Cat 2009 Quanttest 115

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Quant Test 115

1. a, b, c, d and e be non-negative real numbers such that a + b + c + d + e = 10. Let X be the maximum of the numbers a + b, b + c, c + d and d + e. The least possible value of X lies in the interval

j [0, 2] k l m n j [2, 3] k l m n j [3, 4] k l m n j [4, 5] k l m n j [5, 10] k l m n i Skip this question j k l m n

2. A brokerage house offers 3 stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock. 2 municipal bonds and 3 blocks of preferred stock. Portfolio III consists of 2 blocks of common stock. 2 municipal bond and 3 blocks of preferred stock. A customer wants 12 blocks of common stock. 6 municipal bonds and 6 referred stocks. How many portfolio III should be offered?

j 1 k l m n j 2 k l m n j 3 k l m n j 4 k l m n j None of the above k l m n i Skip this question j k l m n

3. If the polynomial x3 + px + q has three distinct roots, then which of the following is a possible value of p?

j -1 k l m n j 0 k l m n j 1 k l m n j 2 k l m n j 3 k l m n i Skip this question j k l m n

4. Let S be the set of rational numbers with the following properties:

Which of the following is true?

1. 2. 3. 4. 5.

j S contains all rational numbers in the interval 0 < x < 1 k l m n j S contains all rational numbers in the interval –1 < x < 1 k l m n j S contains all rational numbers in the interval –1 < x < 0 k l m n j S contains all rational numbers in the interval 1 < x <2 k l m n j S contains all rational numbers in the interval –1<=X<=1 k l m n

i Skip this question j k l m n

5. Which equation can be graphically represented as follow?

j 8x^2 – 15y^2= 169 k l m n j 9x^2 – 16y^2 = 144 k l m n j |(x – 8)(y – 15)| = 12 k l m n j |(x – 9)(y –16)| = 13 k l m n j None of the above k l m n i Skip this question j k l m n Directions for Questions from 6 to 7: Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.

6. Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?

j Spotted came in first k l m n j Red finished last k l m n j White came in second k l m n j Black came in second k l m n j There was one horse between Black and White k l m n i Skip this question j k l m n

7. Which of the following cannot be true?

j At least two horses finished before Spotted k l m n j Red finished last k l m n j There were three horses between Black and Spotted k l m n j There were three horses between White and Red k l m n j Grey came in second k l m n i Skip this question j k l m n

8.

Balancing cards on one another where some are placed horizontally and others diagonally (slant fashion) is a popular trick of all magicians. 30 playing cards of length 12 cm and breadth 6 cm are used to build a pyramidal structure with 4 horizontal cards at the base. 8 cards are then put diagonally on these cards to give four peaks. 3 cards are then put on the 4 peaks. The process continues till the top is a peak made by 2 cards. Find the area covered by the front side of the pyramid.

j 288 sqrt(3) cm2 k l m n j 180 sqrt(3) cm2 k l m n j 360 sqrt(3) cm2 k l m n j 576 sqrt(3) cm2 k l m n j None of these k l m n i Skip this question j k l m n

9.

A traveler, on his way to a certain village A, reaches a road junction, where he can turn left or right. He knows that only one of the two roads leads to village A, but unfortunately, he does not know which one. Fortunately, he sees two twin-brothers standing at the road junction, and he decides to ask them for directions. The traveler knows that one of the two brothers always tells the truth and the other one always lies. Unfortunately, he does not know which one always tells the truth and which one always lies. With which of the following questions can the traveler find out the way

to village A by asking just this one question to one of the two brothers?

j Does the left road lead to village A according to your brother? k l m n j Which road leads to village A according to your brother? k l m n j If I were to take the left road then what according to your brother will be the answer to the question Am I on the right road ? k l m n j Does the right road lead to village A according to your brother? k l m n j None of these k l m n i Skip this question j k l m n

10.

A company manufactures pencils in boxes of 6, 9, and 20. The boxes are sealed and the pencils cannot be sold loose. What is the largest number of pencils that a wholesaler cannot purchase using some combination of these boxes?

j 43 k l m n j 199 k l m n j 99 k l m n j 86 k l m n j None of these k l m n i Skip this question j k l m n

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