CAT 1990 Question Paper

Option B and C are irrelevant and in option D, $$ n_1$$ should be 0
Hence option A will be our answer as $$n_1$$ is the value before instruction as 0 and $$n_2$$ is value after instructions which is also 0.
 

In option A, $$n_1$$ >=5 which is before instruction value so after going 5 backward and 5 forward value of $$n_2$$ will remain equal to $$n_1$$

So our answer will be A as other options have insufficient information

Let's consider each statement one by one

A) Suppose M=50, $$n_1$$=5

In this case, $$n_2$$ = 5 + 10 + 10 = 25. Hence, $$n_2 - n_1 = 20$$ even though $$n_1 \neq 0$$. Hence, statement A is false.

B) Suppose M=21 and $$n_1$$=1

In this case, $$n_2$$ = 1 + 10 + 10 = 21. Hence, $$n_2 - n_1 = 20$$. Thus, if M>20 then this statement is true.

If M = 19

In this case, the process stops when M is reached. Hence, $$n_2$$=19 and $$n_2 - n_1 = 18$$. Hence, option B is true.

C) As we have seen earlier, $$n_2 - n_1 = 20$$ in this case. Hence, option C is false.

D) Suppose $$n_1=M$$. In this case, $$n_2 = n_1$$. Hence, option D is false.

For option A, put $$n_1$$ = 1, then $$n_2$$ will be 2 , hence equation won't hold true.
Now for option B, if we say M = 5 , then $$n_1$$ will be 0 and $$n_2$$ will be 1, hence equation won't hold true.
And equation in option D will not hold true too as put M = 5 , then $$n_1$$ will be 0 and $$n_2$$ will be 1.
Now in option C, equation is valid as put $$n_1$$ = 1 , then $$n_2$$ will be 2. Which is holding the equation valid too.
Hence our answer will be C.

We can start from either city C or D. 

C - A - B - D - C - B - E - D

D - B - A - C - B - E - D - C

We cannot start from any other city.

So, we can either start from C or end at C but not both.

We can start from either city C or D. 

C - A - B - D - C - B - E - D

D - B - A - C - B - E - D - C

We cannot start from any other city.

$$(x+y+z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + xz)$$
as $$xy+yz+xz = 0$$
so equation will be resolved to $$x^2 + y^2 + z^2$$

Assume one person is born every day. In 100 years, there will be 25 leap years. So 25*1 additional people will be born on these days.

So, total people born will be = $$365 \times 100 \times 1 + 25 \times 1$$
And people born on 29th february = $$25 \times 1$$ 
Hence percentage will be = $$\frac{25 \times 1}{365 \times 100 \times 1 + 25 \times 1} \times 100$$ = 0.0684

As it is mentioned that difference in number of books is more than one

Hence option B and D are cancelled.

Now total amount is = 620 = 17M + 19P + 23C

 we can check by putting values from option A and C.

 Option C satifies the above eq.,Hence our answer will be C

According to question Rahul put exact number of 10 rs. notes, hence total price will be a multiple of 10.
And Rahul wants 30 cards, where he took 5 each of two kind and 10 each of other two kind.
So summation of (price of one type card multiplied by number of that type of card) should be a multiple of 10.
By looking at the prices of cards and to make the sum a multiple of 10, we can say that two 5 cards were of rs. 3.5 and 4.5
and two 10 cards were of prices 2 rs.and 5 rs each respectively.
Hence total sum will be 5 $$\times$$ (3.5+4.5) + 10 $$\times$$ (2+5) = 110
So rahul gave 11 notes of 10 rs.