights operated by Air India, AI 9809 and AI
809, depart Delhi at 5:50 hrs and 11:00 hrs
respectively. Flight number IT-3347 operated by
Kingfisher Airlines departs Delhi at 17:10 hrs.
From Tina €™s home Jamshedpur railway station is five
minutes drive, and her destination at Delhi is 90
minutes and 30 minutes drive from airport and
railway station respectively. One has to reach the
airport at least one hour before the scheduled
departure to complete the boarding procedure. At
every railway station she loses five minutes in
navigating through the crowd.
6. If Tina wants to minimize the total time out of
Jamshedpur, the best option for her, from the
options given below, is: (1.5 marks)
(1) AI 9810 and return by IT 3347.
(2) AI 9810 and return by train number 12802.
(3) IT 3348 and return by AI 9809.
(4) Train number 12443 and return by train
number 12444.
(5) AI 9810 and return by train number 12444.
7. Tina gets a message that her work has to be
completed between 9:00 hrs. and 17:00 hrs. If
she wants minimize the total time out of
Jamshedpur, the best option, from the options
given below, for her among the following is to go
by (1.5 marks)

(1) Train 12443 and return by Train 12444.
(2) Train 12801 and return by Train 12802.
(3) AI 9810 and return by AI 9809.
(4) AI 810 and return by AI 9809.
(5) IT 3348 and return by IT 3347.
8. Tina has to appear for an exam on 8th of January
in Jamshedpur and she can start from her
residence in Jamshedpur only after 16:00 hrs of
the same day. Choose the option, from the
options given below, that will help her to
minimize the total time out of Jamshedpur. (1.5
marks)
(1) Go by Train 12443 and return by Train 12444
(2) Go by Train 12443 and return by AI 9809
(3) Go by IT 3348 and return by Train 12801
(4) Go by AI 810 and return by Train 12801
(5) Go by AI 9810 and return by AI 9809
9. If Tina decides to minimize the in-between
waiting period, the option that she should choose
from the options given below, will be: (1.5 marks)
(1) Go by Train 12801 and return by IT 3347
(2) Go by Train 12443 and return by Train 12802
(3) Go by AI 9810 and return by Train 12802
(4) Go by AI 810 and return by AI 9809
(5) Go by IT 3348 and return by AI 809

@sujamait said:
han yar yeh sitters exam mein rah jate hein..pata nhn chal pata...Ram, a farmer, managed to grow shapedwatermelonsinside glass cases of differentshapes. The shapes he used were: a perfect cube,hemi-spherical, cuboid, cylindrical along with thenormal spherical shaped watermelons. Thicknessof the skin was same for all the shapes. Each ofthe glass cases was so designed that the totalvolume and the weight of the all the watermelonswould be equal irrespective of the shape.A customer wants to but water-melons formaking juice, for which the skin of the watermelonhas to be peeled off, and therefore is awaste. Which shape should the customer buy? (1mark)(1) Cube (2) Hemi-sphere(3) Cuboid (4) Cylinder(5) Normal spherical
normal sphere should be answer
@19rsb said:
A train, an hour after starting, meets with anaccident which detains it for a half hour, afterwhich it proceeds at 3/4 of its former rate andarrives 3(1/2) hours late. Had the accidenthappened 90 kilometers farther along the line, itwould have arrived only 3 hour late.What was the length ofthe trip in kilometers?......Dont hav the OA so post answer with your approach
My solution:

Train travels for 1 hour, then halts for 1/2 and then suppose travels for " 4/3*t " hour
4/3*t because speed has become 3/4 of original, where "t" is time if there was no accident

Since the train was 7/2 hours late
hence, 1/2 + t/3 = 7/2 (t/3 is the extra time)
=> t = 9 hours

Had the accident taken place after 90kms, it would have got late by 3 hours
Similarly, t'/3 = 3 - 1/2 = 5/2
Hence t' = 7.5

So, from the above 2 values of "t" we can deduce that train travelled 90km in (9-7.5) = 1.5 hours
So, speed = 60kmph

