XAT2014 Related Question Answers
51.
Read the following case-let and answer the questions that follow
Rajinder Singh was 32 years old from the small town of Bhathinda, Punjab. Most of the families living there had middle class incomes, with about 10% of the population living below the poverty level. The population consisted of 10 percent small traders, 30 percent farmers, besides others. Rajinder liked growing up in Bhathinda, where people knew and cared about each other.
Even as a youngster it was clear that Rajinder was smart and ambitious. Neighbors would often say, “Someday you’re going to make us proud!” He always had a job growing up at Singh’s General Store - Uncle Balwant’s store. Balwant was a well-intentioned person. Rajinder loved being at the store and not just because Balwant paid him well. He liked helping customers, most of who were known by the nicknames. Setting up displays and changing the merchandise for different seasons and holidays was always exciting. Uncle Balwant had one child and off late, his interest in business had declined. But he had taught Rajinder ‘the ins and outs of retailing’. He had taught Rajinder everything, including ordering merchandise, putting on a sale, customer relations, and keeping the books.
The best part about working at the store was Balwant himself. Balwant loved the store as much as Rajinder did. Balwant had set up the store with a mission to make sure his neighbors got everything they needed at a fair price. He carried a wide variety of goods, based on the needs of the community. If you needed a snow shovel or piece of jewelry for your wife, it was no problem - Singh’s had it all. Rajinder was impressed by Balwant’s way of handling and caring for customers. If somebody was going through “hard times”, Balwant somehow knew it. When they came into the store, Balwant would make them feel comfortable, and say something like, “you know Jaswant, let’s put everything on credit today”. This kind of generosity made it easy to understand why Balwant was loved and respected throughout the community.
Rajinder grew up and went to school and college in Bhathinda. Later on, he made it to an MBA program in Delhi. Rajinder did well in the MBA course and was goal oriented. After first year of his MBA, the career advisor and Balwant advised Rajinder for an internship at Bigmart. That summer, Rajinder was amazed by the breadth and comprehensiveness of the internship experience. Rajinder got inspired by the life story of the founder of Bigmart, and the value the founder held. Bigmart was one of the best companies in the world.
The people that Rajinder worked for at Bigmart during the internship noticed Rajinder’s work ethic, knowledge, and enthusiasm for the business. Before the summer ended, Rajinder had been offered a job as a Management Trainee by Bigmart, to start upon graduation. Balwant was happy to see Rajinder succeed. Even for Rajinder, this was a dream job - holding the opportunity to move up the ranks in a big company. Rajinder did indeed move up the ranks quickly, from management trainee, to assistant store manager, to supervising manager of three stores, to the present position - Real Estate Manager, North India. This job involved locating new sites within targeted locations and community relations.
One day Rajinder was eagerly looking forward to the next assignment. When he received email for the same, his world came crashing down. He was asked to identify next site in Bhathinda. It was not that Rajinder didn’t believe in Bigmart’s explanation. What was printed in the popular press,especially the business press, only reinforced Rajinder’s belief in Bigmart. An executive viewed as one of the wisest business persons in the world was quoted as saying, “Bigmart had been a major force in improving the quality of life for the average consumer around the world offering great prices on good, giving them one stop solution for almost everything.” Many big farmers also benefitted through low prices, as middlemen were removed. At the same time, Rajinder knew that opening a new Bigmart could disrupt small business in Bhathinda. Some local stores in small towns went out of business within a year of the Bigmart’s opening.
In Bhathinda, one of the local stores Singh’s,now run by Balwant’s son, although Balwant still came in every day to “straighten out the merchandise.” As Rajinder thought about this assignment, depression set in, and the nightmares followed. Rajinder was frozen in time and space. Rajinder’s nightmares involved Balwant screaming something- although Rajinder could not make out what Balwant was saying. This especially troubled Rajinder, since Balwant never raised his voice.
Rajinder didn’t know what to do - who might be helpful? Rajinder’s spouse, who was a housewife? Maybe talking it through could lead to some positive course of action. Rajinder’s boss?Would Bigmart understand? Could Rajinder really disclose the conflict without fear? Uncle Balwant? Should Rajinder really disclose the situation and ask for advise? He wanted a solution that would make all satkeholders happy.Who is the best person for Rajinder to talk to?
52. After delibertation with many people and a lot of research, Rajinder came across a study published in leading journal, which stated that most local farmers benefited because Bigmart bought agricultural produce directly from the farmers. Which of the following actions would you prefer Rajinder to take, after he got this fresh information?
53. Which is the right ascending order, in terms of proportion of population, benefitting from Bigmart, in and around Bhathinda?
