Official Quant thread for CAT 2013

MBA CAT 2024
7761
@19rsb said:
Usain Bolt(UB) needs {(1000/x)+x}ml of water to travel 1m at a speed of x meters per minute.He also needs 40ml of water per minute irrespective of his speed.What is the approximate optimum speed for UB to cover 500m such that his water intake is minimum.BEGIN YOUR MORNING WITH A "USER FRIENDLY" QUESTION
sqrt(1040) ??
7762
@Torque024 said:
In any case maximum he will have to check 3 machines. time taken to check should be So first 2 will be favourable also each event will have a probability associated with itD+D 1/2*1/3 =1/6 faveND+ND 1/2*1/3 =1/6 faveND+D+D 1/2*2/3*1/2 = 1/6D+ND+D 1/2*2/3*1/2= 1/6D+ND+ND 1/2*2/3*1/2= 1/6ND+D+ND 1/2*2/3*1/2= 1/6P(E)=(2*1/6)/(6*1/6) = 1/3@krum You have selected directly, don't we have to consider the Probability of selecting defective or the other? Would it be true for any case?
Not able to understand how are you calculating 1/2 and 1/3.

He doesn't have to check three machines.. cause it will count to 6*3 = 18 minutes.. and in that case he won't be able to catch the bus. So he has option to check only 2 machines...

The favorable cases can be
1. first two come out to be faulty.
2. first two non faulty => last two must be faulty.

so 2 favourable cases.
Total cases = 4C2 = 6

P(E) = 2/6 = 1/3
7763
@ScareCrow28 said:
Equation formed is coming out to be..:20,000/x + (1000/x +x)*500 = F(x)Differentiatingx=sqrt(1040) = 4root(65)Is the ans 4root(65) ??
@htomar said:
sqrt(1040) ??
u ppl are always ryt ........GENIUSES "in the making"......
@Torque024 said:
10sqrt(10)m/min?
bhai answr is 4rt65 m/min
7764
@19rsb said:
u ppl are always ryt ........GENIUSES "in the making"...... bhai answr is 4rt65 m/min
Bhai!!! Sharminda na karo
7765
In triangle ABC, AB = 13, BC = 15 and CA = 14. Point D is on BC with CD = 6. Point E is on BC such that ∠BAE = ∠CAD. Given that BE = p/q where p and q are relatively prime positive integers, find q.
OPTIONS

1) 338
2) 469
3) 463
4) 336
7766

Cost price of 12 oranges is equal to the selling price of 9 oranges and the discount on 10 oranges is equal to profit on 5 oranges. What is the percentage point difference between the profit percentage and the discount percentage?

Answer is 22.2%

7767
@ananthchief said:
Cost price of 12 oranges is equal to the selling price of 9 oranges and the discount on 10 oranges is equal to profit on 5 oranges. What is the percentage point difference between the profit percentage and the discount percentage?Answer is 22.2%
Let C.P=X, M.P.=Y, S.P.=Z
12X=9Z
10(Y-Z)=5(Z-X)

Solving above equations:
4X=3Z and 2Y=3X and 9Z=8Y
%Profit= (Z/X -1)*100 = ( 4/3 -1) *100 = 100/3%
%Discount = (Z/Y -1) * 100 =(8 /9 -1) =100/9%
Difference =100/3 - 100/9 = 200/9 =22.2%
7768
@ananthchief said:
Cost price of 12 oranges is equal to the selling price of 9 oranges and the discount on 10 oranges is equal to profit on 5 oranges. What is the percentage point difference between the profit percentage and the discount percentage?Answer is 22.2%
we hv
CP/SP=3/4

roughly we can get profit= 1x = SP-CP
Profit %= 1x/3x*100= 33.33

Discount= 5x/10= 0.5x

Discount %= .5x/4.5x*100= 11.11

Required diff= 33.33-11.11= 22.22
7769
@kingsleyx said:
(a) If a^x = b , b^y = c , c^z = a , then xyz = 0(b) If p = a^x, q =a^y, (p^y * q^x)^z = a^z, then xyz = 1.(c) If x^a = y^b = z^c and ab+bc+ca=0, then xyz=1.Find the statements which are true !!
In questions where we have some powers involved then there are then

(i) we should try and take logarithms and then try to multiply/add the logs to get the desired result
(ii) if there are multiple equality given in a single expression (for example in case (c) then we should equate each of them as 'k' and then proceed.


(a) taking logs we get x = log(b)/log(a), y = log(c)/log(b), z = log(a)/log(c)
multiplying all we get xyz=1.


