List of top Questions asked in XAT- 2008

Read the following situation and choose the best possible alternative.

You are a recruitment manager interviewing Mayank, a hard-working young man who has trouble speaking fluent English because he studied in schools and colleges that used a regional language as the medium of instruction. If your company currently has open positions, what would you choose to do?

Team A is a cricket team picking its playing eleven from its regular pool of batsmen for a league where it faces Teams B, C and D. The table below lists the past performance record of Team A's top 10 batsmen: their career batting average, and three tendencies expressed as a percentage of their innings, namely how often they get out for under 20 runs, how often they get out for a score close to their own average, and how often they go on to score more than a century.

For reference, the average score of the top 5 batsmen of each opposing team is: Team C, 270 runs; Team B, 215 runs; Team D, 180 runs; Team A (itself), 215 runs.

Team A would play the third match with B. Based on the statistics above, whom should the manager choose so that A has maximum chances of winning?

There are five sets of digits, Set A, Set B, Set C, Set D and Set E, arranged in a row as shown below. Set A holds one digit, Set B holds two digits, Set C holds three digits, Set D holds two digits and Set E holds one digit.

Set A: 7, Set B: 28, Set C: 196, Set D: 34, Set E: 5.

A rearrangement means picking one digit out of one set and swapping it with one digit from a different set. The goal is to keep making such swaps, one at a time, until the three-digit number in Set C becomes an exact multiple of the numbers formed by every other set, that is, of Set A, Set B, Set D and Set E, all at once. In the starting arrangement above, Set C (196) is already a multiple of Set A (77) and of Set B (28), since \(196 = 7 \times 28\), but it is not a multiple of Set D (34) or of Set E (55).

What is the minimum number of rearrangements needed to reach an arrangement where Set C is a multiple of Set A, Set B, Set D and Set E together? Each rearrangement is one swap of a single digit between two of the five sets; for instance, swapping the 1 in Set C with the 5 in Set E would count as one rearrangement.

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

Which of the following statements must be true?

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

If the Professor conducts a quiz on Tuesday, then her schedule for evaluating quizzes could be:

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

Which one of the following must be a day on which the professor lectures?

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

On Wednesdays, the professor could be scheduled to:

In a game, a "word" is any combination of at least five letters of the English alphabet (the word does not have to have a meaning). A "sentence" in this game consists of exactly six such words, and it must satisfy all of the following rules:
1. The six words are written from left to right on a single line, in strictly increasing alphabetical order.
2. The sentence may start with any word. Each successive word is obtained from the word right before it by applying exactly ONE of three operations: deleting one letter, adding one letter, or replacing one letter with another letter.
3. At most three of the six words can begin with the same letter.
4. Apart from the first word, every word must be formed using an operation different from the one used to form the word immediately before it (so the same operation can never be used twice in a row).

The last letter of the English alphabet that the first word of a sentence in the word game can begin with is

In a game, a "word" is any combination of at least five letters of the English alphabet (the word does not have to have a meaning). A "sentence" in this game consists of exactly six such words, and it must satisfy all of the following rules:
1. The six words are written from left to right on a single line, in strictly increasing alphabetical order.
2. The sentence may start with any word. Each successive word is obtained from the word right before it by applying exactly ONE of three operations: deleting one letter, adding one letter, or replacing one letter with another letter.
3. At most three of the six words can begin with the same letter.
4. Apart from the first word, every word must be formed using an operation different from the one used to form the word immediately before it (so the same operation can never be used twice in a row).

If the first word in a sentence is "illicit" and the fourth word is "licit", then the third word can be

In a game, a "word" is any combination of at least five letters of the English alphabet (the word does not have to have a meaning). A "sentence" in this game consists of exactly six such words, and it must satisfy all of the following rules:
1. The six words are written from left to right on a single line, in strictly increasing alphabetical order.
2. The sentence may start with any word. Each successive word is obtained from the word right before it by applying exactly ONE of three operations: deleting one letter, adding one letter, or replacing one letter with another letter.
3. At most three of the six words can begin with the same letter.
4. Apart from the first word, every word must be formed using an operation different from the one used to form the word immediately before it (so the same operation can never be used twice in a row).

