Official Quant thread for CAT 2013

@sonamaries7 said:
P.Q.R=X.Y.Z=Q.A.YThe 7 letters correspond to the 7 unique digits chosen from 0 to 9.THe value of A is:0236none
question hi galat lag rha hai ab
if all are unique no.s
then the letters cant b 0,5,7 (prime)
then the left will have 3,6,9
now assigning 9 say P to one will lead to assigning 3 & 6 both to some other say X in order to reach equality
there will be no power of 3 left for Q/A/Y
same for 2,4,8
my take questionhi galat hai 😁 :D
@piyushrohella12 said:
question hi galat lag rha hai abif all are unique no.sthen the letters cant b 0,5,7 (prime) then the left will have 3,6,9now assigning 9 say P to one will lead to assigning 3 & 6 both to some other say X in order to reach equalitythere will be no power of 3 left for Q/A/Ysame for 2,4,8 my take questionhi galat hai
na na ...i dont put wrong qs ..it is an actual XAT qs..u may go back a few posts nd check for the soln....someone had put it..else just chk out last yrs XAT papers...the OA is 2
@karan20 said:
Rajiv is a student in a business school. After every test he calculates his cumulative average.QT and OB were his last two tests.83 marks in QT increased his average by 2. 75 marks in OB further increased his average by 1. Reasoning is the next test, if he gets 51 in Reasoning, his average willbe ___?A. 59 B. 60C. 61 D. 62E. 63
E) 63..?
Guyz I know Its not the correct Forum for this Kind of Question but Sab Expert Bhai Log isse Forum pe ha to plz Help :::

Decision Making Question

Read the following and choose the best alternative:

Decisions are often,risky in the sense that their outcomes are not known with certainty.Presented with a choice between a risky prospect that offers a 50 percent chance to win $200(otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighted by their probability of occurrence.) Preference for a sure outcome over risky prospect of equal expected value is called risk averse ; indeed, people tend to be risk averse when choosing between prospects with positive outcomes. The tendency towards risk aversion can be explained by the notion of diminishing sensitivity, fir st formalized by Daniel Bernoulli in 1738. Just as the impact of a candle is greater when it is brought into a dark room than into a room that is well lit so, suggested Ber noulli, the utility resulting from a small increase in wealth will be inversely proportional to the amount of wealth already in one s possession. It has since been assumed that people have a subjective utility function, and that preferences should be described using expected utility instead of expected value. According to expected utility, the worth of a gamble offering a 50 percent chance to win $200 (otherwise nothing) is 0.50 *u($200), where u is the person's concave utility function. (A function is concave or convex if a line joining two points on the curve lies entirely below or above the curves, respectively). Itfollows from a concave function that the subjective value attached to a gain of $100 is more than50 percent of the value attached to a gain of $200, which entails preference for the sure $100 gain and, hence, risk aversion.

Consider now a choice between losses. When asked to choose between a prospect that offers a 50 percent chance to lose $200 (otherwise nothing) and the alternative of losing $100 for sure, most people prefer to take an even chance at losing $200 or nothing over a sure $100 loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: the impact of an initial $100 loss is greater than that of the next $100. This results in a convex function for losses and a preference for risky prospects over sure outcomes of equal expected value, called risk seeking. With the exception of prospects that involve very small probabilities, risk aversion is generally observed in choices involving gains, whereas risk seeking tends to hold in choices involving losses.

Based on above passage, analyse the decision situations faced by three persons: Babu, Babitha and Bablu.

Q1. Suppose instant and further utility of each unit of gain is same for Babu. Babu has decided to play as many times as possible, before he dies. He expected to live for another 50 years. A game does not last more than ten seconds. Babu is confused which theory to trust for making decision and seeks help of a renowned decision making consultant: Roy Associates. What should be Roy Associates advice to Babu?

A. Babu can decide on the basis of Expected Value hypothesis.
B. Babu should decide on the basis of Expected Utility hypothesis.
C. Mr. Babu, I m redundant.
D. A and B
E. A, B and C

Q2. Babitha played a game wherein she had three options with following probalilities: 0.4, 0.5 and 0.8. The gains from three outcomes are likely to be $100, $80 and $50. An expert has pointed out that Babitha is a risk taking person. According to expected utility hypothesis, which optionis Babitha most likely to favour?

