CAT 1997 Question Paper

Distance is not known to find the average speed.

=> Data insufficient

As we know angles of same sectors are equal
Hence angle B and angle D will be equal. Angle BCE and angle EAD will be equal.
So triangles BCE and EAD will be similar triangles with sides ratio as 12:24 or 1:2.
Area will be in ratio of 1:4.

$$AC^2 = 8^2 + 6^2 = 100$$
So AC = 10

$$\frac{10}{EF}$$ = 2

EF = 5

Length of line joining mid-points will be = 5

Time taken to catch the thief = $$\frac{d}{v}$$  (Where d is relative distance achieved in 15 min. = 15km. and v is relative velocity of poiliceman i.e. = 65-60 = 5 kmph)
So time taken = 3hr.
Hence he will catch thief at 3:15 pm

As relative velocity of other poilceman will be 0 , hence distance remain same as starting i.e. = 15 km.

Considering first statement only, nothing absolute can be said about the value of $$a^3 + b^3$$ similarly considering 2nd statement only nothing absolute can be said about the value of $$a^3 + b^3$$.
When we consider both statements together two values of (a+b) can be possible as $$\sqrt{28}$$ and $$-\sqrt{28}$$
By which two possible values of $$a^3 + b^3$$. Nothing absolute can be said about it.
Hence answer will be D).

99 = 9 * 11 => If the number is divisible by 9 and 11, then the number is divisible by 99.

=> We can answer the question using only statement I.

The divisibility rule of 9 is that the sum of the digits in the number must be divisible by 9.

The divisibility rule of 11 is that the difference of sums of digits in odd places and digits in even places must be a multiple of 11.

According to statement II, if the number is reversed then the number is divisible by 9 and 11 => Divisible by 99.

Now, on reversing the number again, the number is still divible by 99 because the sum of the digits remains the same and also the difference of sums of digits in odd places and digits in even places remains the same.

Hence, the question can be answered using either of the statements alone.

Considering first statement alone, we can calculate 1/3rd of the complete distance as $$\sqrt{1^2 + 3^2}$$ Hence, we can evaluate complete distance too.

Considering second statement alone, we can calculate 2/3rd of the complete distance as $$\sqrt{2^2 + 6^2}$$ Hence, we can evaluate complete distance too.

So answer will be B as complete distance can be calculated by using any of the statement alone.

Considering first statement alone, 
As there are 2 variables x and y, and one equation we can't say anything absolute about values of x and y.
Considering second statement alone,
With 2 variables and one equation, we can't say anything absolute about variables x and y.
Even considering both statements together, we can't find values of x and y as equation in 2nd statement is same as in 1st statement after multiplying it 3.5

Considering first statement alone:
Nothing absolute can be said about the hats of Q and R, as Q might have black hat or white hat similarly R might have white or black hat as seen by P.
Considering second statement alone:
Nothing absolute can be said about the hats of P and R as they can have either Black or White caps
Even considering both statements together, we were not be able to reduce the possibilities of having black hats and white hats 
Hence answer will be D.