If "clean" is the first word in a sentence and "learn" is another word in the sentence, then which one of the following is a complete and accurate list of the positions "learn" could occupy?

In a game, a "word" is any combination of at least five letters of the English alphabet (the word does not have to have a meaning). A "sentence" in this game consists of exactly six such words, and it must satisfy all of the following rules:
1. The six words are written from left to right on a single line, in strictly increasing alphabetical order.
2. The sentence may start with any word. Each successive word is obtained from the word right before it by applying exactly ONE of three operations: deleting one letter, adding one letter, or replacing one letter with another letter.
3. At most three of the six words can begin with the same letter.
4. Apart from the first word, every word must be formed using an operation different from the one used to form the word immediately before it (so the same operation can never be used twice in a row).

If the first word in a sentence consists of five letters, then the maximum number of letters that the fifth word in the sentence could contain is

During a four-week period, each one of seven previously unadvertised products, G, H, J, K, L, M and O, will be advertised. A different pair of these products will be advertised during each of the four weeks. Exactly one of these seven products will be advertised during two of the four weeks; none of the other six products is repeated in any pair. The following conditions must hold.

1. J is not advertised during a given week unless H is advertised during the week immediately before it.
2. The product that is advertised twice is advertised during week 4 but is not advertised during week 3.
3. G is not advertised during a given week unless either J or O is also advertised during that same week.
4. K is advertised during one of the first two weeks.
5. O is one of the products advertised during week 3.

Which one of the following is a pair of products that could be advertised during the same week?

In a game, a "word" is any combination of at least five letters of the English alphabet (the word does not have to have a meaning). A "sentence" in this game consists of exactly six such words, and it must satisfy all of the following rules:
1. The six words are written from left to right on a single line, in strictly increasing alphabetical order.
2. The sentence may start with any word. Each successive word is obtained from the word right before it by applying exactly ONE of three operations: deleting one letter, adding one letter, or replacing one letter with another letter.
3. At most three of the six words can begin with the same letter.
4. Apart from the first word, every word must be formed using an operation different from the one used to form the word immediately before it (so the same operation can never be used twice in a row).

Which one of the following could be a sentence in the word game?

During a four-week period, each one of seven previously unadvertised products, G, H, J, K, L, M and O, will be advertised. A different pair of these products will be advertised during each of the four weeks. Exactly one of these seven products will be advertised during two of the four weeks; none of the other six products is repeated in any pair. The following conditions must hold.

1. J is not advertised during a given week unless H is advertised during the week immediately before it.
2. The product that is advertised twice is advertised during week 4 but is not advertised during week 3.
3. G is not advertised during a given week unless either J or O is also advertised during that same week.
4. K is advertised during one of the first two weeks.
5. O is one of the products advertised during week 3.

Which one of the following could be the schedule of the advertisements?

During a four-week period, each one of seven previously unadvertised products, G, H, J, K, L, M and O, will be advertised. A different pair of these products will be advertised during each of the four weeks. Exactly one of these seven products will be advertised during two of the four weeks; none of the other six products is repeated in any pair. The following conditions must hold.

1. J is not advertised during a given week unless H is advertised during the week immediately before it.
2. The product that is advertised twice is advertised during week 4 but is not advertised during week 3.
3. G is not advertised during a given week unless either J or O is also advertised during that same week.
4. K is advertised during one of the first two weeks.
5. O is one of the products advertised during week 3.

If L is the product that is advertised during two of the weeks, which one of the following is a product that MUST be advertised during one of the weeks in which L is advertised?

