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XAT 2017 Mock | Preparation for XAT 2017

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Question 1

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, 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.
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?

Question 2

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, 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.
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 option is Babitha most likely to favour?

Question 3

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

Question 4

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, 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.
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:

Question 5

Direction: Read the given passage carefully and answer the questions that follow.


The Sapir-Whorf hypothesis, also known as the linguistic relativity hypothesis, refers to the proposal that the particular language one speaks influences the way one thinks about reality. The linguistic relativity hypothesis focuses on structural differences among natural languages such as Hopi, Chinese, and English, and asks whether the classifications of reality implicit in such structures affect our thinking about reality. Analytically, linguistic relativity as an issue stands between two others: a semiotic-level concern with how speaking any natural language whatsoever might influence the general potential for human thinking (i.e., the general role of natural language in the evolution or development of human intellectual functioning), and a functional- or discourse-level concern with how using any given language code in a particular way might influence thinking (i.e., the impact of special discursive practices such as schooling and literacy on formal thought).

Although analytically distinct, the three issues are intimately related in both theory and practice. For example, claims about linguistic relativity depend on understanding the general psychological mechanisms linking language to thinking, and on understanding the diverse uses of speech in discourse to accomplish acts of descriptive reference. Hence, the relation of particular linguistic structures to patterns of thinking forms only one part of the broader ray of questions about the significance of language for thought. Proposals of linguistic relativity necessarily develop two linked claims among the key terms of the hypothesis (i.e., language, thought, and reality). First, languages differ significantly in their interpretations of experienced reality- both what they select for representation and how they arrange it. Second, language interpretations have influences on thought about reality more generally- whether at the individual or cultural level. Claims for linguistic relativity thus require both articulating the contrasting interpretations of reality latent in the structures of different languages, and accessing their broader influences on, or relationships to, the cognitive interpretation of reality.
Which of the following conclusions can be derived based on Sapir-Whorf hypothesis?

Question 6

Direction: Read the given passage carefully and answer the questions that follow.


The Sapir-Whorf hypothesis, also known as the linguistic relativity hypothesis, refers to the proposal that the particular language one speaks influences the way one thinks about reality. The linguistic relativity hypothesis focuses on structural differences among natural languages such as Hopi, Chinese, and English, and asks whether the classifications of reality implicit in such structures affect our thinking about reality. Analytically, linguistic relativity as an issue stands between two others: a semiotic-level concern with how speaking any natural language whatsoever might influence the general potential for human thinking (i.e., the general role of natural language in the evolution or development of human intellectual functioning), and a functional- or discourse-level concern with how using any given language code in a particular way might influence thinking (i.e., the impact of special discursive practices such as schooling and literacy on formal thought).

Although analytically distinct, the three issues are intimately related in both theory and practice. For example, claims about linguistic relativity depend on understanding the general psychological mechanisms linking language to thinking, and on understanding the diverse uses of speech in discourse to accomplish acts of descriptive reference. Hence, the relation of particular linguistic structures to patterns of thinking forms only one part of the broader ray of questions about the significance of language for thought. Proposals of linguistic relativity necessarily develop two linked claims among the key terms of the hypothesis (i.e., language, thought, and reality). First, languages differ significantly in their interpretations of experienced reality- both what they select for representation and how they arrange it. Second, language interpretations have influences on thought about reality more generally- whether at the individual or cultural level. Claims for linguistic relativity thus require both articulating the contrasting interpretations of reality latent in the structures of different languages, and accessing their broader influences on, or relationships to, the cognitive interpretation of reality.
If Sapir-Whorf hypothesis were to be true, which of the following conclusions would logically follow?
1. To develop vernacular languages, government should promote public debates and discourses.
2. Promote vernacular languages as medium of instruction in schools.
3. Cognitive and cultural realities are related.

Question 7

Direction: Read the given passage carefully and answer the questions that follow.


The Sapir-Whorf hypothesis, also known as the linguistic relativity hypothesis, refers to the proposal that the particular language one speaks influences the way one thinks about reality. The linguistic relativity hypothesis focuses on structural differences among natural languages such as Hopi, Chinese, and English, and asks whether the classifications of reality implicit in such structures affect our thinking about reality. Analytically, linguistic relativity as an issue stands between two others: a semiotic-level concern with how speaking any natural language whatsoever might influence the general potential for human thinking (i.e., the general role of natural language in the evolution or development of human intellectual functioning), and a functional- or discourse-level concern with how using any given language code in a particular way might influence thinking (i.e., the impact of special discursive practices such as schooling and literacy on formal thought).

