Cat 2009 Quanttest 88

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Quant Test 88

1. Given that p, q and r are the length of three sides of a scalene triangle. If the equation 3x 2 + (5p2 /(p+q+r)) x + 2p2 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

2. 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

3. 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

4. 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

5. Raju went to a shop to buy a certain number of pens and pencils. Raju calculated the amount payable to the shopkeeper and offered that amount to him. Raju was surprised when the shopkeeper returned him Rs. 24 as balance. When he came back home, he realized that the shopkeeper had actually transposed the number of pens with the number of pencils. Which of the following is certainly an invalid statement?

j The number of pencils that Raju wanted to buy was 8 more than the number of pens k l m n j The number of pens that Raju wanted to buy was 6 less than the number of pencils. k l m n j A pen cost Rs.4 more than a pencil. k l m n j A pencil cost Rs.12 less than a pen. k l m n j None of the above k l m n i Skip this question j k l m n

6. Find the digit at the ten’s place of the number N = 7281 × 3264.

j 3 k l m n j 4 k l m n j 5 k l m n j 6 k l m n j 7 k l m n i Skip this question j k l m n

7. The value of a quadratic function f(x) is negative for all values of x, except for x = 2. If f(x = 0) = – 10, then find the value of f(x = – 2).

j – 40 k l m n j – 80 k l m n j – 60 k l m n j – 20 k l m n j Data Inconsistent k l m n i Skip this question j k l m n

8. If the length of the largest straight rod that can be put inside a cuboid is 10 m, then the surface area of the cuboid cannot be more than

j 100 m2 k l m n j 200 m2 k l m n j 400 m2 k l m n j 600 m2 k l m n j Cannot be determined k l m n i Skip this question j k l m n

9. 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

10. Let T be the set of integers 3, 11, 19, 27,…451, 459, 467 and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is

j 32 k l m n j 28 k l m n j 29 k l m n j 30 k l m n

j 27 k l m n i Skip this question j k l m n

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