(b) taking logs we get
xlog(a) =log(p).............(i)
ylog(a) =log(q).............(ii)
yzlog(p) + xzlog(q) = zlog(a)...........(iii)

replacing values of log(p) and log(q) in (iii)

xyzlog(a) + xyzlog(a) = zlog(a) => 2xyzlog(a) = zlog(a) => xy = 1/2

(c) x^a = y^b = z^c = k
=> log(x) = log(k)/a ; log(y) = log(k)/b; log(z) = log(k)c
=>log(x)+log(y)+log(z) = log(k)*(1/a+1/b+1/c)
=>log(xyz) = log(k)*(ab+bc+ca)/abc

since ab+bc+ca = 0 => log(xyz) = 0 => xyz =1.

ATDH.
7770
@pankaj1988 said:
In triangle ABC, AB = 13, BC = 15 and CA = 14. Point D is on BC with CD = 6. Point E is on BC such that ˆ BAE = ˆ CAD. Given that BE = p/q where p and q are relatively prime positive integers, find q.OPTIONS1) 338 2) 469 3) 463 4) 336
463?
7771
@pankaj1988 said:
In triangle ABC, AB = 13, BC = 15 and CA = 14. Point D is on BC with CD = 6. Point E is on BC such that ∠BAE = ∠CAD. Given that BE = p/q where p and q are relatively prime positive integers, find q.OPTIONS1) 338 2) 469 3) 463 4) 336
/_BAE =/_CAD
Hence, /_BAD= /_CAE

Using Sine rule,
CD/AC = sinCAD/sinADC = sinBAE/sinADC
And, CE/AC = sinCAE/sinAEC=sinBAD/sinAEC

Multiplying both equations
CD*CE/AC^2 = sinBAE*sinBAD/sinADC*sinAEC
= sinBAE*sinBAD/sinADB*sinAEB
=BE*BD/AE^2

Hence CD*CE/AC^2 = BE*BD/AE^2

From here, BE = 2535/463

Hence q=463

7772


@Enigma001 said:
R(6^84/49) = R(6^83/49)*R(6/49) ----> 1= x* 6 -----> 41R(8^84/49) = R(8^83/49) *R(8/49) ----> 1= y* 8------> 43Therefore, R{(41+43)/49} = 35.
Enigma001 :Can u explain how did u got values of x & y
7773
@ananthchief said:
Cost price of 12 oranges is equal to the selling price of 9 oranges and the discount on 10 oranges is equal to profit on 5 oranges. What is the percentage point difference between the profit percentage and the discount percentage?Answer is 22.2%
Let CP of 1 org = 300;
Sp of 1 org = 300*12/9= 400
Let MP be x
10(x-400)=5(400-300); Mp=450
%Difference=100((100/300)-(50/450)=200/9=22.2%
7774
@htomar said:
Not able to understand how are you calculating 1/2 and 1/3.He doesn't have to check three machines.. cause it will count to 6*3 = 18 minutes.. and in that case he won't be able to catch the bus. So he has option to check only 2 machines...The favorable cases can be 1. first two come out to be faulty.2. first two non faulty => last two must be faulty.so 2 favourable cases.Total cases = 4C2 = 6P(E) = 2/6 = 1/3
are bhai, for total cases I have considered that at max he have to check 3 machines, fourth one will be automatically D or ND. And here probability of machine to be D or ND is same so your method works. But if it were different, than answer would be not in accord.
7775

Knock Knock!!!
Has the world ended?

7776
A man borrows Rs. 6000 at 5% interest, on reducing balance, at the start of the year. If he repays Rs. 1200 at the end of each year, find the amount of loan outstanding, in Rs., at the beginning of the third year.
7777
@sowmyanarayanan said:
Knock Knock!!!Has the world ended?
Have to wait till 21st DEC for that :P
7778
@19rsb said:
Usain Bolt(UB) needs {(1000/x)+x}ml of water to travel 1m at a speed of x meters per minute.He also needs 40ml of water per minute irrespective of his speed.What is the approximate optimum speed for UB to cover 500m such that his water intake is minimum.BEGIN YOUR MORNING WITH A "USER FRIENDLY" QUESTION
i'll go for 4sqrt(65) m/min

7779
@ScareCrow28 said:
Have to wait till 21st DEC for that
by the speed of this thread i imagined the worst!! OMG!!
7780
@sowmyanarayanan said:
A man borrows Rs. 6000 at 5% interest, on reducing balance, at the start of the year. If he repays Rs. 1200 at the end of each year, find the amount of loan outstanding, in Rs., at the beginning of the third year.
Is it 4155?