54. $$x, 17, 3x - y^{2} - 2$$, and $$3x + y^{2} - 30$$, are four consecutive terms of an increasing arithmetic sequence. The sum of the four number is divisible by:
55. In quadrilateral PQRS, PQ = 5 units, QR = 17 units, RS = 5 units, and PS = 9 units. The length of the diagonal QS can be:
57. There are two windows on the wall of a building that need repairs. A ladder 30 m long is placed against a wall such that it just reaches the first window which is 26 m high. The foot of the ladder is at point A. After the first window is fixed, the foot of the ladder is pushed backwards to point B so that the ladder can reach the second window. The angle made by the ladder with the ground is reduced by half, as a result of pushing the ladder. The distance between points A and B is
58. Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds 50 to the number, and gives the result back to Amitabh, who doubles the number again. The first person, whose result is more than 1000, loses the game. Let ‘x’ be the smallest initial number that results in a win for Amitabh. The sum of the digits of ‘x’ is:
59. Consider four natural numbers: x, y, x + y, and x - y. Two statements are provided below: I. All four numbers are prime numbers. II. The arithmetic mean of the numbers is greater than 4. Which of the following statements would be sufficient to determine the sum of the four numbers?
60. Triangle ABC is a right angled triangle. D and E are mid points of AB and BC respectively. Read the following statements. I. AE = 19 II. CD = 22 III. Angle B is a right angle. Which of the following statements would be sufficient to determine the length of AC?
61. There are two circles $$C_{1}$$ and $$C_{2}$$ of radii 3 and 8 units respectively. The common internal tangent, T, touches the circles at points $$P_{1}$$ and $$P_{2}$$ respectively. The line joining the centers of the circles intersects T at X. The distance of X from the center of the smaller circle is 5 units. What is the length of the line segment $$P_{1} P_{2}$$ ?
62. Consider the formula, $$S=\frac{\alpha\times\omega}{\tau+\rho\times\omega}$$ positive integers. If ⍵ is increased and ⍺, τ and ρ are kept constant, then S:
63. Prof. Suman takes a number of quizzes for a course. All the quizzes are out of 100. A student can get an A grade in the course if the average of her scores is more than or equal to 90.Grade B is awarded to a student if the average of her scores is between 87 and 89 (both included). If the average is below 87, the student gets a C grade. Ramesh is preparing for the last quiz and he realizes that he will score a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will just manage a B. How many quizzes did Prof. Suman take?
64. A polynomial $$ax^{3} + bx^{2 }+ cx + d$$ intersects x-axis at 1 and -1, and y-axis at 2. The value of b is:
65. The probability that a randomly chosen positive divisor of $$10^{29}$$ is an integer multiple of $$10^{23}$$ is: $$a^{2} /b^{2} $$, then ‘b - a’ would be:
66. Circle $$C_{1}$$ has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X axis. P and Q are points on curves given by the equations $$y = a^{x} and y = 2a^{x}$$ respectively, where a < 1. The value of a is:
67. Consider a rectangle ABCD of area 90 units. The points P and Q trisect AB, and R bisects CD. The diagonal AC intersects the line segments PR and QR at M and N respectively. What is the area of the quadrilateral PQNM?
68. Two numbers, $$297_{B}$$ and $$792_{B}$$ , belong to base B number system. If the first number is a factor of the second number then the value of B is:
69. A teacher noticed a strange distribution of marks in the exam. There were only three distinct scores: 6, 8 and 20. The mode of the distribution was 8. The sum of the scores of all the students was 504. The number of students in the in most populated category was equal to the sum of the number of students with lowest score and twice the number of students with the highest score. The total number of students in the class was:
70. Read the following instruction carefully and answer the question that follows: Expression $$\sum_{n=1}^{13}\frac{1}{n}$$ can also be written as $$\frac{x}{13!}$$ What would be the remainder if x is divided by 11?
71. A rectangular swimming pool is 48 m long and 20 m wide. The shallow edge of the pool is 1 m deep. For every 2.6 m that one walks up the inclined base of the swimming pool, one gains an elevation of 1 m. What is the volume of water (in cubic meters), in the swimming pool? Assume that the pool is filled up to the brim.v
73. There are two squares S 1 and S 2 with areas 8 and 9 units, respectively. S 1 is inscribed within S 2 , with one corner of S 1 on each side of S 2 . The corners of the smaller square divides the sides of the bigger square into two segments, one of length ‘a’ and the other of length ‘b’, where, b > a. A possible value of ‘b/a’, is:
74. Diameter of the base of a water - filled inverted right circular cone is 26 cm. A cylindrical pipe, 5 mm in radius, is attached to the surface of the cone at a point. The perpendicular distance between the point and the base (the top) is 15 cm. The distance from the edge of the base to the point is 17 cm, along the surface. If water flows at the rate of 10 meters per minute through the pipe, how much time would elapse before water stops coming out of the pipe?
75. Aditya has a total of 18 red and blue marbles in two bags (each bag has marbles of both colors). A marble is randomly drawn from the first bag followed by another randomly drawn from the second bag, the probability of both being red is 5/16. What is the probability of both marbles being blue?
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