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.

If the number of mynahs is 7 or more and if 7 birds escaped, there is a possibility that no pigeon escaped. But the bird-keeper was able to conclude that atleast one pigeon escaped. So, the number of mynahs is less than 7.

From the options, we can see that only option a) violates this condition.

$$2^{60}$$ or $$4^{30}$$ when divided by 5
So according to remainder theorem 
remainder will be $$(-1)^{30}$$ = 1.

Take 64 for example.

$$\sqrt{64}$$ = 8

$$\sqrt{8}$$ = 2.828

$$\sqrt{2.828}$$ is close to 1.7

So, we can see that the result is tending towards 1.

Given series can be written as:

$$\sum_{n=1}^{100} (\frac{1}{n\times (n+1)})$$

or $$\sum_{n=1}^{100} (\frac{(n+1)-n}{n\times (n+1)})$$

or $$\sum_{n=1}^{100} (\frac{1}{n} - \frac{1}{n+1})$$

After putting values of n from 1 to 100, all terms will cancel out, only first and last terms will be there

i.e. $$1-\frac{1}{101}$$

or $$\frac{100}{101}$$

$$\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}$$
or $$\frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}$$
or $$\frac{4}{1-x^4}+\frac{4}{1+x^4}$$
or $$\frac{8}{1-x^8}$$

Putting value of x=0 or 1 and solving all four options,
We will find that only option A satisfies the equation with both values, hence answer will be A.

Total ways when all 6 boxes have only black balls = 1
Total ways when 5 boxes have black balls = 2
Total ways when 4 boxes have black balls = 3
Total ways when 3 boxes have black balls = 4
Total ways when 2 boxes have black balls = 5
Total ways when only 1 box has black ball = 6
So total ways of putting a black ball such that all of them come consecutively = (1+2+3+4+5+6) = 21

1. x=1 ; y=2

2. x=2 ; y=3

3. x=6 ; y=4

4. x=24 ; y=5

Hence when y=5 , x will be 24

Let's say total products maufactured by M1, M2 and M3 are 100.
So M1 produced 40, M2 produced 30 and M3 produced 30
Defective pieces for M1 = $$\frac{120}{100}$$
Defective pieces for M2 = $$\frac{30}{100}$$
Defective pieces for M3 = $$\frac{150}{100}$$
So total defective pieces are $$\frac{150+30+120}{100}$$ = $$\frac{300}{100}$$ = 3% of total products.

$$x*x < y*y$$
or $$x + 0.5x - x^2 < y + 0.5y - y^2$$
$$y^2 - x^2 + 1.5x - 1.5y < 0$$
$$(y - x)(y + x) - 1.5 (y - x) < 0$$
$$(y - x)(y + x -1.5) < 0$$
$$(x - y)(1.5 - (x + y)) < 0$$
Now there will be two possibilities
$$x < y$$ and $$(x + y) < 1.5$$ ...........(i)
or $$x > y$$ and $$(x + y) > 1.5$$ ............(ii)
Among all options only option B satisfies (ii).
Hence, option B is the correct answer.

$$\frac{-p}{1-p}$$ can be compared with sum of an infinite G.P. series i.e. $$\frac{a}{1-r}$$ (where a is first term and r is common ratio)
Hence here a=(-p)
and r = p
So k^th term will be = $$(-p) (p)^{(k-1)}$$

In second round, number of winners were odd hence 1 winner will be played in next round. Since in third round also number of winners are odd, then last round player will be played in this round and one another player will be played in next round.

Now in 4th round total winners will be (7+1), this 1 winner belongs to 3rd round where he was sent to play in next round.

Summation of all matches will be 115.

$$n^3-n$$ can be written as:
$$(n-1)n(n+1)$$ (where n is a positive integer)
i.e. product of three consecutive integers.
Hence for any number n=2 or >2 , product will have a factor of 6 in it.
When two numbers are prime in product, then third number will always be divisible by 6 
Or product will always have a factor of $$3\times2$$ into it.

$$\frac{(1-d^3)}{(1-d)}$$ = $$1+d^2+d$$ (where $$d \neq 1$$)
Let's say $$f(d)=1+d^2+d$$ 
Now $$f(d)$$ will always be greater than 0 and have its minimum value at d = -0.5. The value is $$\frac{3}{4}$$.
For $$d<-1$$ ; $$f(d) >1$$
$$-1<d<0$$ ; $$\frac{3}{4} <f(d)<1$$
$$0<d<1$$ ; $$1<f(d)<3$$
$$d>1$$ ; $$f(d)>3$$

So, for d > 1, f(d) > 3. Option b) is the correct answer.