During a four-week period, each one of seven previously unadvertised products, G, H, J, K, L, M and O, will be advertised. A different pair of these products will be advertised during each of the four weeks. Exactly one of these seven products will be advertised during two of the four weeks; none of the other six products is repeated in any pair. The following conditions must hold.

1. J is not advertised during a given week unless H is advertised during the week immediately before it.
2. The product that is advertised twice is advertised during week 4 but is not advertised during week 3.
3. G is not advertised during a given week unless either J or O is also advertised during that same week.
4. K is advertised during one of the first two weeks.
5. O is one of the products advertised during week 3.

Which one of the following is a product that could be advertised in any of the four weeks?

Six square states of equal area are arranged in two columns running north to south in a country. State 1, State 3, and State 5 lie on the western side, from north to south, and State 2, State 4, and State 6 lie on the eastern side, from north to south, so the states directly across the street from each other are State 1 and State 2, State 3 and State 4, and State 5 and State 6. Two states share a boundary if they sit next to each other in the same column (north-south) or directly across from each other (east-west). Within these six states there are exactly eight institutions in total: four medical institutes, two management institutes, and two technical institutes, placed according to these rules:

1. No institution is located in more than one state.
2. No state contains more than one management institute, and no state contains more than one technical institute.
3. No state contains both a management institute and a technical institute.
4. Every management institute is located in a state that also contains at least one medical institute.
5. The two technical institutes are located in states that do not share a common boundary.
6. State 3 contains a technical institute, and State 6 contains a management institute.

If each of the six states contains at least one of the eight institutions, then which one of the following must be true?

Six square states of equal area are arranged in two columns running north to south in a country. State 1, State 3, and State 5 lie on the western side, from north to south, and State 2, State 4, and State 6 lie on the eastern side, from north to south, so the states directly across the street from each other are State 1 and State 2, State 3 and State 4, and State 5 and State 6. Two states share a boundary if they sit next to each other in the same column (north-south) or directly across from each other (east-west). Within these six states there are exactly eight institutions in total: four medical institutes, two management institutes, and two technical institutes, placed according to these rules:

1. No institution is located in more than one state.
2. No state contains more than one management institute, and no state contains more than one technical institute.
3. No state contains both a management institute and a technical institute.
4. Every management institute is located in a state that also contains at least one medical institute.
5. The two technical institutes are located in states that do not share a common boundary.
6. State 3 contains a technical institute, and State 6 contains a management institute.

If one of the states contains exactly two medical institutes and exactly one technical institute, then which combination of three states might contain no medical institute?

Directions for questions 49 to 52: There are exactly ten stores and no other buildings on a straight street in Bistupur Market. On the northern side of the street, from west to east, are stores 1, 3, 5, 7, and 9. On the southern side, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the northern side sit directly across the street from the stores on the southern side, facing each other in pairs: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10.

Each store is decorated with lights in exactly one colour: green, red, or yellow. The lighting follows these rules:
1. No store has the same light colour as a store next to it on the same side of the street.
2. No store has the same light colour as the store directly across the street from it.
3. Yellow lights decorate exactly one store on each side of the street.
4. Store 4 has red lights.
5. Store 5 has yellow lights.

Which one of the following could be an accurate list of the colours of the lights that decorate stores 2, 4, 6, 8 and 10, respectively?

Directions for questions 49 to 52: There are exactly ten stores and no other buildings on a straight street in Bistupur Market. On the northern side of the street, from west to east, are stores 1, 3, 5, 7, and 9. On the southern side, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the northern side sit directly across the street from the stores on the southern side, facing each other in pairs: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10.

Each store is decorated with lights in exactly one colour: green, red, or yellow. The lighting follows these rules:
1. No store has the same light colour as a store next to it on the same side of the street.
2. No store has the same light colour as the store directly across the street from it.
3. Yellow lights decorate exactly one store on each side of the street.
4. Store 4 has red lights.
5. Store 5 has yellow lights.

