CAT 1990 Question Paper

Given: P - R = 2370
or P = 2370 + R ;
So if we consider only 1st statement, R can be 2 or 6 as 2372 and 2376 both will be divisible by 4.
And if we consider only 2nd statement, R will be having an absolute value of 6 as 2376 will be divisible by 6.
Hence by taking only 2nd statement into consideration, we can find unique value of R.
So answer will be B).

Concept: Try to find a way with which we can find an absolute/unique answer. 

Concept: Try to see whether we can have a "UNIQUE/ABSOLUTE" answer to given question by applying statements with 3 posibilities.
 If only 1st statement is taken into consideration.
 If only 2nd statement is taken into consideration.
 If both statements are taken into consideration.
In given question with first possibility, we can't have a unique answer as there can be 3 cases. Childs greater than 5 years, childs equal to 5 years and childs less than 5 years and with first possibility we know only that childs greater than 5 years get 5 choclates nothing about other two cases.
With second possibility too, we can't find a unique answer as we can't say anything about childs greater than 5 years
Now with third possibility, we are having a unique answer to given question because we have information about all childs which are either greater than 5 year , lesser or equal to 5 years. Childs older than 5 years will be 5, childs equal to 5 years are 2 and childs younger than 5 years will be 1.

So answer will be C)

1. If only 1st statment taken into consideration:
$$y=0.30x$$ (Where y= distance from Madras to Trivandrum and x= distance from Calcutta to Madras)
Nothing absolute can be said about average speed from Madras to Trivendrum.
2. If only 2nd statement taken into consideration:
$$\frac{y}{t_y} = 2\frac{x}{t_x}$$ ( Where t_x and t_y are time taken for calcutta to madras and madras to trivendrum respectively.)
And nothing absolute can be said about average speed from Madras to Trivendrum.
3. Now when both statements taken into consideration:
We will have $$y=0.30x$$;  $$\frac{y}{t_y} = 2\frac{x}{t_x}$$ and $$\frac{x+y}{t_x+t_y}$$ = 40 (Given)
After solving above three equations we can find a unique value for average speed from Madras to Trivendrum i.e. 
 $$\frac{y}{t_y} = \frac{920}{13}$$
Hence answer will be C.

If only first statement taken into consideration:

y-x = 2 where x, y and z are three odd integers.

Nothing absolute can be said about divisibility of x+z with 4.

Now if only second statement taken into consideration :

z-y=2 and nothing absolute can be said about divisibility of x+z with 4.

If we consider both statement simoultaneously then

we get x+z = 2y

Now as we know y is an odd integer , so 2y will never get a factor of 4.

Hence x+z is not divisible by 4.

As we find an absolute answer by using both statements Hence answer will be C)

Considering first statement only,current unit price of P1 is twice that of P2 and, Rates of P1 and P2 are either decreasing or P1 has constant rate. Now we can't say that which product will be costlier aftre 5 years as nothing certain information is there about rates of decreasing. Similarly if we consider only 2nd statement or consider both statements simultaneously, nothing certain can be said about rate of decreasing hence D will be answer

Taking only first statement into consideration:
Nothing absolute can be said about Z and X
Now taking only second statement into consideration:
$$W \leq V$$
As it is given that X is older than Y; Z is younger than W and V is as old as Y.
and through second statement we know that W is younger or as old as V.
So using above four information we can conclude that Z is not older than X.
Z is either younger or as old as X.
Hence answer will be B).

As it is clear that total time of journey will be = Time taken at stop-overs + Time taken while travelling with avg. speed 66 km/h
Hence both informations are needed to solve the question. So our answer will be D.

Given equation can be resolved to $$\frac{1}{\frac{1}{x} + \frac{1}{y}}$$ ($$xy \neq 0$$ and $$x \neq y$$ )
Now for $$\frac{1}{\frac{1}{x} + \frac{1}{y}}$$ to be greater than 1,
1/x + 1/y has to be less than 1.
For this to be true both x and y should be greater than 2.
Statement I doesn’t give any information about this,
but statement II clearly specifies this. Hence, only
statement II is required to answer the given question.
So it can be answered using statement 2 alone.

When total matchstick is 1, B will surely win as A is the one who is picking up matchstick first.

When total matchstick is 2, A will surely win as A will pick one matchstick then B has to pick last one.

When total matchstick is 3, A will surely win as he takes up a strategy so that B will have last matchstick to pick up. So A will pick 2 matchstick.

When total matchstick is 4, B will surely win as if A picks up one matchstick, remaining matchsticks will be 3 and we know that when total 3 matchsticks are there then the one, who is picking up matchstick first, is winning surely.

When total matchstick is 5, A will surely win as he takes up a strategy so that B will have last matchstick to pick up. So A will pick 1 matchstick first, then 4 matchsticks will be there and we know that the one, who picks up matchstick second now, will win. Hence A will win.

When total matchstick is 6, A will surely win either he takes up a strategy so that B will have last matchstick to pick up. So A will pick 2 matchstick first, then 4 matchsticks will be there and we know that the one, who picks up matchstick second now, will win. Hence A will win.

Hence it is making a pattern when number of matchsticks are 1,4,7,10......N then B is winning the game.

So here minimum value of N greater than 5 will be 7.

When total matchstick is 1, B will surely win as A is the one who is picking up matchstick first.

When total matchstick is 2, A will surely win as A will pick one matchstick then B has to pick last one.

When total matchstick is 3, A will surely win as he takes up a strategy so that B will have last matchstick to pick up. So A will pick 2 matchstick.

When total matchstick is 4, B will surely win as if A picks up one matchstick, remaining matchsticks will be 3 and we know that when total 3 matchsticks are there then the one, who is picking up matchstick first, is winning surely.

When total matchstick is 5, A will surely win as he takes up a strategy so that B will have last matchstick to pick up. So A will pick 1 matchstick first, then 4 matchsticks will be there and we know that the one, who picks up matchstick second now, will win. Hence A will win.

When total matchstick is 6, A will surely win either he takes up a strategy so that B will have last matchstick to pick up. So A will pick 2 matchstick first, then 4 matchsticks will be there and we know that the one, who picks up matchstick second now, will win. Hence A will win.

Hence it is making a pattern when number of matchsticks are 1,4,7,10......N then B is winning the game.

So largest value of N (less than 50) where B will win, is 49.