Let's say total money was $$x$$ rs.
So cost price of 40 mango will be = $$x$$ ;
Hence cost price of 20 mangoes will be = $$\frac{x}{2}$$
Taxi fare = $$\frac{10x}{100}$$
Total expense = $$\frac{x}{2}$$ +  $$\frac{10x}{100}$$ = $$\frac{6x}{10}$$
Remaining money =$$ \frac{4x}{10}$$
Cost price of 1 orange will be = $$\frac{x}{50}$$
Hence in $$\frac{4x}{10}$$ rs. 20 oranges can be purchased.

It is given that the maximum cost is 12 lakhs
$$1200000 <= T \times 10000 + V \times 15000$$ (Where T is number of TV's and V is number of VCR's)
and as we know $$T+V = 100$$
By solving the above two equation, we will get v<=40

We have to keep the no. of VCRs as maximum, as they fetch higher profit than TV, so

$$T = 60$$
$$V = 40$$​​​​​

As we know for maximizing profit, Total Revenue = Marginal Cost
i.e. $$T \times 10000 + V \times 15000 = 1200000$$
and $$T+V = 120$$
By solving above two equations we will get
$$T=120$$
$$V=0$$
Hence ratio will be 0.​​​​​​

The total property consists of cash, gold coins and silver bars.
And ghosh babu gave equal parts to 4 daughters, hence they should have 25% of total property each.
As eldest daughter possess gold coins as 20% worth of total property, so 25000 cash should be equal to 5% of total property.
So total property will be =$$\frac{ 25000 \times 100}{5}$$ = 500000 
Hence property amounting only gold coins and silver bars will be = Total property - Total Cash
i.e. = 500000 - (25000 + 50000 + 75000 + 75000)
= 2,75,000 

The total property consists of cash, gold coins and silver bars.
And ghosh babu gave equal parts to 4 daughters, hence they should have 25% of total property each.
As eldest daughter possess gold coins as 20% worth of total property, so 25000 cash should be equal to 5% of total property.
So total property will be =$$\frac{ 25000 \times 100}{5}$$ = 500000 

Let the number of gold bars be 7a and the number of silver bars be 27a.
The total value of the gold and silver bars is 500000 - 225000 = 275000
Therefore, 4000*7a + 1000*27a = 275000
Or, 55000a = 275000
Or, a = 5

Therefore the number of silver bars with Ghosh Babu is 27a = 135

After my first move of retaining right board will be like

Now second person will force me to retain with the lowest value possible i.e. 2 or 3
So if he retains lower half and i retain with left one (as mentioned) then he can only force me to pick 3.
Or if he retains upper half and i retain with left one(as mentioned) then he can retain upper half so i will be having minimized profit of 2.
Hence second person will have moves as "Retain (upper half) and retain (upper half)"

After second move i will be having from a quarter cell of board to make a move.

Since left quarters have cells with values 1, Hence i will choose to retain right in my first move so that second person can force my profit to be either 2 or 3 not 1.

So now after my first move of retaining right, we have two quarters

Now intelligently he will make a move to retain with lower half so that at fourth move i can retain with choices of 2 and 3 not 2 and 4.

After retaining right in first move, second person will have 2 quarters to choose in which minimum value is 2 and 3.
If he retains upper half, i will retain right as to maximize my profit of either 4 or 7.
If he retains lower half, i will retain left as to maximize my profit of either 3 or 8.
Hence whatever he retains, i won't have a profit less than 3.

If roots of given equation are reciprocal to each other than product of roots should be equal to 1.
i.e. $$\frac{6}{a} = 1$$
hence a=6

Time difference, when second time car's engine failed at a distance of 30 km., is of 9 min.
Hence putting this in equation:
$$\frac{12}{\frac{4v}{5}} - \frac{12}{v} = \frac{9}{60}$$ hr. (Because difference of time is considered with extra travelling of 12 km. in second case)
We will get $$v (velocity) = 20$$ km/hr.
Now for distance $$ \frac{d-18}{16} + \frac{18}{20} - \frac{d}{20} = \frac{45}{60}$$ hr. (As car is 45 min. late after engine's faliure in first case)
So $$d$$ = 78 km. 
Hence none of these will be our answer.

