Cat 2009 Quant Test10

 

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Quant Test 10

1. A customer ordered a fruit seller to prepare a fruit basket with three kinds of fruits namely mangoes, oranges and apples. He instructed him to put 20 fruits, and the fruit seller offered him the basket immediately that contained 20 fruits. Later on, when he returned back to home, his wife asked him if the number of apples are less than the number of oranges; and the number of oranges are less than the number of mangoes in the basket. He answered, “YES”. What is the probability that his answer was correct?

j 1/7 k l m n j 13 /77 k l m n j 3/ 7 k l m n j 10/ 77 k l m n j 3 /19 k l m n i Skip this question j k l m n

2.

Find the sum of the series S, where

j 13/3 k l m n j 11/ 3 k l m n j 25/ 6 k l m n j 23 /6 k l m n j 4 k l m n i Skip this question j k l m n

3. 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

4. Consider the following system of linear equations, in variables x, y and z, where x, y and z belong to real numbers. 2x +3y - 2z =0 4x +3y - 3z =0 14x - 6y - 5z =0 Find the number of integral values of z such that –43 <= (2z + y + x) <=15

j 21 k l m n j 22 k l m n j 23 k l m n j 20 k l m n j 19 k l m n i Skip this question j k l m n

5. In the following figure, the equilateral triangle ABC has an area of 900sqrt(3) m 2 . Points P and Q are the mid-points of AB and AC respectively. Find the area of the shaded region.

 

                                                  

j 64 sqrt(3) k l m n j 80 sqrt(3) k l m n j 75 sqrt(3) k l m n j 72 sqrt(3) k l m n j 60 sqrt(3) k l m n i Skip this question j k l m n

6. Two numbers have 36 factors each and HCF of these two numbers is 36. What is the minimum possible LCM of these two numbers if the power of any prime factor in these two numbers is not more than 3?

j cube(2) × cube(3) × sqr(5) × 7 k l m n j sqr(2) ×sqr( 3) × cube(5) × cube(7) k l m n j cube(2) ×cube( 3) × sqr(5) ×sqr( 7) k l m n j cube(2)× 32 × cube(5) × sqr(7) k l m n j cube(2) × sqr(3) × sqr(5) × sqr(7) k l m n i Skip this question j k l m n

7. Given that p, q and r are the length of three sides of a scalene triangle. If the equation 3x 2 + (5p 2 /(p+q+r)) x + 2p 2 k2   = 0 has distinct and real roots, then which of the following is a possible value of k?

j –0.55 k l m n j –0.45 k l m n j 0.6 k l m n j 0.75 k l m n j 1 k l m n i Skip this question j k l m n

8. 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

9. The sum of two numbers (1P1.431) 8 and (231.213) 8 is (234.820Q125) 10 . What is the sum of P and Q, where P and Q are single digit numbers?

j 8 k l m n j 7 k l m n j 5 k l m n j 3 k l m n j 2 k l m n i Skip this question j k l m n

10. How many integers less than 300 are relatively prime to either 10 or 18?

j 140 k l m n j 141 k l m n j 142 k l m n j 139 k l m n j 138 k l m n i Skip this question j k l m n

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