A. First
B. Second
C. Third
D. Babitha would be indifferent to all three actions.
E. None of the above.

Q3. Continuing with previous question, suppose Babitha can only play one more game, which theory would help in arriving at better decision?

A. Expected Value.
B. Expected Utility.
C. Both theories will give same results.
D. None of the two.
E. Data is insufficient to answer the question.

Q4. Bablu had four options with probalility of 0.1, 0.25, 0.5 and 1. The gains associated with each options are: $1000, $400, $200 and $100 respectively. Bablu chose the first option. As per expected value hypothesis:

A. Bablu is risk taking.
B. Expected value function is concave.
C. Expected value function is convex.
D. It does not matter which option should Babu choose.
E. None of above.
@shadowwarrior said:
E) 63..?
correct ... approach ... m not getting the correct1
@karan20 said:
Rajiv is a student in a business school. After every test he calculates his cumulative average.QT and OB were his last two tests.83 marks in QT increased his average by 2. 75 marks in OB further increased his average by 1. Reasoning is the next test, if he gets 51 in Reasoning, his average willbe ___?A. 59 B. 60C. 61 D. 62E. 63
63?
n=no. of subjects(initially)
x=average (initially)
nx+83=(n+1)(x+2)
2n+x=81...i

nx+83+75=(n+2)(x+3)
3n+2x=152....ii

solving i and ii

n=10,x=61
total marks after adding third subject=610+83+75+51=819

new average=819/13=63
@karan20 said:
Rajiv is a student in a business school. After every test he calculates his cumulative average.QT and OB were his last two tests.83 marks in QT increased his average by 2. 75 marks in OB further increased his average by 1. Reasoning is the next test, if he gets 51 in Reasoning, his average willbe ___?A. 59 B. 60C. 61 D. 62E. 63
E. 63?
@karan20 said:
Rajiv is a student in a business school. After every test he calculates his cumulative average.QT and OB were his last two tests.83 marks in QT increased his average by 2. 75 marks in OB further increased his average by 1. Reasoning is the next test, if he gets 51 in Reasoning, his average willbe ___?A. 59 B. 60C. 61 D. 62E. 63
Initially let total nob of subjects=y
n avg=x
After QT,
(xy+83)/(y+1)=x+2.......(1)
and after OB,
(xy+83+75)/(y+2)=x+3......(2)
on solving 1 and 2
y=10 and x=6
so after reasoning,
=> (xy+83+75+51)/(y+3)
=>819/13=63
Correct??
@Sumi99 said:
Guyz I know Its not the correct Forum for this Kind of Question but Sab Expert Bhai Log isse Forum pe ha to plz Help :::Decision Making Question Read the following and choose the best alternative:Decisions are often,risky in the sense that their outcomes are not known with certainty.Presented with a choice between a risky prospect that offers a 50 percent chance to win $200(otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighted by their probability of occurrence.) Preference for a sure outcome over risky prospect of equal expected value is called risk averse ; indeed, people tend to be risk averse when E. None of above.
Please share OA. I'm unable to crack this..
@sujamait -
A
A
E
D