Money will be distributed in the ratio of work done in an hour.
i.e. $$\frac{1}{6} : \frac{1}{8} : \frac{1}{15}$$
or 20:15:8
Hence part of A will be = $$\frac{20}{43} \times 94.6 = 44$$
part of B will be = $$\frac{15}{43} \times 94.6 = 33$$
part of C will be = $$\frac{8}{43} \times 94.6 = 17.60$$

let's $$l_s$$ is length of slower train and $$l_f$$ is length of faster train.
So according to second condition when two trains are moving in same direction
$$l_s = v_{fs} \times t$$  (where $$v_{fs}$$ is relative velocity of faster train w.r.t. slower train and t is time taken to cross it)
or $$l_s = \frac{(60-50) \times 5}{18} \times 18$$ = 50 meter
Only option which has length of slower train as 50 is C.
 

According to given question $$S_{50}$$ will have 50 terms 
And its first term will be 50th number in the series 1,2,4,7,.........$$T_{50}$$
$$T_1 = 1$$
$$T_2 = 1+1$$
$$T_3 = 1+1+2$$
$$T_4 = 1+1+2+3$$
$$T_n = 1+(1+2+3+4+5....(n-1))$$
       = $$1+\frac{n(n-1)}{2}$$
So $$T_{50} = 1+1225 = 1226$$
Hence $$S_{50} = (1226,1227,1228,1229........)$$
And summation will be = $$\frac{50}{2} (2\times 1226 + 49 \times 1 ) = 62525$$

Side of first square = 8cm. 

Side of second square made by joining mid-points of first square = $$\frac{8}{\sqrt2}$$

Similarly side of third square =  $$\frac{8}{\sqrt2\times\sqrt2}$$ and so on.

Now summation of areas will be $$8^2+(\frac{8}{\sqrt2})^2+(\frac{8}{\sqrt2\times\sqrt2})^2$$ .........

or $$8^2 ( 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}.....)$$

or $$64 \times (\frac{1}{1-\frac{1}{2}})$$ (As we know sum of an infinite G.P. is $$\frac{a}{1-r}$$ where a is first term and r is common ratio)

or 128 sq. cm.

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.

The difference in the excise duty as a percentage is least amongst AP and Maharashtra and it equals (60-52)/52 * 100 
This equals 8/52*100 = 200/13 = 15.38% which is approximately equal to 15%

In the question we are only provided with the data of five states. We don't know the excise duty rates for other states. Thus, the answer cannot be determined.

We know that the Excise duty is levied on the total value of liquor produced by the 5 distilleries. Since the excise duty remains constant, the excise duty will be in the same order as the order of the amount of the liquor produced by them.
Thus, the correct order is DCEBA.

Average simple annual growth of the distilleries are-

A->$$\frac{12.89-6.41}{2\times6.41}\times100=50.54$$%
B->$$\frac{12.07-3.15}{2\times3.15}\times100=141.58$$%
C->$$\frac{11.92-1.64}{2\times1.64}\times100=313.41$$%
D->$$\frac{5.79-1.05}{2\times1.05}\times100=225.71$$%

E->$$\frac{4.21-2.45}{2\times2.45}\times100=35.91$$%

We can see that the highest growth rate was in C and lowest in E.
So, if E would have grown by 313.41% in 2 years, its supply would have been-

$$\frac{2.45\times 313.41\times 2}{100}=15.11$$ lts

Assume the first statement is true. So, Saira has the ball. The other two statements are false. But if Saira has the ball, the statement that Mumtaz does not have the ball is true. But that statement should be false. Therefore, the first statement cannot be true.

Assume the second statement is true. So, Mumtaz does not have the ball. Also, since the other two statements are false, Saira also does not have the ball. So, Zeenat has the ball. But the third statement "Zeenat does not have a pen" becomes true in this case, which is incorrect. So, the second statement also cannot be true.

The only possibility is the statement has to be true. So, the second statement is false => Mumtaz has the ball.

According to given question Jerome + Tommy = Albert + David  eq.(1)    ;    Jerome < Tommy  eq. (3)
                                                   Albert + Tommy < David + jerome eq. (2)
Now adding above two equations we will get
2David  > 2Tommy
or David > Tommy
or Tommy > Jerome > Albert ( from eq.(3) )
Now David should earn most pocket money as to hold equation (2) to be true.
Hence David > Tommy > Jerome > Albert.

