XAT 2016 Question Paper

Instructions

For the following questions answer them individually

XAT 2016 - Question 51


In an amusement park, a visitor gets to ride on three different rides (A, B and C) for 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 the amusement park on that day?

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XAT 2016 - Question 52


$$\triangle$$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.

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XAT 2016 - Question 53


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?

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XAT 2016 - Question 54


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?

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XAT 2016 - Question 55


Rani bought more apples than oranges. She sells apples at Rs. 23 apiece and makes 15% profit. She sells oranges at Rs. 10 a piece and makes 25% profit. If she gets Rs. 653 after selling all the apples and oranges, find her profit percentage.

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XAT 2016 - Question 56


Consider the set of numbers {1, 3, $$3^{2}$$, $$3^{3}$$,…...,$$3^{100}$$}. The ratio of the last number and the sum of the remaining numbers is closest to:

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XAT 2016 - Question 57


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)

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XAT 2016 - Question 58


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.

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XAT 2016 - Question 59


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?

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XAT 2016 - Question 60


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.

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