This is given by the Person who Posted it ...
@Sumi99 said:
Guyz I know Its not the correct Forum for this Kind of Question but Sab Expert Bhai Log isse Forum pe ha to plz Help :::Decision Making Question Read the following and choose the best alternative:Decisions are often,risky in the sense that their outcomes are not known with certainty.Presented with a choice between a risky prospect that offers a 50 percent chance to win $200(otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighted by their probability of occurrence.) Preference for a sure outcome over risky prospect of equal expected value is called risk averse ; indeed, people tend to be risk averse when choosing between prospects with positive outcomes. The tendency towards risk aversion can be explained by the notion of diminishing sensitivity, fir st formalized by Daniel Bernoulli in 1738. Just as the impact of a candle is greater when it is brought into a dark room than into a room that is well lit so, suggested Ber noulli, the utility resulting from a small increase in wealth will be inversely proportional to the amount of wealth already in one s possession. It has since been assumed that people have a subjective utility function, and that preferences should be described using expected utility instead of expected value. According to expected utility, the worth of a gamble offering a 50 percent chance to win $200 (otherwise nothing) is 0.50 *u($200), where u is the person's concave utility function. (A function is concave or convex if a line joining two points on the curve lies entirely below or above the curves, respectively). Itfollows from a concave function that the subjective value attached to a gain of $100 is more than50 percent of the value attached to a gain of $200, which entails preference for the sure $100 gain and, hence, risk aversion.Consider now a choice between losses. When asked to choose between a prospect that offers a 50 percent chance to lose $200 (otherwise nothing) and the alternative of losing $100 for sure, most people prefer to take an even chance at losing $200 or nothing over a sure $100 loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: the impact of an initial $100 loss is greater than that of the next $100. This results in a convex function for losses and a preference for risky prospects over sure outcomes of equal expected value, called risk seeking. With the exception of prospects that involve very small probabilities, risk aversion is generally observed in choices involving gains, whereas risk seeking tends to hold in choices involving losses.Based on above passage, analyse the decision situations faced by three persons: Babu, Babitha and Bablu.Q1. Suppose instant and further utility of each unit of gain is same for Babu. Babu has decided to play as many times as possible, before he dies. He expected to live for another 50 years. A game does not last more than ten seconds. Babu is confused which theory to trust for making decision and seeks help of a renowned decision making consultant: Roy Associates. What should be Roy Associates advice to Babu?A. Babu can decide on the basis of Expected Value hypothesis. B. Babu should decide on the basis of Expected Utility hypothesis.C. Mr. Babu, I m redundant.D. A and BE. A, B and CQ2. Babitha played a game wherein she had three options with following probalilities: 0.4, 0.5 and 0.8. The gains from three outcomes are likely to be $100, $80 and $50. An expert has pointed out that Babitha is a risk taking person. According to expected utility hypothesis, which optionis Babitha most likely to favour?A. First B. SecondC. ThirdD. Babitha would be indifferent to all three actions.E. None of the above.Q3. Continuing with previous question, suppose Babitha can only play one more game, which theory would help in arriving at better decision?A. Expected Value. B. Expected Utility.C. Both theories will give same results.D. None of the two.E. Data is insufficient to answer the question.Q4. Bablu had four options with probalility of 0.1, 0.25, 0.5 and 1. The gains associated with each options are: $1000, $400, $200 and $100 respectively. Bablu chose the first option. As per expected value hypothesis:A. Bablu is risk taking. B. Expected value function is concave.C. Expected value function is convex.D. It does not matter which option should Babu choose. E. None of above.
wats d OA ? ....
@karan20 -
A
A
E
D

