*DI Marathon for CAT 2007*

[writetotanveer]

Here is something to start off with for Basics...

Regards
Tanveer

[writetotanveer]

I am posting old problems that had come as a part of the PG DI Problem-a-Day newsletter in 2006 (provided by a CAT Prep website)
Lets discuss these problems as a warm up...

Regards
Tanveer

Rahul Sharma has a factory which manufactures Alpha I, Beta I and Gamma I. All these are manufactured by processing Omega 34. Alpha I requires 1 kg/unit, Beta I requires 2 kg/unit and Gamma I Gamma I requires 2.5 kg per unit of Omega 34, which costs Rs. 2 per kilogram. The total availability of Omega 34 is 350 kilogram. the processing is done on a machine having production hours of 160 hours in day shift and 182 hours in the night shift. The time required per unit production is as follows.

Product// Day Shift// Night Shift

Alpha I //2 hours//2.5 hours

Beta I// 3 hours// 4.0 hours

Gamma I// 1 hour// 1.5 hours




The machine costs Rs. 1 per hour. Selling price of Alpha I Beta I and Gamma I are Rs. 8 per Unit, Rs. 12 per Unit and Rs. 3.50 per Unit respectively. At least 5o units of Alpha I have to be produced and at the most 150 units of Gamma I can be produced.

1. Which of the following is possible?
a) 75 units of Alpha 1, 4 units of Beta I in day shift, manufacture 40 units of
Beta I and 40 units of Gamma I and 10 units of Alpha I in night shift.
b) 75 units of Alpha I, 4 units of Beta I, in the day shit. Manufacture 40 units of
Beta I and 40 units of Gamma I and 5 units of Alpha I in night shift.
c) 74 units of Alpha I, 4 units of Beta I in day shift, 25 units of Beta I, and 10
units of Gamma I and 30 units of Alpha I in night shift.
d) 74 units of Alpha I, 5 units of Beta I in day shift, 40 units of Beta I, 10 units
of Gamma I and 30 units of Alpha I in night shift.

2. What percentage of the available raw material is utilised if 100 units of Alpha I, 40 units of Beta I, and 10 units of Gamma I are produced?

a) 50% b) 58% c) 68% d) 78%



3. If Rahul Sharma spends initially 150 machine hours in day shift to manufacture Gamma I, 10 hours to manufacture Alpha I, and in the night shift manufactures 53 units of Gamma I and spends the rest of the night shift to manufacture Alpha 1. What will be his profit/loss?

a) loss of Rs. 65 b) profit Rs. 65
c) No profit to loss d) This manufacturing pattern is not possible



4. If the minimum possible manufacturing requirement for Alpha I is met and the remaining raw material is utilised for the manufacture of the other 2 products then

a) 10 units of Beta I can be manufactured
b) 0 units of Beta I can be manufactured
c) 5 units of Beta I can be manufactured
d) Any of the above



5. If in the shift, 65 units of Alpha I, 4 units of Beta I, 15 units of Gamma I and in the night shift. 20 units of Beta 1,40 units of Gamma I and 20 units of Alpha I are manufactured then which of the following is true?

I. 5 hours of machine time is unutilised
II. Total cost of production is Rs. 54
III. More than 20% of the available raw material is unutilised

a) I only b) II only c) I and III d) I and II

[amrutesh666]

Aw right, W.R.T CAT 07, we’ve seen that there are enough threads running for both QA and VA but in the case of DI, this seems to be the only thread and unfortunately dormant. My humble efforts in infusing some life into this thread To begin with, can we have the title of the thread changed to *DI Marathon*,just to catch everyone’s attention.

Just to keep things in order, the caselets will be numbered. I’ll be posting the first question today evening. Anybody can post the next caselet, but only after the previous one is stripped open completely . A maximum of 2 days will be given to solve it. If no one is unable to do it with in 2 days, then the person who gave the question will post the detailed solution.

Since, there are no pre requisites to go about with this section, Im expecting some participation right from today.

