Cat 2009 Quanttest 116

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Quant Test 116

1. Four black cows and three brown cows give as much milk in five days as three black cows and five brown cows give in four days. If a black cow gives 10 L of milk per day, then how much milk would be given by a brown cow per day under the same conditions.

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

2. I cut a piece of paper in four equal parts. Now, I cut exactly one out of these four parts into four equal parts. Now, again if I keep on repeating the same process for infinite number of times, then which of the following can be the number of parts of paper at any instant of time?

j 2048 k l m n j 2049 k l m n j 2050 k l m n j 2051 k l m n j 2052 k l m n i Skip this question j k l m n

3. Two cyclists are travelling at a speed of 3 km/hr and 10 km/hr around a circular track. What should be the ratio of number of distinct points that they would meet on that track if they travel in the same direction first and in the opposite direction next?

j 7 : 13 k l m n j 3 : 10 k l m n j 3:7 k l m n j 30 : 13 k l m n j Cannot be determined k l m n i Skip this question j k l m n

4. Assume r, s and t be three distinct integers between 0 and 10. If 1/r + 1/s -3/t = 2/r then find the number of distinct values of (r + s – t).

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 5 k l m n i Skip this question j k l m n

5. In Triangle ABC, D and E are points on side AC such that AD:DE:EC is 2:1:1. BD and BE are joined. Point F divides BD in the ratio 1:2 and point G divides BE in the ratio 2:1. Find the ratio of the area of Triangles (AFG + BFG) to the area of the Triangle ABC.

j 2:5 k l m n j 3 : 10 k l m n

j 1:3 k l m n j 1:4 k l m n j 2:7 k l m n i Skip this question j k l m n

6. If the sum of the digits of a three-digit number is subtracted from that number, it results in a two-digit number. This process of subtracting the sum of digits of a number from that number is continued further with that resulting two-digit number also, till we get a factor of the original three-digit number. Which of the following is a factor of the original three-digit number?

j 5 k l m n j 6 k l m n j 7 k l m n j 11 k l m n j 13 k l m n i Skip this question j k l m n

7. There are two numbers A and B. A can be expressed as a product of 13 and a two-digit prime number and B can be expressed as a product of 17 and a two-digit prime number. If the unit’s digit of the product of A and B is 7, then how many distinct products of A and B are possible?

j 48 k l m n j 55 k l m n j 80 k l m n j 110 k l m n j 120 k l m n i Skip this question j k l m n

8. In the figure given below, the two circles touch externally. AB is a diameter of the larger circle and C is the centre of the smaller circle. If ΔABC has an area of 289 sq. cm, then which of the following can be the length of the line segment CD?

j 26 cm k l m n j 28 cm k l m n j 30 cm k l m n j 32 cm k l m n j None of these k l m n i Skip this question j k l m n

9. In the figure given below ABCD is a square and ΔPDC is isosceles with PD = PC. If the area of ΔPDC is twice the area of the square, then find the ratio of the area of ΔPDC that lies outside the square to the area of the square.

j 3/2 k l m n j 9/8 k l m n j 3/4 k l m n j 9/7 k l m n j 1/2 k l m n i Skip this question j k l m n

10. Consider the set P = –5, –3, –1, 1, 3, 5…. consisting of 1998 numbers. If ‘a’ be the average of the elements in P and ‘b’ be twice the average of the first 1998 natural numbers, then which of the following is equal to (a – b)?

j –6 k l m n j 5 k l m n j –8 k l m n j –7 k l m n j –9 k l m n i Skip this question j k l m n

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