Total travel time = 1+ 9 =10 hrs
Hence total distance = 60*10 = 600 kms
@sujamait said:
A quick search revealed that ticket from Jamshedpurto Delhi is available in two trains. Trains 12801 and12443 depart from Jamshedpur station at 06:45 hrsand 15.55 hrs and reach Delhi next day at 04:50 hrsand 10:35 hrs respectively. Trains 12444 and 12802start from Delhi at 17:20 hrs and 22:20 hrs and reachJamshedpur next day at 10:35 hrs and 20:05 hrsrespectively.Another option is to reach Ranchi by a three hourroad trip and take a flight to Delhi from Ranchi. Thedistance between Ranchi and Delhi is covered in 105minutes both-ways by any of the scheduled flights.Air India operates two flights, AI 9810 and AI 810,which depart Ranchi at 8:00 hrs and 15:25 hrsrespectively. Flight number IT-3348 operated byKingfisher Airlines departs Ranchi at 19:20 hrs.Return flights operated by Air India, AI 9809 and AI809, depart Delhi at 5:50 hrs and 11:00 hrsrespectively. Flight number IT-3347 operated byKingfisher Airlines departs Delhi at 17:10 hrs.From Tina €™s home Jamshedpur railway station is fiveminutes drive, and her destination at Delhi is 90minutes and 30 minutes drive from airport andrailway station respectively. One has to reach theairport at least one hour before the scheduleddeparture to complete the boarding procedure. Atevery railway station she loses five minutes innavigating through the crowd.6. If Tina wants to minimize the total time out ofJamshedpur, the best option for her, from theoptions given below, is: (1.5 marks)(1) AI 9810 and return by IT 3347.(2) AI 9810 and return by train number 12802.(3) IT 3348 and return by AI 9809.(4) Train number 12443 and return by trainnumber 12444.(5) AI 9810 and return by train number 12444.7. Tina gets a message that her work has to becompleted between 9:00 hrs. and 17:00 hrs. Ifshe wants minimize the total time out ofJamshedpur, the best option, from the optionsgiven below, for her among the following is to goby (1.5 marks)(1) Train 12443 and return by Train 12444.(2) Train 12801 and return by Train 12802.(3) AI 9810 and return by AI 9809.(4) AI 810 and return by AI 9809.(5) IT 3348 and return by IT 3347.8. Tina has to appear for an exam on 8th of Januaryin Jamshedpur and she can start from herresidence in Jamshedpur only after 16:00 hrs ofthe same day. Choose the option, from theoptions given below, that will help her tominimize the total time out of Jamshedpur. (1.5marks)(1) Go by Train 12443 and return by Train 12444(2) Go by Train 12443 and return by AI 9809(3) Go by IT 3348 and return by Train 12801(4) Go by AI 810 and return by Train 12801(5) Go by AI 9810 and return by AI 98099. If Tina decides to minimize the in-betweenwaiting period, the option that she should choosefrom the options given below, will be: (1.5 marks)(1) Go by Train 12801 and return by IT 3347(2) Go by Train 12443 and return by Train 12802(3) Go by AI 9810 and return by Train 12802(4) Go by AI 810 and return by AI 9809(5) Go by IT 3348 and return by AI 809
decision making wale thread mein post karo sir. :)
Data Sufficency question.

S and T are two water pumps that run at constant rates. If pump T pumped alone, how many more hours would it take for it to finish pumping a large container than it would take for pump S to accomplish the same task by itself?

(1) When both the water pumps work together, they finish pumping a large container in 23 rd the time it takes for pump S to finish the task alone.

(2) Pump T is capable of pumping a large container in twice the time that it takes pump S to accomplish the same task alone


a) using 1 alone
b) using 2 alone
c) using both
d) using either
e) cannot be answered using both
@grkkrg said:
Is it 144000 words?h = 70r = 2.5V = 1/3 * 22/7 * 2.5 * 2.5 * 70 = 1375/31375/3 cubic mm writes 330 words3/5 * 10^6 cubic mm writes 330 * 3/5 * 10^6 *3 / 1375= 144000 words
bhai.....43200 aa raha hai mera to with same calculation....
Answer none hi hai kya @sujamait
@ashish100 said:
bhai.....43200 aa raha hai mera to with same calculation....Answer none hi hai kya @sujamait
yup

consider f(x) =9^x/(9^x + 3) what is value of f(1/401) + f(2/401) + f(3/401).... f(400/401)..?

@hedonistajay said:
consider f(x) =9^x/(9^x + 3) what is value of f(1/401) + f(2/401) + f(3/401).... f(400/401)..?
200?
Here, f(x) + f(1-x) = 1
Hence, f(1/401) + f(400/401) = 1
And so on...
There are 200 pairs so, f(1/401) + f(2/401) + f(3/401).... f(400/401) = 200
In a recent election for class president, Monika received 7 of the 10 votes and Alfred received 3 of the 10 votes that were cast by the class. When the machine was counting the votes, it malfunctioned and instead of giving the vote to the correct person, it gave the vote to each candidate with probability 1/2 (regardless of whom the vote was cast for). The probability that the machine gave each student the correct number of votes in the election can be expressed as a/b where a and b are positive, coprime integers. What is the value of a+b ?
@hedonistajay said:
In a recent election for class president, Monika received 7 of the 10 votes and Alfred received 3 of the 10 votes that were cast by the class. When the machine was counting the votes, it malfunctioned and instead of giving the vote to the correct person, it gave the vote to each candidate with probability 1/2 (regardless of whom the vote was cast for). The probability that the machine gave each student the correct number of votes in the election can be expressed as a/b where a and b are positive, coprime integers. What is the value of a+b ?
12 hai kya?
@ScareCrow28 said:
12 hai kya?
12,9,17 nahi hai... exact answer nahi hai mere pass
@hedonistajay said:
12,9,17 nahi hai... exact answer nahi hai mere pass
smjh ni aya..what are the options??