Good Day
Amrutesh

[krsh.vik]

Originally Posted by amrutesh666

Aw right, W.R.T CAT 07, we’ve seen that there are enough threads running for both QA and VA but in the case of DI, this seems to be the only thread and unfortunately dormant. My humble efforts in infusing some life into this thread To begin with, can we have the title of the thread changed to *DI Marathon*,just to catch everyone’s attention.

Just to keep things in order, the caselets will be numbered. I’ll be posting the first question today evening. Anybody can post the next caselet, but only after the previous one is stripped open completely . A maximum of 2 days will be given to solve it. If no one is unable to do it with in 2 days, then the person who gave the question will post the detailed solution.

Since, there are no pre requisites to go about with this section, Im expecting some participation right from today.

Good Day
Amrutesh

Good initiative bro
I will try to participate actively in the discussions here ...

[amrutesh666]

Solution to the problem given by Tanveer

Rahul Sharma has a factory which manufactures Alpha I, Beta I and Gamma I. All these are manufactured by processing Omega 34. Alpha I requires 1 kg/unit, Beta I requires 2 kg/unit and Gamma I Gamma I requires 2.5 kg per unit of Omega 34, which costs Rs. 2 per kilogram. The total availability of Omega 34 is 350 kilogram. the processing is done on a machine having production hours of 160 hours in day shift and 182 hours in the night shift. The time required per unit production is as follows.

Product// Day Shift// Night Shift

Alpha I //2 hours//2.5 hours

Beta I// 3 hours// 4.0 hours

Gamma I// 1 hour// 1.5 hours




The machine costs Rs. 1 per hour. Selling price of Alpha I Beta I and Gamma I are Rs. 8 per Unit, Rs. 12 per Unit and Rs. 3.50 per Unit respectively. At least 5o units of Alpha I have to be produced and at the most 150 units of Gamma I can be produced.

1. Which of the following is possible?
a) 75 units of Alpha 1, 4 units of Beta I in day shift, manufacture 40 units of
Beta I and 40 units of Gamma I and 10 units of Alpha I in night shift.
b) 75 units of Alpha I, 4 units of Beta I, in the day shit. Manufacture 40 units of
Beta I and 40 units of Gamma I and 5 units of Alpha I in night shift.
c) 74 units of Alpha I, 4 units of Beta I in day shift, 25 units of Beta I, and 10
units of Gamma I and 30 units of Alpha I in night shift.
d) 74 units of Alpha I, 5 units of Beta I in day shift, 40 units of Beta I, 10 units
of Gamma I and 30 units of Alpha I in night shift.

Solution: 75 units of Alpha, 4 units of Beta in day shift accounts to 75*2 + 4*3 =162 hrs, but day shift is only for 160 hrs. so a) and b) ruled out.
74 units of Alpha nd 4 units of Beta accounts to 160 hrs. cool. but 25 units of Beta, 10 units of Gamma and 30 units of Alpha in night ashift accounts to 25*4 + 10*1.5 + 20*2.5 =190 hrs, but a night shift is for 182 hrs
So where is the answer

2. What percentage of the available raw material is utilised if 100 units of Alpha I, 40 units of Beta I, and 10 units of Gamma I are produced?

a) 50% b) 58% c) 68% d) 78%

Answer: b) 58%
Solution: (100*1 + 40*2 + 10*2.5)/ 350 =58%

3. If Rahul Sharma spends initially 150 machine hours in day shift to manufacture Gamma I, 10 hours to manufacture Alpha I, and in the night shift manufactures 53 units of Gamma I and spends the rest of the night shift to manufacture Alpha 1. What will be his profit/loss?

a) loss of Rs. 65 b) profit Rs. 65
c) No profit to loss d) This manufacturing pattern is not possible

Answer: d)
Solution: Since 1 unit of Gamma 1 requires 1 hr of processing, eventually more than 150 units will be produced, which shouldnt be according to the question.