Given informations are as follows:

Akhila got 13 marks in coherence and divya got 10 marks in Machinary

Divya's marks = Ela's Marks (Hence they both are not winners as winner is only one)

Bhanu's marks < Akhila's marks ( Hence bhanu is also not a winner)

So winner will be either Akhila or Charulata

As Akhila got 13 marks in coherence so she must have 20 marks in some head as highest marks are 90

That's why winner will be Charulata.

Average of numbers 100.5 , 67, 141, 143.9 and 65 will be

$$100 + \frac{41+0.5+43.9-33-35}{5} = 103.48 $$

Base value must be taken as 100 => 1985 is 100

1984 => $$\frac{100.5}{67}*100$$ = 150

1986 => $$\frac{141}{67}*100$$ = 211

Only option A has the same values => Option A is the answer

Decline occur in years 1985 and 1988 respectively.
In year 1985, decline was nearly 33%
Whether in year 1988 decline was nearly 54%
Hence answer will be B.

Total expenditure is = 52.1 + 267.5 + 196.4 + 209.5 = 725.5

So 25.5 will be cut off on administration equally in all years.

Hence in 1989 cut off will be $$\frac{25.5}{4} = 6.375$$

Percentage cut off will be = $$\frac{6.375}{15} \times 100 = 42.5$$

Till third year expense was 407.1 and total expenditure is 597.1

So ratio will be $$\frac{407.1}{597.1}$$ = 0.7
That will be fraction of length which is supposed to be completed by third year

Total material for all the years will be = 250+175+43+64 = 532
Total labour cost for all the years = 65.1
Hence ratio will be $$\frac{65.1}{532}$$ nearly equal to 8:1.

In the year 1990, total increment will be 4+2.25+0.6+0.9 = 7.75
And in the year 1991, total increment be 3.75+3+0.8+1.05=8.60
Hence total increase in estimated cost will be = 16.35 Lakhs

It is said that till 1990, all estimated cost has been spent i.e. 725.5
Then 209.5 is spent in the year 1991. Hence, that will be exceeding the cost.
So percentage increase will be = $$\frac{209.5}{725.5} \times 100$$ = 29 
​

Total estimated cost before increment = 52.1+267.5+196.4+209.5 = 725.5

Increment in contingencies will be = 25.2

Hence, total estimated cost will also be increased with the same amount.

So percentage increment in total estimated cost will be = $$\frac{25.2}{725.5} \times 100 = 3.47$$

Sales to stock percentage values are given in table 3 
And at region 4, Brown colour, percentage is maximum compared to all.
Hence answer will be C

As the most popular colours will have more sale than any other colour
Since table 2 gives us value of sales, Brown colour in region 1 has maximum no. of sales
Hence, our answer will be Brown.

Since table 2 gives us the sales values of saris
Hence, for the magenta sari, Region1 has the maximum number of sales out of total magenta sales. 
I.e. 71 out of 161.

Given we have 6 regions where sales are defined in the table number two . Now given that we need to find the region where green saris as a percentage of the total sales is lowest . In order to do that we calculate Green saris sold in a region/ Total sales of a particular region by considering the values from table 2 . 

Now for option 1 which is region 1 the value is (164/788)*100  = 20.81 %

For option 2 which is region 4 the value is (85/511)*100 = 16.63 %

For option 1 which is region 6 the value is (3/18)*100 = 16.66 %

For option 1 which is region 2  the value is (200/676)*100 = 29.58  % .

Hence among the given options the percentage of region 4 is lowest which is option 2 .

From Table 5, we can see that out of all the regions, the maximum number of blue saries were sold in region 2

Hence, the lowest ratio will be for 84-85.

The answer is 1988-89 as there were three crops which declined during this period: Wheat, Jowar, Bajra.

In Major and Medium = 24 - 23.2 = 0.8 million hectares

In Minor = 34.2 - 32.77 = 1.43 million hectares

In total, 2.23 million hectares.

There is a decrease in the area of minor irrigation land in 1987-88.

Hence, during this year land is brought into maor irrigation area.

Among the options, the only word that is applicable in the second blank is 'hereditary', because that is what 'genes' are associated with. Option d) is the correct answer.

A claim should be supported by relevant documents.
The phrasal verb to be used in this context is 'backed up', which means 'supported'.
Option c) is the correct answer.

