Cat 2009 Quanttest 91

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Quant Test 91

1. What is the probability of hitting a dart 1 cm away from the corner of a cardboard of dimensions 10 cm × 8 cm

j 22/141 k l m n j 11/140 k l m n j 11/280 k l m n j 11/140 k l m n j 11/150 k l m n i Skip this question j k l m n

2. 10000! = (100!)K × P, where P and K ∈ I. What can be the maximum value of K?

j 97 k l m n j 102 k l m n j 103 k l m n j 104 k l m n j 107 k l m n i Skip this question j k l m n

3. If p, q, r, and s are four positive real numbers, the minimum value of

j 1 k l m n j 2 k l m n j 2 sqrt(2) k l m n j 4 k l m n j 5 k l m n i Skip this question j k l m n

4. A container contains pure orange juice. Harish mixes pure water equal to 1/4 th of the volume of the orange juice in the container. Manish does not know it and sells 1/4 th of this mixture and adds water to it to replenish the quantity that he sold. What is the current proportion of water and orange juice in the container?

j 2:3 k l m n j 3:2 k l m n j 1:3 k l m n j 3:4 k l m n j 4:3 k l m n i Skip this question j k l m n Directions for Questions from 5 to 6: Answer the questions on the basis of the information given below. A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1, the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of 30 ? km/hr on the OR road, 20 ? km/hr on the IR road, and 15sqrt(5) km/hr on all the chord roads

5.

Amit wants to reach E2 from N1 using first the chord N1 – W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question?

j 60 k l m n j 45 k l m n j 90 k l m n j 105 k l m n j None of these k l m n i Skip this question j k l m n

6.

Amit wants to reach N2 from S1. It would take him 90 minutes if he goes on minor arc S1 – E1 on OR, and then on the chord road E1 – N2. What is the radius of the outer ring road in kms?

j 60 k l m n j 40 k l m n j 30 k l m n j 20 k l m n j 10 k l m n i Skip this question j k l m n

7. How many 4-digit positive integral numbers are there in base 7, if you are counting the numbers in the same base system?

j 2058 k l m n j 5666 k l m n j 6000 k l m n j 6666 k l m n j None of these k l m n i Skip this question j k l m n

8. The height of an apple tree is given by the sum of two terms. The first term is directly proportional to the weight of the tree and the second term is directly proportional to the square of the weight of the tree. The height of the tree was 6 m and 8 m, when its weight was 40 kg and 50 kg respectively. Find the approximate weight of the tree when its height was 5 m.

j 39 kg k l m n j 44 kg k l m n j 25 kg k l m n j 35 kg k l m n j 32 kg k l m n i Skip this question j k l m n

9. Tania prepares for the CAT examination by practicing for 100 days. On any of these 100 days she does not solve more than 20 questions. If on any day, she solves more than 12 questions, then she solves at most 6 questions each on the next two days. What is the maximum possible number of questions that she can solve over the period of 100 days?

j 1200 k l m n j 1208 k l m n j 1220 k l m n j 960 k l m n j 1240 k l m n i Skip this question j k l m n

10. If the sum of lengths of three sides of a rectangle is 100 units, then find the maximum possible area of the rectangle ?

j 1110.9 sq. units k l m n

j 1250 sq. unit k l m n j 990 sq. units k l m n j 1008 sq. units k l m n j 1225 sq. units k l m n i Skip this question j k l m n

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