CAT1999 Related Question Answers
28.
DIRECTIONS for the following two questions: The following table presents the sweetness of different items relative to sucrose, whose sweetness is taken to be 1.00. 
What is the maximum amount of sucrose (to the nearest gram) that can be added to one-gram of saccharin such that the final mixture obtained is atleast 100 times as sweet as glucose?
29. Approximately how many times sweeter than sucrose is a mixture consisting of glucose, sucrose and fructose in the ratio of 1: 2: 3?
30.
DIRECTIONS for the following two questions: These questions are based on the situation given below: A, B, C, D, E and F are a group of friends from a club. There are two housewives, one lecturer, one architect, one accountant and one lawyer in the group. There are two married couples in the group. The lawyer is married to D who is a housewife. No lady in the group is either an architect or an accountant. C, the accountant, is married to F who is a lecturer. A is married to D and E is not a housewife.What is E?
34.
DIRECTIONS for the following two questions: These questions are based on the situation given below:A rectangle PRSU, is divided into two smaller rectangles PQTU, and QRST by the line TQ. PQ=10cm, QR = 5 cm and RS = 10 cm. Points A, B, F are within rectangle PQTU, and points C, D, E are within the rectangle QRST. The closest pair of points among the pairs (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) are $$10 \sqrt{3}$$ cm apart.Which of the following statements is necessarily true?
35. AB > AF > BF; CD > DE > CE; and BF = $$6\sqrt{5}$$ cm. Which is the closest pair of points among all the six given points?
36.
DIRECTIONS for the following questions: These questions are based on the situation given below: In each of the questions a pair of graphs F(x) and F1(x) is given. These are composed of straight-line segments, shown as solid lines, in the domain $$x\epsilon (-2, 2)$$.choose the answer as a. If F1(x) = - F(x)b. if F1(x) = F(- x) c. if F1(x) = - F(- x)d. if none of the above is true
40.
DIRECTIONS for the following questions: These questions are based on the situation given below:There are in blue vessels with known volumes $$V1, V2 , ...., V_m$$, arranged in ascending order of volume, where $$v_1 > 0.5$$ litre, and $$V_m < 1$$ litre. Each of these is full of water initially. The water from each of these is emptied into a minimum number of empty white vessels, each having volume 1 litre. The water from a blue vessel is not emptied into a white vessel unless the white vessel has enough empty volume to hold all the water of the blue vessel. The number of white vessels required to empty all the blue vessels according to the above rules was n.Among the four values given below, which is the least upper bound on e, where e is the total empty volume in the m white vessels at the end of the above process?
41. Let the number of white vessels needed be n1 for the emptying process described above, if the volume of each white vessel is 2 liters. Among the following values, which is the least upper bound on n1?
42.
DIRECTIONS for the following questions: These questions are based on the situation given below: There are fifty integers $$a_1, a_2,...,a_{50}$$, not all of them necessarily different. Let the greatest integer of these fifty integers be referred to as $$G$$, and the smallest integer be referred to as $$L$$. The integers $$a_1$$ through $$a_{24}$$ form sequence $$S1$$, and the rest form sequence $$S2$$. Each member of $$S1$$ is less than or equal to each member of $$S2$$.All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true?
43. Elements of $$S1$$ are in ascending order, and those of $$S2$$ are in descending order. $$a_{24}$$ and $$a_{25}$$ are interchanged. Then, which of the following statements is true?
44. Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then x cannot be less than:
45.
DIRECTIONS for the following questions: These questions are based on the situation given below: Let x and y be real numbersf(x, y) = | x + y |F(f(x, y)) = -f(x, y)G(f(x, y)) = -F(f(x, y))What is the value of f(G(f(1, 0)), f(F(f(1, 2)), G(f(1, 2))))?
47.
DIRECTIONS for the following questions:These questions are based on the situation given below: A robot moves on a graph sheet with x and y-axes. The robot is moved by feeding it with a sequence of instructions. The different instructions that can be used in moving it, and their meanings are: Instruction Meaning GOTO(x,y) move to point with coordinates (x, y) no matter where you are currently WALKX(P) Move parallel to the x-axis through a distance of p, in the positive direction if p is positive, and in the negative direction if p is negative WALKY(P) Move parallel to the y-axis through a distance of p, in the positive direction if p is positive, and in the negative direction if p is negative.The robot reaches point (6, 6) when a sequence of three instructions is executed, the first of which is a GOTO(x, y) instruction, the second is WALKX(2) and the third is WALKY(4). What are the values of x and y?
48. The robot is initially at (x, y), x > 0 and y < 0. The minimum number of instructions needed to be executed to bring it to the origin (0,0) if you are prohibited from using the GOTO instruction is:
49.
DIRECTIONS for the following three questionsThese questions are based on the situation given below:A road network (shown in the figure below) connects cities A, B, C and D. All road segments are straight lines. D is the midpoint on the road connecting A and C. Roads AB and BC are at right angles to each other with BC shorter than AB. The segment AB is 100 km long. Ms. X and Mr. Y leave A at 8:00 am, take different routes to city C and reach at the same time. X takes the highway from A to B to C and travels at an average speed of 61.875 km per hour. Y takes the direct route AC and travels at 45 km per hour on segment AD. Y's speed on segment DC is 55 km per hour.
What is the average speed of Y in km per hour?
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