List of top Questions asked in XAT- 2007

Eight cities A, B, C, D, E, F, G and H are connected with one-way roads \(R_1\), \(R_2\), \(R_3\), \(R_4\), \(R_5\) and \(R_6\) in the following manner:
- \(R_1\) leads from A to C via B;
- \(R_2\) leads from C to D and then via B to F;
- \(R_3\) leads from D to A and then via E to H;
- \(R_4\) leads from F to B via G;
- \(R_5\) leads from G to D; and
- \(R_6\) leads from F to H.

The minimum number of road segments that have to be blocked in order to make all traffic from B to D impossible is:
If the polynomial \(x^3 + px + q\) has three distinct roots, then which of the following is a possible value of \(p\)?
In a certain factory, each day the expected number of accidents is related to the number of overtime hours by a linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported, and on another day there were 400 overtime hours logged and 5 accidents. What are the expected numbers of accidents when no overtime hours are logged?
Let \(S\) be the set of rational numbers with the following properties:
(i) \(\dfrac{1}{2} \in S\);
(ii) If \(x \in S\), then both \(\dfrac{1}{x+1} \in S\) and \(\dfrac{x}{x+1} \in S\).
Which of the following is true?
Directions for questions 49 and 50: Read the information given below and answer the question.
Let \(f\) be a function defined on the set of integers. Assume that \(f\) satisfies the following properties:
1. \(f(0) \neq 0\);
2. \(f(1) = 3\); and
3. \(f(x)f(y) = f(x+y) + f(x-y)\) for all integers \(x\) and \(y\).

What is \(f(3)\)?
Directions for questions 49 and 50: Read the information given below and answer the question.
Let \(f\) be a function defined on the set of integers. Assume that \(f\) satisfies the following properties:
1. \(f(0) \neq 0\);
2. \(f(1) = 3\); and
3. \(f(x)f(y) = f(x+y) + f(x-y)\) for all integers \(x\) and \(y\).

What is \(f(7)\)?
48. ABC is a triangle with \(\angle CAB = 15^{\circ}\) and \(\angle ABC = 30^{\circ}\). If M is the midpoint of AB, then \(\angle ACM = ?\)
Let \(p\) be any positive integer, and let
\[ 2x + p = 2y, \quad p + y = x, \quad x + y = z \]
For what value of \(p\) would \(x + y + z\) attain its maximum value?
47. Which equation can be graphically represented as follows?
44. For how many integers n is \(\frac{n}{20-n}\) the square of an integer?
DIRECTIONS for questions 45 and 46: Read the information below and answer the question that follows.
It is possible to arrange eight of the nine numbers 2, 3, 4, 5, 7, 10, 11, 12, 13 in the vacant squares of the 3 by 4 array shown below so that the arithmetic average of the numbers in each row and column is the same integer.
115
9
14

46. Which one of the nine numbers must be left out when completing the array?
DIRECTIONS for questions 45 and 46: Read the information below and answer the question that follows.
It is possible to arrange eight of the nine numbers 2, 3, 4, 5, 7, 10, 11, 12, 13 in the vacant squares of the 3 by 4 array shown below so that the arithmetic average of the numbers in each row and column is the same integer.
115
9
14

45. The arithmetic average is:
DIRECTIONS for questions 42 and 43: Read the information below and answer the question that follows.
A truck travelled from town A to town B over several days. During the first day, it covered \(\frac{1}{p}\) of the total distance, where p is a natural number. During the second day, it travelled \(\frac{1}{q}\) of the remaining distance, where q is a natural number. During the third day, it travelled \(\frac{1}{p}\) of the distance remaining after the second day, and during the fourth day, \(\frac{1}{q}\) of the distance remaining after the third day. By the end of the fourth day, the truck had travelled \(\frac{3}{4}\) of the distance between A and B.

42. The value of p + q is:
Directions for questions 37 to 41: Analyze the statements given and provide an appropriate answer for the questions that follow.

Industry experts expect improvements in job safety training programs to lead to safer work environments. A recent survey indicated, however, that for manufacturers who improved job safety training programs during the 1980s, the number of on-the-job accidents increased in the months following the imparting of improved training programs.

Which one of the following, if true, most helps to resolve the apparent discrepancy in the passage above?
DIRECTIONS for questions 42 and 43: Read the information below and answer the question that follows.
A truck travelled from town A to town B over several days. During the first day, it covered \(\frac{1}{p}\) of the total distance, where p is a natural number. During the second day, it travelled \(\frac{1}{q}\) of the remaining distance, where q is a natural number. During the third day, it travelled \(\frac{1}{p}\) of the distance remaining after the second day, and during the fourth day, \(\frac{1}{q}\) of the distance remaining after the third day. By the end of the fourth day, the truck had travelled \(\frac{3}{4}\) of the distance between A and B.