The word in the first blank should be a verb in the past tense. This rules out options a) and b). The meaning of 'peremptory' is 'insisting on immediate obedience or attention'. This is a better fit in the second blank compared to 'reckless'. Option c) is the correct answer.

The sentence is trying to convey the idea that high prices often accompany a scarcity of goods. From the options, the best combination of words in this context is 'accompaniment' and 'dearth', which means 'scarcity'. Option a) is the correct answer.

The correct phrasal verb that should be used in this context is 'blow over', which means 'fade away without any serious consequences'. Option b) is the correct answer.

An alliance is an association or organization formed between two parties for the mutual benefit of each other. In this case, the sentence is trying to convey the idea that the alliance is not working. In other words, it is a 'misalliance'. Option b) is the correct answer.

An involuntary response to a stimulus is called a reflex. So, the word that best replaces the phrase is 'reflexes'. Option b) is the correct answer.

Gastronomy is the study of food and culture. This word fits well in the given context. Option a) is the correct answer.

The sentence is conveying the idea that the thrilling narrative caused an intense feeling of fear among the audience. In other words, it cause horror among the audience. Option d) is the correct answer.

A phalanx is a rectangular military formation, usually composed of heavy infantry. This is the most suitable word in the context. Option a) is the correct answer.

It's is a concise way of writing 'it is'. We can rule out options a) and d) because of this. The meaning of 'enhance' is 'increase the quality of'. However, in this sentence, there is only an increase in expense. So, 'increase' is a more suitable word in this context. Option b) is the correct answer.

The sentence is talking about three things. There is no need of commas within each part of the sentence. We can rule out options a) and b). The three parts of the sentence are independent clauses, so they are best separated by a semi-colon. Option d) is the correct answer.

A comma is needed after the name of the person. Also, 'who' is used while referring to the subject of the sentence. Both these requirements are satisfied in option b).

Here the author mentions the category of people who believe everything they hear. The people in this category are plural. Hence "believe" should be the correct usage rather than "believes."

'The Board of Directors' is a collective noun. So, it takes the singular verb 'its'. It's is an incorrect usage in this context because it actualy means 'it is'. Option a) is the correct answer.

The correct option is B. All other options have subject verb disagreement. The state of his affairs is the main subject which is singular. The correct usage would be "The state of affairs was/is such" which is only mentioned in B.

Since 'one' is used in the sentence, it's pronoun form should be one's. So, the correct sentence is "Cannot one do what one likes with one's own?". Option a) is the correct answer.

The verb used with the word 'each' should be in the singular form. Also, the group to which 'each' refers should be a plural noun. Option a) satisfies both the criteria and it is the answer.

The phrase 'none of us' takes a singular verb. The grammatically correct sentence should read "None of us was comfortable with what was happening". Option b) is the correct answer.

When the construct 'neither...nor' is used, the verb should be in agreement with the subject that is placed after 'nor'. In this case, it is 'ministers', which is a plural subject. So, the verb should be singular - 'desire'. Also, the definite article 'the' should be used before 'king'. Option c) is the correct answer.

Option A and D are incorrectly framed. Among B and C, C is correct as we want to highlight the history of performance of the industry. C is correctly framed in this context.

Option A and B are incorrectly framed grammatically as well as contextually. Among Options C and D, C is the best fit. The construction of D is little ambiguous and does not convey the full meaning of the sentence.

The use of phrases like 'limited conceptual grasp' is unnecessary to convey the meaning of this sentence. We can rule out options a) and b). Both c) and d) convey the same meaning but c) is more concise and clear. Option c) is the correct answer.

A request for milk powder is being made. In option c), the word 'please' is redundant after the use of the word 'request'. The sentence in option d) is incorrect because of the use of the word 'can'. The word 'may' should replace it. Between options a) and b), b) is a better construction. It is concise and clear.

Options a) and b) are verbose and can be ruled out in comparison with options c) and d). In d), the mistake is the usage of the word 'when'. It should be 'whenever' as used correctly in c). The use of 'whenever' conveys the meaning that the process is repetitive. So, option c) is the correct answer.

The use of the word unexpected in option c) is redundant. Similarly, the use of the word in the sentence in option a) is also redundant. Between b) and d), option b) is better. The development will lead to unexpected/unanticipated results i.e., consequences and not implications. Option b) is the correct answer.

