Cat 2009 Quanttest 87

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Quant Test 87

1. 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

2. 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

3. A semicircle with center at C and radius equal to 4 units is drawn with AB as the diameter as shown in the figure given below. CDEF is a rectangle such that the ratio of area of the semicircle to the area of the rectangle is 2p : 3 . CE cuts the semicircle at P. Find the length of the line segment PB.

j 8/5 sqrt (5) units k l m n j 5/3 sqrt (5) units k l m n j 17/9 sqrt (5) units k l m n j 9/5 sqrt (5) units k l m n j 17/11 sqrt (5) units k l m n i Skip this question j k l m n

4. Two concentric circles are drawn with O as the center as shown in the figure given below. The ratio of the area of the annular ring bounded by these two circles and the quadrilateral EBCH is 3pi : 2 . Find the ratio of the radii of the smaller circle to the larger circle.

j 1:4 k l m n j 2:7 k l m n j 1:6 k l m n j 3 : 19 k l m n j 1:7 k l m n i Skip this question j k l m n

5. A point P is randomly chosen at a distance of 5 cm from the center of a circle. A chord AB is drawn passing through P. C is a point on the circumference of the circle such that AC = BC. If the radius of the circle is 13 cm, then which of the following cannot be a value of area(ΔABC)?

j 96 cm2 k l m n j 216 cm2 k l m n j 169 cm2 k l m n j 84 cm2 k l m n j Both (2) and (3) k l m n i Skip this question j k l m n

6. There were ten friends four of whom are Sanjay, Salim, Reena and Teena. A team of six is to be formed such that Reena & Teena are never together but Sanjay and Salim are always together. How many teams can be made?

j 110 k l m n j 68 k l m n j 77 k l m n j 76 k l m n j 108 k l m n i Skip this question j k l m n

7. 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

8. In the coming state elections, Bharat Mata Party (BMP) will contest for 77 assembly seats. As BMP’s majority vote bank is distributed amongst three communities viz. A, B and C, it will give election tickets only to those workers who belong to these communities. The workers of communities B and C are split into factions. Every faction of community B has 15 workers and that of community C has 25 workers. There were no factions among the workers belonging to community A. If BMP gives a ticket to a worker, it must give tickets to every other worker belonging to the same faction. BMP distinguishes between any two workers only on the basis of their communities. In how many ways can BMP distribute its election tickets giving at least one ticket to each community?

j 14 k l m n j 8 k l m n j 12 k l m n j 4 k l m n j 6 k l m n i Skip this question j k l m n

9. There are 6 boxes numbered 1, 2, …6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is

j 5 k l m n j 21 k l m n j 33 k l m n j 60 k l m n j 55 k l m n i Skip this question j k l m n

10. Consider the following two curves in the x-y plane: y = x3  + x2  + 5 y = x2  + x + 5 Which of the following statements is true for -2 < x < 2?

j The two curves intersect once k l m n j The two curves intersect twice k l m n j The two curves do not intersect k l m n j The two curves intersect thrice k l m n j None of the above k l m n i Skip this question j k l m n

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