Cat 2009 Quanttest 125

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Quant Test 125

1. There are three natural numbers X, Y and Z such that the LCM of (X, 120) is 1320, LCM of (Y, 120) is 1680 and LCM of (Z, 120) is 1800. Which of the following statement is true?

j X, Y and Z all three can be perfect square. k l m n j Only Y and Z can be perfect square. k l m n j Only Y can be both perfect square and perfect cube. k l m n j Z is definitely a perfect square. k l m n j Z can be a perfect square. k l m n i Skip this question j k l m n

2. When the air-conditioner is on, a typist can type X pages per hour. However, when the air-conditioner is off, she can type at 65 % of the earlier efficiency (when the air-conditioner is on). How many hours would she take to type out 575 pages when the air-conditioner is off?

j 375.4 X k l m n j 884.6 X–1 k l m n j 36.5 X k l m n j 454.3 X–1 k l m n j None of these k l m n i Skip this question j k l m n Directions for Questions from 3 to 4:

3. 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

4. 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

5. If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be

j equal to the side of the cube k l m n j sqrt(3) times the side of the cube k l m n j 1/sqrt(3) times the side of the cube k l m n j impossible to find from the given information k l m n j half of the side of the cube k l m n i Skip this question j k l m n

6. In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If Ð CBE = 65°, then what is the value of Ð DEC?

j 35 k l m n j 55 k l m n j 45 k l m n j 25 k l m n j 20 k l m n i Skip this question j k l m n

7. A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?

j 4Sqrt(2) k l m n j 2Sqrt(2) k l m n j Sqrt(2) k l m n j Sqrt(1/2) k l m n j None of these k l m n i Skip this question j k l m n Directions for Questions from 8 to 10: Answer the questions on the basis of the information given below. In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have a common tangent that touches them at points Rand S respectively. This common tangent meets the line joining P and Q at O. Thediameters of I andll are in the ratio 4:3, It is also known that the length of PO is 28 cm.

8. The length of SO is

j 83 cm k l m n j 103 cm k l m n j 123 cm k l m n j 143 cm k l m n j 150 cm k l m n i Skip this question j k l m n

9. What is the radius of the circle II?

j 2 cm k l m n j 3 cm k l m n j 4 cm k l m n j 5 cm k l m n j 6 cm k l m n i Skip this question j k l m n

10. What is the ratio of the length of PQ to that of QO?

j 1:4 k l m n j 1:3 k l m n j 3:8 k l m n j 3:4 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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