@Sumi99 said:
Decisions are often,risky in the sense that their outcomes are not known with certainty.Presented with a choice between a risky prospect that offers a 50 percent chance to win $200(otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighted by their probability of occurrence.) Preference for a sure outcome over risky prospect of equal expected value is called risk averse ; indeed, people tend to be risk averse when choosing between prospects with positive outcomes. The tendency towards risk aversion can be explained by the notion of diminishing sensitivity, fir st formalized by Daniel Bernoulli in 1738. Just as the impact of a candle is greater when it is brought into a dark room than into a room that is well lit so, suggested Ber noulli, the utility resulting from a small increase in wealth will be inversely proportional to the amount of wealth already in one s possession. It has since been assumed that people have a subjective utility function, and that preferences should be described using expected utility instead of expected value. According to expected utility, the worth of a gamble offering a 50 percent chance to win $200 (otherwise nothing) is 0.50 *u($200), where u is the person's concave utility function. (A function is concave or convex if a line joining two points on the curve lies entirely below or above the curves, respectively). Itfollows from a concave function that the subjective value attached to a gain of $100 is more than50 percent of the value attached to a gain of $200, which entails preference for the sure $100 gain and, hence, risk aversion.Consider now a choice between losses. When asked to choose between a prospect that offers a 50 percent chance to lose $200 (otherwise nothing) and the alternative of losing $100 for sure, most people prefer to take an even chance at losing $200 or nothing over a sure $100 loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: the impact of an initial $100 loss is greater than that of the next $100. This results in a convex function for losses and a preference for risky prospects over sure outcomes of equal expected value, called risk seeking. With the exception of prospects that involve very small probabilities, risk aversion is generally observed in choices involving gains, whereas risk seeking tends to hold in choices involving losses.Based on above passage, analyse the decision situations faced by three persons: Babu, Babitha and Bablu.Q1. Suppose instant and further utility of each unit of gain is same for Babu. Babu has decided to play as many times as possible, before he dies. He expected to live for another 50 years. A game does not last more than ten seconds. Babu is confused which theory to trust for making decision and seeks help of a renowned decision making consultant: Roy Associates. What should be Roy Associates advice to Babu?B. Babu should decide on the basis of Expected Utility hypothesis.Q2. Babitha played a game wherein she had three options with following probalilities: 0.4, 0.5 and 0.8. The gains from three outcomes are likely to be $100, $80 and $50. An expert has pointed out that Babitha is a risk taking person. According to expected utility hypothesis, which optionis Babitha most likely to favour?A. First Q3. Continuing with previous question, suppose Babitha can only play one more game, which theory would help in arriving at better decision? B. Expected Utility.Q4. Bablu had four options with probalility of 0.1, 0.25, 0.5 and 1. The gains associated with each options are: $1000, $400, $200 and $100 respectively. Bablu chose the first option. As per expected value hypothesis:A. Bablu is risk taking.


BABA??

@crooked -
A
A
E
D

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.

Ajit invested a certain amount of money in a FD. It pays at r% interest p.a. compounded annually If interest credited for 4th and 6th year is Rs. 12000 and Rs. 14520 respectively, what is the amount invested by ajit?


(a) 90157 (b) 88157 (c) 92157 (d) 93517 (e) 94157

OA is (a). Please explain your approach.
@gautam22 said:
x/36+x *28+x/8+x =8+x/28+x.........x=12 oa (c).............ratio is of the distances travelled
what is 'x' here. And how did arrive at the mentioned equation. Please explain in detail.
@gautam22 i m not able to determine x value .... what its correct soln ... i reach ti d ratio of fastest to slowest is (x+18)/(x-18).....

@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 Qare in a straight line.(a) 2:1 (b)3:2 (c) 4:1 (d) 5:2 (e) Can't be determinedOA is (c). Please explain your approach.
let A be d faster one and c the slower one..
and let track be p........s........r.......q
sq=18
rq=10
so, sr=8
let ps=x
AS A is faster and C is slower they will meet at s (ie onward journey of C n backward of A)
(x+36)/A=x/c....(1)
similarly B and C will meet at R.. (ie onward journey of C n backward of B)
(X+28)/B=(X+8)/c...(2)
and also A and C will meet at R..(ie onward journey of B n backward of A)
(X+28)/A=(X+8)/B...(3)
now from 1 and 2,
(A/C)*(C/B)=(X+36)/X * (x+8)/(x+28)......(4)
Now by comparing 3 and 4, x=12
and by putting it in 1
A/C=4/1

PS:my approach really took a lot of time..plzz let me know if u get any shorter approach..
@sharmaa.abhay said:
Ajit invested a certain amount of money in a FD. It pays at r% interest p.a. compounded annually If interest credited for 4th and 6th year is Rs. 12000 and Rs. 14520 respectively, what is the amount invested by ajit?(a) 90157 (b) 88157 (c) 92157 (d) 93517 (e) 94157OA is (a). Please explain your approach.
The interetst for the 6th year is the CI on the interest in 4th year(i.e 12000 ) for two years
So 14520 = 12000(1+r/100)^2 => r=10%
Now, int in 4th year is the SI on the Amount after 3 years. So
12000 = P [(1+r/100)^3 ] (r/100) => 12000 = P [ (11/10)^3 ] (1/10) => P = 90157