CAT 1998 Question Paper

The definition of the given function is expressed in statement 2, where  $$a \circledast b=\frac{a+b}{a}$$

Hence $$2\circledast3=\frac{2+3}{2}$$.

Hence the answer can be determined by b alone. A does not give any releant information.

Let the total questions be x and the questions solved by Radha and Rani be y and z respectively.

According to the first statement, y+z = 20% of x

Accoding to the second statement, y = 5/3rd of z

There are 2 equations and three variables. Hence the solution cannot be determined.

Let price of tea be t, coffee be c and cold drink be d.

Statement 1: c=t+5, we cannot infer value of t from this information

Statement 2: c=d-5 and d=3t, we cannot infer the value of t from this information

Using the statements together, c=t+5 and c=3t-5.

=>t+5=3t-5

=>2t=10

=> t=5

Hence, we can answer the questions using both statements together.

We cannot uniquely determine a value for a using either statement alone.

Using both statements together, we get an inconsistent set of equations. Hence, there is no solution using both statements together.

Thus, the question cannot be answered using both statements together.

Let the number of girls be g and boys be b. Hence, b+g=150

Statement 1: 50g+25b=4900 => 2g+b=196. Solving the two equations, g=46. Hence, answer can be obtained using statement 1 alone.

Statement 2: 30b+30g=4500 => b+g=150. As both the equations are equal, we cannot find a unique solution.

Thus, the question can be answered using one of the statements alone and not the other.

From the statements we need to infer which envelope contains L2.

From statement 1, we know that C2 should open E1.

From statement 2, we cannot tell which envelope contains L2.

Hence, the question can be answered using one of the statements alone and not the other.

Let's take the two statements individually:

Statement 1: If the second book is in Rack 3, then the fourth book must be in the only remaining odd numbered rack i.e. rack 1. Hence, we can infer the position of book 4 using the first statement.

Statement 2: If the third book is in Rack 2, then the first book must be in Rack 4. However, we don't know anything about the position of Book 4. Hence, we cannot infer the position of book 4 using the second statement.

Hence, the question can be answered using one of the statements but not the other.

Statement 1: a = (X+Y)/2 and $$a^2 = XY$$. Hence, $$a=(X+a^2/X)/2$$. Hence, we can re-arrange the equation to represent X in terms of a

Statement 2: There is no relation given between X and a. Hence, we cannot find value of X in terms of a.

Hence, the question can be answered by one statement alone and not the other.

We know that r1>r2.

Statement 1: $$2\pi(r1-r2) $$ = k. We cannot determine r1 from this information

Statement 2: $$\pi(r1^2-r2^2)$$ = m. We cannot determine r1 from this information.

Using both statements together, (r1+r2)/2 = m/k. We now have two linear equations with two variables. Hence, we can determine the value of r1 in terms of m and k.

Hence, the answer can be found using both statements together.

As the circle circumscribes the square, diameter of the circle= diagonal of the square. Let the side of the circle be s. If we can determine the value of s, then we can find the area of the square $$s^2$$.

Statement 1: Let the radius be r. 2r = $$s \sqrt{2}$$. Hence, s = $$r\sqrt{2}$$. Thus, we can find the area of the circle using this information.

Statement 2: This scenario can be drawn as shown below:

A line drawn from the center of the circle intersects the tangent at an angle of 90°. Hence, the triangle formed is a right-angled triangle with the hypotenuse of 5 cm, one side equal to the radius of the circle and second side equal to the length of the tangent. If the length of the tangent is known then we can calculate the radius using Pythogoras theorem. If the radius is known, the area of the square can be calculated as shown above.