CAT 1999 Question Paper

For a country to be on the coverage frontier, it should not be dominated by any other country. That is no other country should have both (sanitation facilities and drinking water coverage) better than it.
The first three options, though true, are not the reason for India not being on the coverage frontier. That is because they don't mention the other parameter at all.

For example, option A doesn't mention sanitation facilites while options B and C don't mention drinking water coverage. Hence, none of A,B and C are the reason India is not on the coverage frontier.

Option D is factually wrong as Indonesia has lesser drinking water coverage than India and doesn't dominate it.

Hence, none of the options given are correct.

The most disparity in rural sector is in India = 79-14 = 65

The disparity in all other countries is less than 65.

The least disparity => The least difference between the coverage in urban drinking water facilities and the coverage in urban sanitation facilities.

Phillipines has a disparity of 92-88 = 4, which is the least.

Hence, option C is the answer.

Using statement A, we cannot infer the number of students in the class.

Using statement B, we can say that the sum of weights of heaviest and the lighest persons is equal to twice the average weight of the class. But we cannot infer the number of students in the class.

Using both the statements as well, we do not have any information through which we can find the answer.

Hence, option D is the answer.

Using statement 1, we come to know that if the inner radius is r, then the outer radius is r+1

Using statement 2, Volume = 20 l = 20000$$cm^3$$

$$\frac{4}{3} \pi (r+1)^3-r^3$$ = 20000

We can calculate r using this equation.

Using only statement A, we know that the shape of th field is rectangle. We cannot infer anything else with only statement A.

Using only statement B, we know that C is one of the vertices, but we do not know how many vertices exist.

Using both A and B, we know that the field is rectangular in shape and the length and breadth are 300 metres and 100 metres.

Hence, we can find the value of the diagonal which is the maximum distance between any two points inside the field.

Hence, option C is the answer.

Growth = Change in value on Y-axis / Change in value on X-axis = Tangent of the angle made by the line with the X-axis

In statement 1, since we know both the angles, we can calculate the growth for both the periods and hence the ratio of growths.

Using statement 2 alone, we cannot determine the answer. Option a) is the correct answer.

From statement I, We can draw the following figure

From the figure we can say that in triangle GCD we know 2 sides GC and CD, so we can find the third side
Also we can find the angle GDC(Using trigonometric ratios)

Similarly in triangle CDE, we know CE and DE, so we can find angle CDE.
From this we can get the angle FDE. Now in right angled triangle FDE, we can find the angle DFE.
So we can answer from statement I
Now let us consider statement II

By using trigonometric relations angle CFG can be calculated.
From this we can get angle DFE
Iin triangle CGD we can find angles GDC(Using trigonometric ratios)
Now GDC = CDJ
Thus we can find EDH and from that we can find EHD.
Hence the question can be answered from statement II alone.

ax + by = c

dx + ey = f

Using statement A, we can modify the equation ax + by + c to k(dx+ey=f) 

=> We cannot find the point (x,y).

Using statement B, we can change the equations to x + y = c and 2x + 2y = f (f not equal to 2c)

As the slopes are equal and the intercepts are not equal, we can say that the equations do not have a solution.

Hence, we can answer the question using statement B but not A.

The value of b is unknown in this question.

Using Statement a, we can say that B is not a mathematician. A may be or may not be a mathematician as we do not know whether he can add three numbers correctly or not. Similarly C may be or may not be a mathematician as we do not know the value of b.

Using statement b, We cannot find out for sure if A and C are mathematicians or not.

So the question cannot be answered even by using both statements together.