XAT2016 Related Question Answers
52. In an amusement park along with the entry pass a visitor gets two of the three available rides (A, B and C) free. ON a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visitors did not opt for ride A and B, or both. How many visited with the entry pass on that day?
53. $$\triangle$$ABC and $$\triangle$$XYZ are equilateral triangles of 54 cm sides. All smaller triangles like $$\triangle$$ANM, $$\triangle$$OCP, $$\triangle$$QPX etc. are also equilateral triangles. Find the area of the shape MNOPQRM.
54. Akhtar plans to cover a rectangular floor of dimensions 9.5 meters and 11.5 meters using tiles. Two types of square shaped tiles are available in the market. A tile with side 1 meter costs Rs. 100 and a tile with side 0.5 meters costs Rs. 30. The tiles can be cut if required. What will be the minimum cost of covering the entire floor with tiles?
55. Anita, Biplove, Cheryl, Danish, Emily and Feroze compared their marks among themselves. Anita scored the highest marks, Biplove scored more than Danish. Cheryl scored more than at least two others and Emily had not scored the lowest. Statement I: Exactly two members scored less than Cheryl. Statement II: Emily and Feroze scored the same marks. Which of the following statements would be sufficient to identify the one with the lowest marks?
56. Rani bought more apples than oranges. She sells apples at Rs. 23 apiece and makes 15% profit. She sells oranges at Rs. 10 apiece and marks 25% profit. If she gets Rs. 653 after selling all the apples and oranges, find her profit percentage.
57. Consider the set of numbers {1, 3, $$3^{2}$$, $$3^{2}$$,…...,$$3^{100}$$}. The ratio of the last number and the sum of the remaining numbers is closest to:
58. f is a function for which f(1)= 1 and f(x) = 2x + f(x - 1) for each natural number x$$\geq$$2. Find f(31)
59. Two numbers in the base system B are 2061$$_{B}$$ and 601$$_{B}$$. The sum of these two numbers in decimal system is 432. Find the value of 1010$$_B$$ in decimal system.
60. A water tank has M inlet pipes and N outlet pipes. An inlet pipe can fill the tank in 8 hours while an outlet pipe can empty the full tank in 12 hours. If all pipes are left open simultaneously, it takes 6 hours to fill the empty tank. What is the relationship between M and N?
61. Company ABC starts an educational program in collaboration with Institute XYZ. As per the agreement, ABC and XYZ will share profit in 60 : 40 ratio. The initial investment of Rs.100,000 on infrastructure is borne entirely by ABC whereas the running cost of Rs. 400 per student is borne by XYZ. If each student pays Rs. 2000 for the program find the minimum number of students required to make the program profitable, assuming ABC wants to recover its investment in the very first year and the program has no seat limits.
62. Study the figure below and answer the question:
Four persons walk from Point A to Point D following different routes. The one following ABCD takes 70 minutes. Another person takes 45 minutes following ABD. The third person takes 30 minutes following route ACD. The last person takes 65 minutes following route ACBD. IF all were to walk at the same speed, how long will it take to go from point B to point C?
63. Each day on Planet M is 10 hours, each hour 60 minutes and each minute 40 seconds. The inhabitants of Planet M use 10 hour analog clock with an hour hand, a minute hand and a second hand. If one such clock shows 3 hours 42 minutes and 20 seconds in a mirror what will be the time in Planet M exactly after 5 minutes?
64. a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc - (a + b + c)]?
65. A square piece of paper is folded three times along its diagonal to get an isosceles triangle whose equal sides are 10 cm. What is the area of the unfolded original piece of paper?
66. The difference between the area of the circumscribed circle and the area of the inscribed circle of an equilateral triangle is 2156 sq. cm. What is the area of the equilateral triangle?
67. A person standing on the ground at point A saw an object at point B on the ground at a distance of 600 meters. The object started flying towards him at an angle of 30° with the ground. The person saw the object for the second time at point C flying at 30° angle with him. At point C, the object changed direction and continued flying upwards. The person saw the object for the third time when the object was directly above him. The object was flying at a constant speed of 10 kmph.
Find the angle at which the object was flying after the person saw it for the second time. You may use additional statement(s) if required.
Statement I: After changing direction the object took 3 more minutes than it had taken before.
Statement II: After changing direction the object travelled an additional 200√3 meters.
Which of the following is the correct option?
68. For two positive integers a and b, if $$(a + b)^{(a + b)}$$ is divisible by 500, then the least possible value of a $$\times$$ b is:
69. Pradeep could either walk or drive to office. The time taken to walk to the office is 8 times the driving time. One day, his wife took the car making him walk to office. After walking 1km, he reached a temple when his wife called to say that he can now take the car. Pradeep figure that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office.
70. If a, b and c are 3 consecutive integers between -10 to +10 (both inclusive), how many integer values are possible for the expression? $$\frac{a^3+b^3+c^3+3abc}{(a+b+c)^2}$$=?
71. In the figure below, two circular curves create 60° and 90° angles with their respective centres. If the length of the bottom curve Y is 10p, find the length of the other curve.
72. ABCD is a quadrilateral such that AD = 9 cm, BC = 13 cm and ⎿DAB = ⎿BCD = 90°. P and Q are two points on AB and CD respectively, such that DQ : BP = 1 : 2 and DQ is an integer. How many values can DQ take, for which the maximum possible area of the quadrilateral PBQD is 150 sq.cm?
73.
Study the data given in the table below and answer the question that follow:
All figures are in percentage
Based on survey of ‘shop types’ Kamath categorized Indian states into four geographical regions as shown in the table above. His boss felt that the categorization was inadequate since important labels were missing. Kamath argued that no further labels are required to interpret the data.A consultant observing the data made the following two inferences:
Inference I: The number of Grocers per-thousand-population is the highest in North India.
Inference II: The number of Cosmetic per-thousand-population is the highest in South India.
Which of following options is DEFINITELY correct?
74. The average size of Food Shops in East India was twice that of Food Shops in West India. Which of the following cannot be inferred from the above data?
75. Bala collected the same data five years after Kamath, using the same categorization. His data is presented below: Graph: Which of the following statements can DEFINITELY be concluded?
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