Current GD topics with answers for CAT group discussion

1 Richard wrote all the possible two-digit numbers such that whenever one of the two digits is prime, the other is even ,and whenever one of the two digits is even, the other is prime. How many two-digit numbers did he write in all?

a. 35

b. 37

c. 39

d. None

2 If there are 10 positive real numbers n1 < n2 < n3 . . . . < n10. how many triplets of these numbers (n1 ,n2 ,n3 ) , ( n2, n3, n4). . . can be generated such that in each triplet the first number is always less than the second number , and the second number is always less than the third number ?

a. 45

b. 90

c. 120

d. 180

3 A rectangular pool of 20m wide and 60m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516m2, how wide, in meters, is the walkway?

a. 43 m

b. 2m

c. 3m

d. 3.5m

4 AA unit circle is divided into 10 sectors such that the area of the second sector is twice that of the first sector, the area of the third sector is twice that of the second and so on. Find in radians, the angle made by the first sector.

a. 2?/1023

b. ?/1024

c. 2?/511

d. ?/511

5 TOne bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million , what is the number in first generation ?

a. 1 million

b. 2 million

c. 4 million

6 ection for questions 26 & 27 A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the total production cost. Current gain is 20%. Due to change in the international scenario, cost of the German mark increased by 30% and that of USA dollar increased by 22%. Due to market conditions, the selling price cannot be increased beyond 10%. 26.What is the maximum current gain possible ?

a. 10%

b. 12.5%

c. 0%

d. 7.5%

7 If the USA dollar becomes cheap by 12% over its original cost and the cost of German mark increased by 20% , what will be the gain ?( the selling price is not altered ?)

a. 20%

b. 15%

c. 10%

d. 7.5%

8 ection for questions 28& 29 Consider the following 2 equations for answering the below questions (k + 1)X + 8Y = 4K kX + (k+3)Y = 3K -1 28. For what value of K will these equations have no solution ?

a. -3

b. 0

c. 3

d. None

9 For what value of K will these equations have more than one solution?

a. 1

b. 0

c. 2

d. -2

10 Four positive integers are such that any two of thefour have the same common factors and no two have any other factor in common.If the LCM ( Least Common Multiple ) of two of the four numbers is 2585 and theLCM of the other two numbers is 4277 , find the highest common factor of thefour numbers?

a.55

b.47

c. 91

d.235

11 The maximum number of regions into which a plane can be divided by five straight line is

a. 14

b. 15

c. 16

d. 17

12 A solid cube is cut into two equal halves by a plane passing through exactly two corners of the cube. Find the ratio of the total surface area of both the halves put together and the original total surface area of the cube.

a. ?3 : ?3 + ?2

b. ?6 + 1 : ?6

c. 6 : 6 + ?6

d. 3 + ?2 : 3

13 At whDirection for question number 3 & 4 Ajay , Bahnu and Chandu plan to travel from P and reach Q at 4:00 p.m. Bhanu starts 24 minutes after Ajay started from P. Had Chandu startred 12 minutes after Bhanu, all of them would have reached Q at 4:00 p.m But before Chandu left P, he recived a call from Ajay and was told to start immediately towards Q and at exactly the same time Ajay reversed his direction and traveled towards P. All the three of them meet at 3:24 p.m. at R (somewhere between P and Q). Each of them traveled with his own uniform speed. 3.At what time did Ajay start from P?

a. 2:12 p.m

b. 2:36 p.m

c. 2:48 p.m

d. cannot be determined

14 In the entire journey, if Ajay traveled 9 km more than chandu , what is the speed Bhanu?

a. 90 km/h

b. 30 km/h

c. 45 km/h

d. cannot be determined

15 There are two poles separated by a distance of 41 feet with their height as 21 feet and 20 feet respectively. There are two birds A and B on the two poles respectively. Both of them simultaneously startred moving towards an almond , which is placed in between two ploes. They reach the almond at the same time traveling at the same speed. What is the distance between the almond and the foot of first pole if both the birds take the shortest route ?

a. 20 feet

b. 21 feet

c. 25 feet

d. 29 feet

16 Raman has some gold coins with him. His friend Vaman asks him how many gold coins he has. Raman replied �The number of gold coins I have is a two-digit number which can be expressed as a sum of two perfect squares in tow different ways. Which of the following could not be the gold coins with Reman ?

a. 65

b. 58

c. 85

d. 50

18 A metal solid is in the form of a hemisphere with a cone hollowed out in the middle. The diameters of the hemisphere and the cone are 20cm and 18cm respectively. If the depth of the cone is 9cm, what is the volume of the metal in the solid?

a. 423.67p cm3

b. 1090.33p cm 3

c. 604.33pcm 3

d. 4361.33p cm3

19 All the page numbers of a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. which page number was added twice ?

a.44

b.45

c.10

d.12

20 Mohan draws a square ABCD of side 10 cm . He then draws 9 straight lines connecting A to each of 11 equally spaced points lying on CD (including C and D as the extremes). Find the total area of all possible triangles that can be formed.

a.325 sq.cm

b.1100 sq.cm

c.1150 sq.cm

d.2250 sq.cm

MATHS-SET23