Although analytically distinct, the three issues are intimately related in both theory and practice. For example, claims about linguistic relativity depend on understanding the general psychological mechanisms linking language to thinking, and on understanding the diverse uses of speech in discourse to accomplish acts of descriptive reference. Hence, the relation of particular linguistic structures to patterns of thinking forms only one part of the broader ray of questions about the significance of language for thought. Proposals of linguistic relativity necessarily develop two linked claims among the key terms of the hypothesis (i.e., language, thought, and reality). First, languages differ significantly in their interpretations of experienced reality- both what they select for representation and how they arrange it. Second, language interpretations have influences on thought about reality more generally- whether at the individual or cultural level. Claims for linguistic relativity thus require both articulating the contrasting interpretations of reality latent in the structures of different languages, and accessing their broader influences on, or relationships to, the cognitive interpretation of reality.
Which of the following proverbs may be false, if above passage were to be right?
1. If speech is silver, silence is gold.
2. When you have spoken a word, it reigns over you. When it is unspoken you reign over it.
3. Speech of yourself ought to be seldom and well chosen.

Question 8

A rural child specialist has to determine the weight of five children of different ages. He knows from his past experience that each of the children would weigh less than 30 Kg and each of them would have different weights. Unfortunately, the scale available in the village can measure weight only over 30 Kg. The doctor decides to weigh the children in pairs.
However his new assistant weighed the children without noting down the names. The weights were: 35, 36, 37, 39, 40, 41, 42, 45, 46 and 47 Kg. The weight of the lightest child is:

Question 9

Let a and b be the roots of the quadratic equation Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image016.pngIf Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image017.pngfor Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image018.pngthen, Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image019.pngfor Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image020.png

Question 10

Steel Express stops at six stations between Howrah and Jamshedpur. Five passengers board at Howrah. Each passenger can get down at any station till Jamshedpur. The probability that at five persons will get down at different station is:

Question 11

Instructions: Consider the information given below
In the diagram below, the seven letters correspond to seven unique digits chosen from 0 to 9. The relation among the digits is such that:
P.Q.R = X.Y.Z = Q.A.Y
Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image035.png
The value of A is:

Question 12

The sum of the digits which are not used is:

Question 13

A cake chain manufactures two types of products – ‘cakes/pastries/gateaux’ and savouries. The chain was concerned about high wastage (in terms of leftover) and wanted to reduce it. Table 1 provides information about sales, costs and wastage for both products.
Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image014.png
Which of the following statement(s) is (are) right?
1- The worth of leftover for cakes/pastries/gateaux increased from 1993 to 2004.
2- The worth of leftover for cakes/pastries/gateaux, kept on fluctuating, many a times, between 1993 and 2004.
3- The worth of leftover for savouries and cakes/pastries/gateaux was highest in 2004.
4- The worth of leftover for savouries kept on fluctuating, many a times, between 1993 and 2004.
Choose the right combination from the following:

Question 14

A cake chain manufactures two types of products – ‘cakes/pastries/gateaux’ and savouries. The chain was concerned about high wastage (in terms of leftover) and wanted to reduce it. Table 1 provides information about sales, costs and wastage for both products.
Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image014.png
Which of the following statement(s) is (are) right?
1- The worth of leftover for cakes/pastries/gateaux increased from 1993 to 2004.
2- The worth of leftover for cakes/pastries/gateaux, kept on fluctuating, many a times, between 1993 and 2004.
3- The worth of leftover for savouries and cakes/pastries/gateaux was highest in 2004.
4- The worth of leftover for savouries kept on fluctuating, many a times, between 1993 and 2004.
Maximum decline in amount of leftover of cakes/pastries/gateaux occurred in the year:

Question 15

A cake chain manufactures two types of products – ‘cakes/pastries/gateaux’ and savouries. The chain was concerned about high wastage (in terms of leftover) and wanted to reduce it. Table 1 provides information about sales, costs and wastage for both products.
Description: Description: E:\CAT\XAT\XAT_2009_Question_Paper_and_Ans_Key_files\image014.png
Which of the following statement(s) is (are) right?
1- The worth of leftover for cakes/pastries/gateaux increased from 1993 to 2004.
2- The worth of leftover for cakes/pastries/gateaux, kept on fluctuating, many a times, between 1993 and 2004.
3- The worth of leftover for savouries and cakes/pastries/gateaux was highest in 2004.
4- The worth of leftover for savouries kept on fluctuating, many a times, between 1993 and 2004.
If profit = sales cost leftover, in which year did the cakes chain was in losses?
1- 1993
2- 1997
3- 1998
4- 2000
Choose the right option:
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Dec 22CAT & MBA