CAT 1991 Question Paper

Considering first statement and second statement alone, information will not suffice to find the sequence of stations,
But if we consider both statements together we can tell about the sequence of stations as between A and B, Mr. Thomas travels with Mr. Murthy but not with Mr. Rahman. That means Mr. Thomas must have departed from station C and arrived at station D.
And it is also given that between C and D there are two segments. Hence, E lies between C and D, and Mr. Rahman departed from station D.

Putting y as x and x as y in given options, only options B satisfies the function property as follows.

x = $$\frac{2y+3}{3y-2}$$

or 3xy - 2x = 2y+3

or y(3x-2) = 2x+3

or $$y = \frac{2x+3}{3x-2}$$

On solving both equations, we will get $$x = \frac{23}{2+2k}$$
now for having no solutions to system 2+2k should be 0.
Hence k=-1

For a number to be even, its unit digit should be 0,2,4,6,8
Case 1: One of the digit is 5
Hence according to question, 5 can't come in middle and at unit's place, so numbers will be 570,572,574,576,578.
Case 2: No digit is 5
Hence the hundreds place can be filled in 8 ways (except 0,5) and tens place can be filled in 9 ways (except 5).
Number of ways = 8 * 9 * 5 = 360
Hence total number of ways = 360 + 5 = 365

Suppose he appointed x persons and y of them didn't come. Hence work done by each of them increases by 32.

So $$\frac{480}{x-y} - \frac{480}{x} = 32$$

Now we can check options by putting in the above eq. 

x=10 and y=4 will be our answer

Let's say Iqbal has x cards initially and Mushtaq has y number of cards initially.

So first Mushtaq gave t cards to Iqbal, hence (x+t) = 4(y-t)

Now second time, Iqbal gave t cards to Mushtaq, hence x-t = 3(y+t)

Solving above two equations we will get x=31t and y=9t

And we know x+y<52 hence 40t<52 

because t should be a whole number it will be 1 here and x=31 and y=9

Number of people owning exactly 2 articles = 9

Number of people owning exactly 3 articles = 1

Applying AUBUC formula, we get

AUBUC = 22+15+14 - 9 -2*(1)=40

Number of people who do not own any article = 50-40 = 10

Suppose consecutive odd integers are: (a-2), a, (a+2)

Hence, 3a-6 = 2(a+2) + 3 => a=13

a+2 = 15

4 first level nodes are connected to A => 4 ways.

Each of these first level nodes are connected to 1 second level node by four connections => 4 ways

Each of these second level nodes are connected to 2 third level nodes => 2 ways.

Each of these third level nodes are connected to B by 1 route => 1 way

=> 4 * 4 * 2 * 1 = 32 ways.

Let the side of the square be 1 cm

So, area of triangle AGE = 1/2 * 1/2 * 1/2 = 1/8

Similarly, area of triangle EBF = 1/8

Area of triangle DFC = 1/2 * 1 * 1/2 = 1/4

Area of the square = 1*1 = 1

So, area of the quadrilateral = 1 - (1/8 + 1/8 + 1/4) = 1 - 1/2 = 1/2

Option a) is the correct answer.