Cat 2009 Quant Test 76

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Quant Test 76

1. In a unit square ABCD, points E and F are marked on the sides AB and BC respectively such that AE = BF. G is the point of intersection of the line segments DE and AF. What is the minimum possible length (in units) of the line segment BG?

j 1/sqrt(2) k l m n j 1/2 k l m n j sqrt(8) - 1/7 k l m n j 1/3 k l m n j 1/6 k l m n i Skip this question j k l m n

2. Mr. X while buying cloth uses a faulty meter tape which actually measures 110 cm and while selling cloth, he uses a faulty meter tape which actually measures 90 cm. If he buys the cloth at a discount of 5% on the marked price and sells it on a discount of 10% on the same marked price, then what is his percentage gain or loss?

j 15.8% profit k l m n j 4.21% loss k l m n j 5% loss k l m n j 25% profit k l m n j None of these k l m n i Skip this question j k l m n

3. A sheet in the form of an equilateral triangle of side 20 cm is cut only once from one of the corners to form a trapezium. Two such identical trapeziums are placed on a table to form a parallelogram such that the sides of trapezium touch each other. What is the perimeter of the parallelogram formed?

j 60 k l m n j 80 k l m n j 100 k l m n j 120 k l m n j Data Insufficient k l m n i Skip this question j k l m n

4. Given that the cost price of 10 oranges is equal to the cost price of 1 kg of apples and the cost price of 12 apples is equal to the cost price of 1 kg of oranges. If the selling price of 15 oranges is equal to the selling price of 1 kg of apples, then the selling price of 1 kg of oranges is equal to selling price of (Assume that all the apples are identical and this holds true for the oranges as well.)

j 8 apples k l m n j 9 apples k l m n j 10 apples k l m n j 12 apples k l m n j 9 apples k l m n i Skip this question j k l m n

5. Consider the sequence of numbers a 1 , a2 , a3 ...to infinity where a1 = 81.33 and a2 = -19 and a j = a j-1 -a j-2 for j > 3 . What is the sum of the first 6002 terms of this sequence?

j -100.33 k l m n

j -30.00 k l m n j 62.33 k l m n j 119.33 k l m n j 125.33 k l m n i Skip this question j k l m n Directions for Questions from 6 to 7:

6. Which of the following is necessarily true?

j f 4 (x) = f1 (x) for all x k l m n j f 1(X)= -f 3 (-x) for all x k l m n j f 2 (-x) = f 4 (x) for all x k l m n j f 1(X) +f 3 (x) =0 for all x k l m n j f 1(X) - f 3 (x) =0 for all x k l m n i Skip this question j k l m n

7. How many of the following products are necessarily zero for every x: f 1(X) f 2(x), f 2 (X) f 3 (x), f 2 (x) f 4 (x).

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

8. A new flag is to be designed with six vertical stripes using some or all of thecolours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is

j 12x81 k l m n j 16x192 k l m n j 20x125 k l m n j 24x216 k l m n j 26x125 k l m n i Skip this question j k l m n Directions for Questions from 9 to 10: 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.

9. 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

10. 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

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