# Analytical Reasoning and Decision Making for XAT

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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”.

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) **