Analytical Reasoning and Decision Making for XAT

Dear readers,

This quiz consists of questions from past
actual XAT papers. Leave your answers/ responses in the comments section below
and soon we’ll let you know the correct answers!

Questions (1-3):

Four married couples competed in a singing competition. Each couple had
a  unique team name. Points scored
by  the teams were  2,  4,
6 and 8. The  “Sweet Couple”  won 2 
points. The “Bindas Singers” won two more points than Laxman’s team.
Mukesh’s team won four   points more  than Lina’s team, but Lina’s team  didn’t score 
the least amount  of  points. “Just 
Singing” won 6 points. Waheda wasn’t on the team called “New Singers”.
Sanjeev’s team won 4
points. Divya wasn’t on the “Bindas Singers” team. Tapas and Sania were on
the same team, but it  wasn’t the “Sweet
Couple”.  

1. Laxman’s teammate and team’s name were:  

A. Divya and Sweet Couple 

B. Divya and Just Singing 

C. Waheda and Bindas Singers  

D. Lina and Just Singing  

E. Waheda and Sweet couple  

2. The teams arranged in the ascending order of points are:  

A. Bindas Singers, Just Singing, New Singers, Sweet Couple 

B. Sweet Couple, New Singers, Just Singing, Bindas Singers 

C. New Singers, Sweet Couple, Bindas Singers, Just Singing 

D. Sweet Couple, Bindas Singers, Just Singing, New Singers 

E. Just Singing, Bindas Singers, Sweet Couple, New Singers  

3. The Combination which has the couples rightly paired is:

A. Mukesh, Lina 

B. Mukesh, Waheda 

C. Sanjeev, Divya 

D. Sanjeev, Lina 

E. Sanjeev, Waheda  

Questions (4-7):

The regular mathematics faculty could not teach because of being sick. As a
stop gap  arrangement, different  visiting 
faculty  taught  different topics on 4 different days in
a  week. The scheduled time for class was
7:00 am with maximum permissible delay of 20 minutes. The  monsoon made 
the city  bus schedules
erratic  and therefore  the classes started on different  times on different days.  

Mr. Singh didn’t teach on Thursday. Calculus was taught in the class that
started at 7:20 am. Mr.  Chatterjee  took the class on Wednesday, but he  didn’t teach probability.  The class on Monday  started at 7:00 am, but Mr. Singh didn’t teach
it. Mr. Dutta didn’t teach ratio and proportion. Mr. Banerjee, who didn’t teach
set theory, taught a class that started five minutes later than the class 

4. The class on Wednesday started at:  

A. 7:05 am and topic was ratio and proportion. 

B. 7:20 am and topic was calculus. 

C. 7:00 am and topic was calculus. 

D. 7:20 am and topic was set theory. 

E. 7:05 am and topic was probability.  

5. The option which gives the correct teacher- subject combination is:  

A. Mr. Chatterjee – ratio and proportion  

B. Mr. Banerjee – calculus 

C. Mr. Chatterjee – set theory 

D. Mr. Singh – calculus 

E. Mr. Singh – set theory  

6. Probability was taught by:  

A. Mr. Dutta on Monday  

B. Mr. Dutta on Thursday 

C. Mr. Singh on Wednesday 

D. Mr. Singh on Monday 

E. None of these  

7. The option which gives a possible correct class time – week day
combination is:  

A. Wednesday – 7:10 am, Thursday – 7:20 am, Friday – 7:05 am 

B. Wednesday – 7:20 am, Thursday – 7:15 am, Friday – 7:20 am 

C. Wednesday – 7:05 am, Thursday – 7:20 am, Friday – 7:10 am 

D. Wednesday – 7:10 am, Thursday – 7:15 am, Friday – 7:05 am 

E. Wednesday – 7:20 am, Thursday – 7:05 am, Friday – 7:10 am

Questions (8-12): 

Five  people joined different
engineering  colleges. Their first names
were  Sarah (Ms.), Swati  (Ms.), Jackie, Mohan and Priya  (Ms.). The 
surnames were  Reddy, Gupta,  Sanyal, Kumar and Chatterjee. Except for one
college which was rated as 3 star, all other colleges  were rated either 4 star or 5 star.  

The  “Techno Institute”  had a 
higher rating  than  the college 
where  Priya  studied. The 
three-star college was not “Deccan College.” Mohan’s last name was Gupta
but he didn’t study at “Barla  College.”  Sarah, whose 
last name wasn’t Sanyal, joined “Techno Institute.”    Ms. Kumar and Jackie both studied at
four-star  colleges. Ms. Reddy  studied 
at the  “Anipal Institute,”  which 
wasn’t a five-star college. The “Barla College” was a five-star college.
Swati’s last name wasn’t Chatterjee. The 
“Chemical College”  was rated with
one star less than the college where Sanyal studied. Only one college was rated
five star.  

8. Which is the correct combination of first names and surnames?  

A. Mohan Gupta, Sarah Kumar, Priya Chatterjee 

B. Priya Chatterjee, Sarah Sanyal, Jackie Kumar 

C. Jackie Sanyal, Swati Reddy, Mohan Gupta 

D. Mohan Gupta, Jackie Sanyal, Sarah Reddy 

E. Jackie Chatterjee, Priya Reddy, Swati Sanyal  

9. Which option gives a possible student – institute combination?

 A. Priya – Anipal, Swati – Deccan, Mohan – Chemical 

B. Swati – Barla, Priya – Anipal, Jackie – Deccan 

C. Joydeep – Chemical, Priya – Techno, Mohan – Barla 

D. Priya – Anipal, Joydeep – Techno, Sarah – Barla 

E. Swati – Deccan, Priya – Anipal, Sarah – Techno  

10. Mohan Gupta may have joined:

A. Techno – Institute which had 5 star rating 

B. Deccan College which had 5 star rating 

C. Anipal Institute which had 4 star rating 

D. Chemical College which had 4 star rating 

E. Techno – Institute which had 4 star rating  

11. In which college did Priya study?  

A. Anipal Institute 

B. Chemical Institute 

C. Barla College 

D. Deccan College 

E. Techno- Institute  

12. The person with surname Sanyal was:  

A. Sarah studying in Chemical College 

B. Swati studying in Barla College 

C. Priya studying in Deccan College 

D. Jackie studying in Deccan College 

E. Sarah studying in Techno- Institute

Read the following and choose the best alternative (Questions 13-15):  

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, first 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 Bernoulli, 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). 
It  follows from a concave
function that the subjective value attached to a gain of $100 is more than 50
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.  

13. 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 Associate’s 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

14. 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.  

15. Bablu had four options with probability 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.  

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Answers

1(e)    2(d)    
3(d)    4(b)     5(e)   
 6(a)   7(e)   
8(e)     9(b)    10(d)   
11(a)    12(b)     13(e)   
14(e)     15(d)    

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