The correct option is C. The agreement of someone else's point of view is correct rather than the coincidence or coincide with the point of view.

The word 'very' is redundant. We can rule out options a), c) and d). The sentence in option b) is the most concise of the lot.

The sentences in options b) and c) are verbose and can be ruled out. Similarly, between options a) and d), a) is more concise and to-the-point. It is the best possible choice.

The proper usage is 'in hindsight...'. Also, 'looking with hindsight' is incorrect usage. We can rule out options b), c) and d). The sentence in option a) is the most concise and clear construction of the sentence.

As car runs on the road, similarly electricity flows through the cable.
Hence, option A is the correct answer.

Foresight and farsightedness are synonyms. Similarly, thinker and visionary are synonyms.
Hence, option D is the correct answer.

A group of ships used by the Navy of any country is known as fleet. Similarly, a collection of chapters comprises a book.
Hence, option A is the correct answer.

A group of feathers constitute a wing. Similarly, a group of bricks make a wall.
Hence, option D is the correct answer.

Just as sugar goes into "tea" a button goes into a "button-hole"

If we take something on lease, we have to pay rent.
If we borrow money, we have to pay interest.
If we employ someone, we have to pay salary.
If we buy something, we have to pay the price.
However, if we govern someone, we do not pay the tax rather we tax them.
Hence, option D is the correct answer.

Temperature is the measurement of heat.
Number of votes is the measurement of popularity.
IQ is the measurement of intelligence.
Ohms is the measurement of resistance.
However, speed is not a measure of distance. Speed is the rate at which distance is covered per unit time.
Hence, option D is the correct answer.

One who progresses is progressive.
One who terrorize is terrorist.
One who bring revolution is revolutionary.
One who bring reforms is reformist.
However, sympathizer is not someone who has sympathy rather sympathizer is someone who agrees with or supports a sentiment, opinion, or ideology.
Hence, option B is the correct answer.

The given pair of words are antonyms. All other options except B are pairs of antonyms.
Hence, option B is the correct answer.

Clips bind papers.
Threads bind the beads.
Cement holds together the brick.
Ribbon binds hairs.
Bags do not bind vegetables rather vegetables are kept inside bags.
Hence, option D is the correct answer.

There are six sentences given. So, there can be many combinations of the sentences possible. Therefore, we will check each of the option to find the correct answer.

In option A, BCD is given. Statement C says all of my closest friends disapprove of me and D says all who disapprove of me are aardvarks. So, all my closest friends must be aardvarks. But, this contradicts with statement B. Thus, option A is incorrect.

In option B, statement D cannot be inferred from A and B.

In option C, all three statements are logically connected.

In option D, E cannot be inferred from A and B.

Hence, option C is the correct answer.

In option A , A is inconsistent with E. It is not given in A that only those who achieve great ends are happy.

In option B, F contradicts with B.

In option C, B can be inferred from A and C.

In option D, F cannot be concluded from A and D.

Hence, option C is the correct answer.

In option A, E is not a valid conclusion from A and B.

In option B, F cannot be inferred from A and C.

In option C, E cannot be concluded from A and D.

In option D, If some learned men are candid but all candid men recognize merit in a rival, it can be concluded that some men recognize merit in a rival are learned.

Hence, option D is the correct answer.

In option A, D can be concluded from C and E.
In option B, A, C and B are not connected.
In option C, C cannot be inferred from B and D.
In option D, E and F are not related.

Hence, option A is the correct answer.

Some men are men of artistic genius and all men are men of scientific ability. Therefore, all men of artistic genius are men of scientific ability.
Thus, ACE is the correct combination.

Hence, option B is the correct answer.

No fishes breathe through lungs but all whales breathe through lungs. So, no whale can be a fish. Therefore, ADE is a valid combination of logically connected statements.
Hence, option C is the correct answer.

ADF is false as we cannot infer F(Some mammals are whales.) even if A(Some mammals are carnivores.) and D(All whales are carnivores.) are true.

ABC and  AEF all statements are different, the set is not related.

All whales are mammals and all whales are aquatic animals. So, some aquatic animals are mammals. Therefore, BCE is valid combination.

Hence, option D is the correct answer.

All students of this college rank as University students and all University students are eligible to enter for the prize. Therefore, all first year students are entitled to enter for the prize.
Hence, option C is the correct answer.

