Official Quant thread for CAT 2013

MBA CAT 2024
12181
@choosen04 said:
A manufacturer produces two types of products-A and B, which are subjected to two types of
operations, viz. grinding and polishing. Each unit of product A takes 2 hours of grinding and 3 hours of polishing whereas product B takes 3 hours of grinding and 2 hours of polishing. The manufacturer has 10 grinders and 15 polishers. Each grinder operates for 12 hours/day and each
polisher 10 hours/day. The profit margin per unit of A and B are Rs. 5/- and Rs. 7/- respectively. If
the manufacturer utilises all his resources for producing these two types of items, what is the
maximum profit that the manufacturer can earn?
A. Rs.280/- B. Rs.294/- C. Rs.515/- D. Rs.550/- E. None of the above
Profit = 5A + 7B
Also ; 2A + 3B
Solving we Get Profit = 5 x 42 + 7 x 12 = 294 /-
12182
@IIM-A2013 said:

Mini and vinay are quiz masters preparing for a quiz. in x minutes, Mini makes y questions more than vinay. If it were possible to reduce the time needed by each to make a question by two minutes, then in x minutes Mini would make 2y questions more than vinay. How many questions does Mini make in x minutes?
a. 1/4[2(x+y)-(2x^2 + 4y^2)^1/2]

b.1/4[2(x-y)-(2x^2 + 4y^2)^1/2]

c. either a or b

d. 1/4[2(x-y)-(2x^2 - 4y^2)^1/2]

please suggest .

@19rsb ;
@soumitrabengeri ; @grkkrg ----- > Bhai log any 1 tried dis .....m get a weird ans
12183
@choosen04 said:
A manufacturer produces two types of products-A and B, which are subjected to two types ofoperations, viz. grinding and polishing. Each unit of product A takes 2 hours of grinding and 3 hours of polishing whereas product B takes 3 hours of grinding and 2 hours of polishing. The manufacturer has 10 grinders and 15 polishers. Each grinder operates for 12 hours/day and eachpolisher 10 hours/day. The profit margin per unit of A and B are Rs. 5/- and Rs. 7/- respectively. Ifthe manufacturer utilises all his resources for producing these two types of items, what is themaximum profit that the manufacturer can earn?A. Rs.280/- B. Rs.294/- C. Rs.515/- D. Rs.550/- E. None of the above
294?
12184
@karan20 said:
@19rsb ;@soumitrabengeri ; @grkkrg ----- > Bhai log any 1 tried dis .....m get a weird ans
Had tried this from Arun Sharma..i have solved this on PG earlier too..nahi aaya tha :(
Here is the link where i referred
http://www.pagalguy.com/forums/quantitative-ability-and-di/time-speed-work-alligations-mixtures-problems-t-9280/p-229611/r-2920263
12185
@choosen04 said:
A manufacturer produces two types of products-A and B, which are subjected to two types ofoperations, viz. grinding and polishing. Each unit of product A takes 2 hours of grinding and 3 hours of polishing whereas product B takes 3 hours of grinding and 2 hours of polishing. The manufacturer has 10 grinders and 15 polishers. Each grinder operates for 12 hours/day and eachpolisher 10 hours/day. The profit margin per unit of A and B are Rs. 5/- and Rs. 7/- respectively. Ifthe manufacturer utilises all his resources for producing these two types of items, what is themaximum profit that the manufacturer can earn?A. Rs.280/- B. Rs.294/- C. Rs.515/- D. Rs.550/- E. None of the above
xi is number of units of product A
y is number of units of product B

2x+3y=120
3x+2y=150

5y=60
y=12
x=42

42*5+12*7
210+84
294


12186
@IIM-A2013

Should be Option A:1/4[2(x+y)-(2x^2 + 4y^2)^1/2]

Approach:

Let r be the no. of ques made by Mini in x min
Then, No. of ques made by Vinay in x min= (r-y)

Thus, New time of Mini to make 1 ques=(x/r -2) min..
Conversely, Mini makes 1/(x/r -2) ques in 1 min

Therefore, Mini will make = x/(x/r -2) ques in x min

Furthermore, New time of Vinay to make 1 ques=(x/r-y -2) min
Conversely, Vinay makes 1/(x/r-y -2) ques in 1 min

Therefore, Vinay will make= x/(x/r-y - 2) ques in x min

Given, x/(x/r - 2) = x/(x/r-y -2) + 2y

=> r^2 - r(x+y) +x/8(x +4y)= 0

=>r = {(x+y) +/- [(x+y)^2 - 4*x/8*(x+4y)]^(1/2)}/2

=> r = {(x+y) +/- [1/2*x^2 +y^2]}/2

=>r = 1/2*{(x+y) +/- 1/2*[2x^2 + 4y^2]}

=>r = 1/4*{2(x+y) +/- (2x^2 + 4y^2)}

Since, in the options, there no value corresponding to +ve sign... we have only Option A as our correct answer..