4

. If the minimum possible manufacturing requirement for Alpha I is met and the remaining raw material is utilised for the manufacture of the other 2 products then

a) 10 units of Beta I can be manufactured
b) 0 units of Beta I can be manufactured
c) 5 units of Beta I can be manufactured
d) Any of the above

Answer: d)
Solution: Min of 50 units of Alpha I have to be produced, ie it'll take up 50 kgs of the raw material. From the remaining 300 kgs, a max of 120 units of Gamma I can be produced, which is way below the upper limit of 150. Hence d)

5. If in the shift, 65 units of Alpha I, 4 units of Beta I, 15 units of Gamma I and in the night shift. 20 units of Beta 1,40 units of Gamma I and 20 units of Alpha I are manufactured then which of the following is true?

I. 5 hours of machine time is unutilised
II. Total cost of production is Rs. 54
III. More than 20% of the available raw material is unutilised

a) I only b) II only c) I and III d) I and II

Solution:
(I) Time utilised in the morning shift: 65*2 + 4*3 + 15*1 =157 hrs(3 hrs unutilised)
Time utilized in the night shift: 20*4 + 40*1.5 + 20*2.5 =190 hrs
so, actually 5 hrs of time overutilised. so False
(II) Total production cost: Defintely not 54. Machine costs only exceed 54 so False
(III) Raw material utilised: 85*1 + 24*2 + 55*2.5 = 270.5 kgs . sos untilised = 80 kgs approx= 80/350 > 20% True
But look at the choices

[Mahip]

This is the official thread for Di,
*DI Marathon for CAT 2007*

[amrutesh666]

Q.No.1

The points tally table of the mini-worldcup that is to be played in 2037 is hacked by a time traveler from Cybernetics Corporation, so that it can be used to revive the betting industry that would be well dead by then.

Twelve cricket teams participated and they were put into 2 different Pools A and B. In the first round each tean played a match against all other teams in its pool. 3 top teams (ie with better averages) from each pool qualified for Supersix round, where all the teams played against each other once. Again 3 teams with highest average qualified for the final round. In the final round , the 3 teams played against each other and the team with the highest average was declared the winner.

The points system.
2 points for a win.
-1 for a loss.
1 to each team in case of a tie.
Average= Total points/ Number of matches played by the team.

Also, the following info is known.
1. The winner won both its matches in the final round.
2. In the super six round, the total points earned by all the teams are 50.

Pool A
Team / Ban / Ind / Ken / Nz / Eng / SA
Total /14 / 0 / 5 / 0 / 8 / 3
Average /1.17 / 0 / 0.5 / 0 / 0.8 / 0.6

Pool B
Team / Aus / Ire / Pak / SL / WI / Zim
Total / -3 / 13 / 3 / 6 / 2 / 7
Average / -0.6 / 1.08 / 0.6 / 0.6 / 0.4 / 0.58

Note: The formatting has gone haywire. Kindly adjust.



1. Which 2 teams do not play against each other in the finals?
a) Ban, Ire b)Ban,Zim c)Eng, Ire d)Ire, Zim

2.Find the number of matches won by Ind and Nz in the first round.
a) 0 b) 1 c) 2 d) 3

3. How many points did the second runner up earn in the final round?
a) -2 b) 1 c) 2 d) Cannot be determined

4.After supersix round, the highest average points of any team are
a) 1 b)1.2 c)1.3 d) Cannot be determined

[Fabio capello]

Originally Posted by amrutesh666

Q.No.1

right now at office will solve at home

[doomsayer]

Originally Posted by amrutesh666

Q.No.1


1. Which 2 teams do not play against each other in the finals?
a) Ban, Ire b)Ban,Zim c)Eng, Ire d)Ire, Zim

Thanks amrthesh for the initiative..

1) ans c

after that i am stuck.
"In the super six round, the total points earned by all the teams are 50."

This statement is very ambiguous.If it's means total points obtained in super6 only
(with out taking points from first round) then it's not feasible.Beause in sup6 total no matches r 15.So max total points possible is 30.

if it's meant total from first and sup6 then also a prob.
after sup6 total points =50.
total after final =58.
In three matches we cannt obtain 8 points.

plz throw some light here..

[Fabio capello]

Originally Posted by amrutesh666

Q.No.1

The number of guess are more than tries...
1-c
2-c
3-D
4-D