If green lights decorate store 7, then each of the following statements could be false EXCEPT:

Directions for questions 49 to 52: There are exactly ten stores and no other buildings on a straight street in Bistupur Market. On the northern side of the street, from west to east, are stores 1, 3, 5, 7, and 9. On the southern side, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the northern side sit directly across the street from the stores on the southern side, facing each other in pairs: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10.

Each store is decorated with lights in exactly one colour: green, red, or yellow. The lighting follows these rules:
1. No store has the same light colour as a store next to it on the same side of the street.
2. No store has the same light colour as the store directly across the street from it.
3. Yellow lights decorate exactly one store on each side of the street.
4. Store 4 has red lights.
5. Store 5 has yellow lights.

Which one of the following statements MUST be true?

Directions for questions 49 to 52: There are exactly ten stores and no other buildings on a straight street in Bistupur Market. On the northern side of the street, from west to east, are stores 1, 3, 5, 7, and 9. On the southern side, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the northern side sit directly across the street from the stores on the southern side, facing each other in pairs: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10.

Each store is decorated with lights in exactly one colour: green, red, or yellow. The lighting follows these rules:
1. No store has the same light colour as a store next to it on the same side of the street.
2. No store has the same light colour as the store directly across the street from it.
3. Yellow lights decorate exactly one store on each side of the street.
4. Store 4 has red lights.
5. Store 5 has yellow lights.

Suppose that yellow lights decorate exactly two stores on the south side of the street and exactly one store on the north side. If all other conditions remain the same, then which one of the following statements MUST be true?

Questions 43 and 44 are based on the following instructions: each question gives a statement followed by three conclusions, I, II and III. Pick the option that tells you which of the three conclusions can be derived from the statement alone.

Statement: \(A_0, A_1, A_2, \ldots\) is a sequence of numbers with \(A_0 = 1\), \(A_1 = 3\), and \(A_t = (t+1)A_{t-1} - tA_{t-2}\) for \(t = 2, 3, 4, \ldots\)

Conclusion I: \(A_8 = 77\)
Conclusion II: \(A_{10} = 121\)
Conclusion III: \(A_{12} = 145\)

Six square states of equal area are arranged in two columns running north to south in a country. State 1, State 3, and State 5 lie on the western side, from north to south, and State 2, State 4, and State 6 lie on the eastern side, from north to south, so the states directly across the street from each other are State 1 and State 2, State 3 and State 4, and State 5 and State 6. Two states share a boundary if they sit next to each other in the same column (north-south) or directly across from each other (east-west). Within these six states there are exactly eight institutions in total: four medical institutes, two management institutes, and two technical institutes, placed according to these rules:

1. No institution is located in more than one state.
2. No state contains more than one management institute, and no state contains more than one technical institute.
3. No state contains both a management institute and a technical institute.
4. Every management institute is located in a state that also contains at least one medical institute.
5. The two technical institutes are located in states that do not share a common boundary.
6. State 3 contains a technical institute, and State 6 contains a management institute.

Which one of the following could be true?

Six square states of equal area are arranged in two columns running north to south in a country. State 1, State 3, and State 5 lie on the western side, from north to south, and State 2, State 4, and State 6 lie on the eastern side, from north to south, so the states directly across the street from each other are State 1 and State 2, State 3 and State 4, and State 5 and State 6. Two states share a boundary if they sit next to each other in the same column (north-south) or directly across from each other (east-west). Within these six states there are exactly eight institutions in total: four medical institutes, two management institutes, and two technical institutes, placed according to these rules:

1. No institution is located in more than one state.
2. No state contains more than one management institute, and no state contains more than one technical institute.
3. No state contains both a management institute and a technical institute.
4. Every management institute is located in a state that also contains at least one medical institute.
5. The two technical institutes are located in states that do not share a common boundary.
6. State 3 contains a technical institute, and State 6 contains a management institute.

A complete and accurate list of the states, any one of which could contain the management institute that is not in State 6, would be _____.