PS:: Jo bhi ques tha..G***R F***U lengthy tha...
12187
@soumitrabengeri in how many ways can we select 3 dots out of a 5Ä‚—5 grid of square dots to form triangle? help

12188
@jaiswalicsi said:
@soumitrabengeri in how many ways can we select 3 dots out of a 5 —5 grid of square dots to form triangle? help
2160?

total dots = 25
number of colinear dots = 5C3*5*2 + 2*(2*1 + 2*4 + 10) = 100 + 2*(20) = 140

So answer = 25C3 - 140 = 2300 - 140 = 2160
12189
@grkkrg said:
2160?total dots = 25number of colinear dots = 5C3*5*2 + 2*(2*1 + 2*4 + 10) = 100 + 2*(20) = 140So answer = 25C3 - 140 = 2300 - 140 = 2160
bhai ye colinear wala explain kr do kaise nikala
m dong like this
selecting 3 consecutive points out of 5 points in a row =5-3+1=3 ways now this can happen in a row or column in25 ways so total collinear =75 ways

p.s dont have oa pls check my approach,and explain yours
12190
@jaiswalicsi said:
bhai ye colinear wala explain kr do kaise nikalam dong like this selecting 3 consecutive points out of 5 points in a row =5-3+1=3 ways now this can happen in a row or column in25 ways so total collinear =75 waysp.s dont have oa pls check my approach,and explain yours
1) They need not be consecutive 😁 So you can select any 3 out of 5 points => 5C3
So 5C3*5 for 5 rows
Repeat same for columns => 2 * (5C3 * 5) = 100

2) The points can also be linear diagonally. Here again we have to cases:
bottom left to top right:
3C3 + 4C3 + 5C3 + 4C3 + 3C3 = 1 + 4 + 10 + 4 + 1 = 20

top left to bottom right:
20

Total = 100 + 20 + 20 = 140

So exclude this in your count.
You will get 25C3 - 140 as the answer. :)
12191
The Data section of the JMAT exam has 4 caselets of equal length (in words), with 5, 8, 8 and 6 questions respectively. While writing this test, Bilu can answer exactly 12 questions in the time that he takes to read any one of the four caselets. If his rate of answering questions remains the same, by what percent should Bilu increase his speed of reading the caselets so that he can reduce his total time by 10% ?
options
20
18.5
25
15

actually i m nt able t undrstnd que?
wht he is saying?
12192
@jaiswalicsi Sorry..i could not answer the question posted by you as i was studying offline..i would have used the same method as @grkkrg
12193
@hari_bang said:
The Data section of the JMAT exam has 4 caselets of equal length (in words), with 5, 8, 8 and 6 questions respectively. While writing this test, Bilu can answer exactly 12 questions in the time that he takes to read any one of the four caselets. If his rate of answering questions remains the same, by what percent should Bilu increase his speed of reading the caselets so that he can reduce his total time by 10% ?options2018.52515actually i m nt able t undrstnd que?wht he is saying?
18.5?
12194
@19rsb said:
18.5?
plz provide sol?
12195
@hari_bang said:
The Data section of the JMAT exam has 4 caselets of equal length (in words), with 5, 8, 8 and 6 questions respectively. While writing this test, Bilu can answer exactly 12 questions in the time that he takes to read any one of the four caselets. If his rate of answering questions remains the same, by what percent should Bilu increase his speed of reading the caselets so that he can reduce his total time by 10% ?options2018.52515actually i m nt able t undrstnd que?wht he is saying?
18.5?

total time taken 4*12 + (27) = 75
new time = 67.5
new reading time = (4*12 - 7.5)/12 = 4 - 7.5/12
Percentage increase in speed = (12/40.5 - 12/48)/(12/48) = (12/40.5 - 1/4)/(1/4)
= 48/40.5 - 1
= 7.5/40.5 = 1.5/8.1 = 18.51%
12196
@19rsb said:
18.5?
ur ans is rite...:)
12197
@sharmaa.abhay said:
Three people A, B, C participate in a cycling race. They start simultaneously from point P, reach another point Q, turn back without changing their speeds and return to P. In the process, each person meets each of the other 2 at either of the points R or S(b/w P and Q). RQ=10 km, SQ=18 km.What is the ratio of the fastest to the slowest? Assume P and Q are in a straight line.

(a) 2:1 (b)3:2 (c) 4:1 (d) 5:2 (e) Can't be determined

OA is (c). Please explain your approach.
P______S_________R________Q
Let PS =m ; SR = 8Km ; RQ = 10 km
A = Fastest ; B = Medium ; C = Slowest
Xa; Xb ; Xc be the speeds...
Xa/Xc =( m + 36)/m ; (m+28)/Xb = (m+8)/Xc ; (m+28)/Xa = (m + 8 )/ Xb
Solving above equations we get m = 12
Hence Xa/Xc = 4:1
12198
@grkkrg said:
18.5?total time taken 4*12 + (27) = 75new time = 67.5new reading time = (4*12 - 7.5)/12 = 4 - 7.5/12Percentage increase in speed = (12/40.5 - 12/48)/(12/48) = (12/40.5 - 1/4)/(1/4)= 48/40.5 - 1= 7.5/40.5 = 1.5/8.1 = 18.51%
bro
apki 1st line smjh nhi aa rhi in both sol?
12199
@hari_bang said:
broapki 1st line smjh nhi aa rhi in both sol?
I'm taking the time taken to answer one question as 1 unit.
Time taken to read 1 caselet = Time taken to answer 12 questions = 12 units
Time taken to read 4 caselets = 4*12 = 48 units
Time taken to answer all questions = 5 + 8 + 8 + 6 = 27 units
Total time = 48 + 27 = 75 units
12200
@grkkrg said:
I'm taking the time taken to answer one question as 1 unit.Time taken to read 1 caselet = Time taken to answer 12 questions = 12 unitsTime taken to read 4 caselets = 4*12 = 48 unitsTime taken to answer all questions = 5 + 8 + 8 + 6 = 27 unitsTotal time = 48 + 27 = 75 units
thnx a lot..bro
:)