43. If the total distance is 100 kilometres, the minimum distance that can be covered on day 1 is ____ kilometres.
DIRECTIONS for questions 33 to 36: Choose the option that correctly un-scrambles the paragraphs below.

1. Individuals and firms moving into a new and unfamiliar field of activity are increasingly using information resources provided over the Internet.
2. The economic importance of a strong, viable business sector, especially a strong and viable small business sector with its potential for employment and export generation, makes it imperative that government agencies provide encouragement, leadership and effective support.
3. Governments undertake a wide variety of initiatives to achieve these ends and online information provision is one of many such initiatives.
4. The power of the Internet to deliver information and services online offers an opportunity for governments to support businesses and the economies they serve.
5. Many small to medium-size enterprises may turn initially to a government agency for business-related information, in part because they lack the confidence and financial resources to engage private consultants at the initial stages of the planning process.
6. This is an important issue, both for government economic development strategies and to help them meet the rising public expectations of online service provision.
Directions: The six sentences below (1 to 6) form one paragraph if put in the right order. Pick the option that gives that order.

1. Employees are seeing organizational leaders who appear to have only their personal interests in sight.
2. All the while, these same leaders appear to be walking away from their failures with multimillion-dollar exit bonuses or millions in forgiven "loans".
3. They are feeling increasingly expendable and disposable, all for the purpose of enriching CEOs and top leaders.
4. Workers are feeling less and less connected with top management.
5. Some corporate leaders are simply losing touch.
6. Those they lead are, understandably, losing confidence and trust in their leaders.
Directions for questions 37 to 41: Analyze the statements given and provide an appropriate answer for the questions that follow.

Prediction, the hallmark of natural sciences, appears to have been possible by reducing phenomena to mathematical expressions. Some social scientists also want the power to predict accurately and assume they ought to perform the same reduction. But this would be a mistake, it would neglect data that are not easily mathematized and thereby would only distort the social phenomena.

Which one of the following most accurately expresses the main conclusion of the argument?
Directions for questions 37 to 41: Analyze the statements given and provide an appropriate answer for the questions that follow.

Chandra: Hailey's Comet, now in a part of its orbit relatively far from the Sun, recently flared brightly enough to be seen by telescope on earth. This has never happened before, so such a flare must be highly unusual.
Surya: Nonsense. Usually no one bothers to observe comets when they are so far from the Sun. This flare was observed only because an observatory was tracking Hailey's Comet very carefully.

Surya challenges Chandra's reasoning by:
Directions for questions 37 to 41: Analyze the statements given and provide an appropriate answer for the questions that follow.

Most antidepressant drugs cause weight gain. While dieting can help reduce the amount of weight gained as one takes such antidepressants, some weight gain is unlikely to be preventable.

The information above most strongly supports which one of the following?
Directions for questions 37 to 41: Analyze the statements given and provide an appropriate answer for the questions that follow.

The number of airplanes equipped with a new anti-collision device has increased steadily during the past two years. During the same period, it has become increasingly common for key information about an airplane's altitude and speed to disappear suddenly from air traffic controllers' screens. The new anti-collision device, which operates at the same frequency as air traffic radar, is therefore responsible for the sudden disappearance of key information.

Which one of the following, if true, most seriously weakens the argument above?
Which revision best combines ideas without losing out on information?

There are still ample physical reminders of the history of the Ao tribe in Meghalaya. Impressive burial mounds, dating back hundreds of years, can be found along many of the rivers, for instance.
Choose the best revision of the following wordy sentence.

It seems that the library board will meet tomorrow, as a matter of fact.
Amongst the options below, choose the one which is correctly punctuated.
DIRECTIONS for questions 33 to 36: Choose the option that correctly un-scrambles the paragraphs below.

1. The same is true for less fraught examples: dispensing with 'Truth' does not mean dispensing with accuracy and attention to detail, and to suggest for example that the colonization of the New World never happened would be equally untenable.
2. To relinquish 'Truth' and the idea of one history does not lead to absolute relativism, where any version of events is taken as being equally valid as any other.
3. It does not, for example, give succour to those charlatans and ideologues who seek to deny that the Holocaust ever happened.
4. What I am suggesting here is complex, but its importance demands a careful reading.
5. The evidence for the systematic murder of more than six million people by the Nazis is overwhelming.
6. To try to argue that it never occurred is to violate the voices of the past, to suppress that evidence which goes against the twisted thesis.