Cat 2009 Quant Test 24

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Quant Test 24 Directions for Questions from 1 to 2: Answer the questions on the basis of the information given below. A square ABDE and a regular pentagon BPQRC are drawn on the sides AB and BC respectively of an equilateral triangle ABC. The square and the pentagon lie completely outside the triangle ABC and the length of the side of the triangle ABC is 1 unit. Several isosceles triangles are drawn such that all the vertices of the triangle is among the points A, B, C, D, E, P, Q and R. Also, atleast one of the points A, B and C is a vertex of such an isosceles triangle.

1. What is the area(in square units) of the ΔAEC?  

j 1/2 k l m n j 1/4 k l m n j 1/ 2 sqrt(2) k l m n j 2/3 k l m n j 1 /sqrt( 2) k l m n i Skip this question j k l m n

2. How many distinct such isosceles triangles can be drawn?  

j 16 k l m n j 17 k l m n j 18 k l m n j 19 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 3 to 4: Answer the questions on the basis of the information given below. Given that f(1) = 1, f(2x) = 4f(x) + 6 and f(x + 2) = f(x) + 12x + 12 for all real values of x.

3. What is the value of f(20)?  

j 502 k l m n j 1068 k l m n j 1198 k l m n j 4678 k l m n j None of these k l m n i Skip this question j k l m n

4. What is the value of f(22) – f(5)?  

j 1247 k l m n j 681 k l m n j 1741 k l m n j 1547 k l m n j 1377 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

www.complore.com/test4PDF.php?id=72 j None of these k l m n i Skip this question j k l m n

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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. Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?

j 1/12 k l m n j 1/6 k l m n j 1/4 k l m n j 1/3 k l m n j 1/8 k l m n i Skip this question j k l m n

7. 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

8. Suppose n is an integer such that the sum of the digits of n is 2, and 101 0 < n < 101 1. The number of different values for n is

j 11 k l m n j 10 k l m n j 9 k l m n j 8 k l m n j 7 k l m n i Skip this question j k l m n

9. 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

10. On January 1, 2004 two new societies, SI and S2, are formed, each with n members. On the first day of each subsequent month, S1 adds b members while S2 multiplies its current number of members by a constant factor r. Both the societies have the same number of members on July 2, 2004. If b =10.5n, what is the value of r?

j 2.0 k l m n j .9 k l m n j 1.8 k l m n j 1.7 k l m n j 1.5 k l m n i Skip this question j k l m n

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