QUANTITATIVE APTITUDE

Questions asked in XLRI Examination held on January 9, 2005

Directions: In each question below, choose the correct alternative from the four options provided. 1. Last year Mr Basu bought two scooters. This year he sold both of them for Rs 30,000 each. On one, he earned 20% profit, and on the other he made a 20% loss. What was his net profit or loss? (A) He gained less than Rs 2000 (B) He gained more than Rs 2000 (C) He lost less than Rs 2000 (D) He lost more than Rs 2000 2. In an examination, the average marks obtained by students who passed was x%, while the average of those who failed was y%. The average marks of all students taking the exam was z%. Find in terms of x, y and z, the percentage of students taking the exam who failed. ( z – x) (A) ( y – x) ( x – z) (B) ( y – z)

and at the point P, forming a loop. The straight line OP divides the loop into two parts. What is the ratio of the areas of the two parts of the loop? (A) 3 : 1 (B) 3 : 2 (C) 2 : 1 (D) 1 : 1 7. How many numbers between 1 to 1000 (both excluded) are both squares and cubes? (A) none (B) 1 (C) 2 (D) 3 8. An operation ‘$’ is defined as follows: For any two positive integers x and y, x$y =

F GH

x + y

y x

I JK then which of the following is an

(C)

( y – x) (z – y)

(D)

( y – z) ( x – z)

3. Three circles A, B and C have a common centre O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle is: 1 2 (A) (B) 3 5 (C)

integer? (A) 4$9 (B) 4$16 (C) 4$4 (D) None of the above 9. If f(x) = cos(x) then 50th derivative of f(x) is: (A) sin x (B) – sin x (C) cos x (D) – cos x 10. If a, b and c are three real numbers, then which of the following is NOT true?...

(1)