Cat 2009 Quanttest 124

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Quant Test 124

1. If a/(b+c) = b/(b+c) = c/(b+c) = r, then r cannot take any value except

j 1/2 k l m n j -1 k l m n j 1/2 or -1 k l m n j -1/2 or -1 k l m n j None of these k l m n i Skip this question j k l m n

2. If the sum of the first 11 terms of an arithmetic progression equals that of the first l9 terms, then what is the sum of the first 30 terms?

j 0 k l m n j -1 k l m n j 1 k l m n j 2 k l m n j Not unique k l m n i Skip this question j k l m n

3. In NutsAndBolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

j 130 minutes k l m n j 135 minutes k l m n j 170 minutes k l m n j 180 minutes k l m n j 200 minutes k l m n i Skip this question j k l m n

4. Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families in the locality is

j 4 k l m n j 5 k l m n j 2 k l m n j 3 k l m n j None of these k l m n i Skip this question j k l m n

5. The total number of integer pairs (x, y) satisfying the equation x + y = xy is

j 0 k l m n j 1 k l m n j 2 k l m n j 3 k l m n

j None of these k l m n i Skip this question j k l m n

6. There are “n” necklaces in a safe box (n > 1). Every necklace has the same number of diamonds. Each necklace has at least 2 diamonds. The total number of diamonds in these “n” necklaces is between 500 and 600. If this data is sufficient to find the value of n, then what can be the value of “n”?

j 22 k l m n j 23 k l m n j 27 k l m n j 29 k l m n j None of these k l m n i Skip this question j k l m n Directions for Questions from 7 to 8: Answer the questions on the basis of the information given below. The total number of students in three different sections namely I, II and III is ‘AA’, ‘BB’ and ‘CC’ respectively. The total number of students in the mentioned three sections is ‘DD0’. Assume that A, B and C are distinct natural numbers and D is a non zero digit. All the mentioned numbers are in the same base and the base is not greater than 9.

7. What is the maximum value of (A + B + C) ?

j 12 k l m n j 14 k l m n j 16 k l m n j 18 k l m n j None of these k l m n i Skip this question j k l m n

8. How many distinct values of (A, B and C) are possible?

j 10 k l m n j 12 k l m n j 14 k l m n j 8 k l m n j 6 k l m n i Skip this question j k l m n

9. Gautam decided to go to a temple only on first and the last day of a year. He continues to go to the temple in this fashion till the time he finds that he has visited the temple atleast once on each of the different days of a week. The minimum number of days required to achieve this is

j 1255 k l m n j 1462 k l m n j 1463 k l m n j 1827 k l m n j 1826 k l m n i Skip this question j k l m n

10. In a triangle ABC, the incircle touches the three sides AB, BC and CA at the points D, E and F respectively. If the length(in cm) of the sides AB, BC and CA are three consecutive even numbers, then which of the following cannot be the radius(in cm) of the incircle?

j 2 k l m n j sqrt(7) k l m n j sqrt(15) k l m n j sqrt(32) k l m n

j sqrt(3) k l m n i Skip this question j k l m n

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