Cat 2009 Quant Test 49

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Quant Test 49

1. How many different points in the X-Y plane are at a distance of 5 units from the origin and have co-ordinates (a, b), where ‘a’ and ‘b’ are integers?

j 6 k l m n j 8 k l m n j 10 k l m n j 12 k l m n j 16 k l m n i Skip this question j k l m n

2. S is a set of triangles such that no two triangles in S are similar, all triangles in S are having angles in integral degrees. What is the maximum possible number of different isosceles triangles in S?

j 88 k l m n j 89 k l m n j 90 k l m n j 91 k l m n j 92 k l m n i Skip this question j k l m n

3. A rectangle with perimeter 88 m is partitioned into 5 congruent rectangles, as indicated in the diagram given below. Find the perimeter of each of the congruent rectangles.

j 20 m k l m n j 32 m k l m n j 48 m k l m n j 96 m k l m n j 40 m k l m n i Skip this question j k l m n

4. Srinivas was able to find the two natural numbers, both greater than one as soon as their product was told to him. There is no other piece of information that was given to him. If the product of the two natural numbers is greater than 40, then which of the following could be the product of the two numbers?

j 48 k l m n j 55 k l m n j 60 k l m n j 63 k l m n j 42 k l m n

i Skip this question j k l m n

5. A trapezium DEFG is circumscribed about a circle that has centre C and radius 2 cm. If DE = 3 cm and the measure of ∠DEF=∠EFG=90°, then find the area of trapezium DEFG.

j 18 k l m n j 16 k l m n j 15 k l m n j 12 k l m n j 20 k l m n i Skip this question j k l m n

6. The total number of dogs in a colony is a composite number less than 200. The ratio of the number of dogs which are Pomeranian, to those who are not, could be

j 100 : 49 k l m n j 102 : 55 k l m n j 87 : 76 k l m n j 94 : 85 k l m n j 86 : 101 k l m n i Skip this question j k l m n

7. A trader used to make 5% profit on an item selling at usual marked price. One day, he trebled the marked price of the item and finally offered a discount of 30%. Find the percentage profit he made on the item that day.

j 120.5% k l m n j 100% k l m n j 99.5% k l m n j 94.5% k l m n j None of these k l m n i Skip this question j k l m n

8. Find the sum of the series

j n(n + 1) / 2 k l m n j 2/ n(n +1) k l m n j n(n+ 1)(2n + 1)/ 12 k l m n j n(n +1)/ 4 k l m n j 4 / n(n +1) k l m n i Skip this question j k l m n

9. The number of integral solutions for (x, y) satisfying the equation x2 = 14 + y2 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 More than 3 k l m n i Skip this question j k l m n

10. A picnic invites two kinds of charges: bus fare, which is independent of the number of people attending the picnic and buffet lunch, which increases directly with an increase in the number of people. The charges are calculated to be Rs. 165 per head when there are 200 invitees and Rs. 170 per head when there are 150 invitees. What would be the charges per head when there are 100 invitees?

j Rs.175 k l m n j Rs.180 k l m n j Rs.185 k l m n j Rs.190 k l m n j Rs.195 k l m n i Skip this question j k l m n

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