 Nothing uncertain is worth dying for. and all beliefs are uncertain. So, no belief is worth dying for.
Hence, option D is the correct answer.

Everyone who is sane can do logic and all who can do logic are fit to serve on a jury. So, all who can do logic are fit to serve on a jury.
Hence, option B is the correct answer.

Refer to the following lines of the passage:"The therapeutic promise of psychoanalysis came as the most novel, most ambitious, most releasing of the long procession of curative systems that mark the History of mental healing. "

In this line, the author clearly mentions the use of psychoanalysis for mental healing. Besides that, in whole of the passage the author discuss the mental healing aspects of psychoanalysis and how it is accomplished.

Refer to the following lines:"With the practical purpose of applied psychology directed to human efficiency it had no direct relation and thus no quarrel. The solution of behaviorism, likewise bidding for popular approval by reducing adjustment to a program of conditioning, it inevitably found alien and irrelevant, as the behaviorist in reciprocity found psychoanalytic doctrine mystical, fantastic, assumptive, remote. Even to the cognate formulations of mental hygiene, as likewise in its contacts with related fields of psychology, psychoanalysis made no conciliatory advances."

Here the author states that the behaviorism reduces the adjustment to conditioning gradually by making the patients comfortable and habitual.

Option B is incorrect as the author clearly mentions that psychoanalysis had no relation to other branches of psychology and hence had no quarrel with them. Refer to the following lines:" With the practical purpose of applied psychology directed to human efficiency it had no direct relation and thus no quarrel. The solution of behaviorism, likewise bidding for popular approval by reducing adjustment to a program of conditioning, it inevitably found alien and irrelevant, as the behaviorist in reciprocity found psychoanalytic doctrine mystical, fantastic, assumptive, remote."

Refer to the last line of the passage:"Create a belief in theory and facts will create themselves."

Refer to the second last line of the passage:" Psychoanalysis belongs to the typical groups of therapies in which practice is entirely a derivative of theory."

Here the author clearly mentions that the theory leads to practice.

Refer to the following lines:" From the outset in the days of struggle, when it had but a sparse and scattered discipleship, to the present position of prominence, Freudianism went its own way, for the most part neglected by academic psychology. Of dreams, lapses and neuroses, orthodox psychology had little say."

In this the author clearly states that Freudianism went on its own way due to its concepts which were hardly followed by others.

Refer to the following lines:" The therapeutic promise of psychoanalysis came as the most novel, most ambitious, most releasing of the long procession of curative systems that mark the History of mental healing. To the contemporary trends in psychology psychoanalysis actually offered a rebuke, a challenge, a supplement, though it appeared to ignore them."

In this line, the author states that psychoanalysis broke the conventions due to its dealing with the crucial human issues.

The answer can be determined from the following lines:"The second reason for the impression made by psychoanalysis when once launched against the tide of academic resistance was its recognition of depth psychology, so much closer to human motivation, so much more intimate and direct than the analysis of mental factors." The author mentions that the popularity was due to its intimacy with the human issues.

In the second last line, the author clearly mentions the accidental mixing up of the words by computer can result in poetry which is clearly mentioned in D.

In this passage, the author compares the aspects of organizing and communication between computers and human brains which is similar in both the cases. Refer to the following line for better illustration:" Further more, brains and computers can both be organized so as to solve problems. The mode of communication is very similar in both the cases,"

The author compares the functional aspects of organizing and communication between computers and human brains when he states that machines are becoming more and more like humans.

In the last line of the passage, the author states that there is no break of continuity between what is human and what is mechanical. It means that human and mechanical forms are continuous which is mentioned in D.

Before the word "recognize", "by accident" has been used. Thee author wants to convey that computers might produce poetry by accident but they cannot produce the poetry by will because poetry requires emotional height that man is capable of attaining.

The author clearly states that computers compose the poetry by accident while the mode of communication is same in both the cases.

Refer to the following lines:"But has he considered what would be the moral effect of life imagined as possible in the highly mechanized state of future? Has he thought of the possibility of bands of unemployed and under-employed workers marching on the capital to demand not income (which they will have but work?"

In this line, the author clearly states that the highly mechanized future may render many workers unemployed.

Refer to the following lines: "But has the socialist thought about what he would do if owing to technological advance, the amount of human labour were catastrophically reduced? So far as I know, he has no plan beyond drastically lining the hours of work, and sharing out as much work as there may be."

The author clearly mentions that the socialists have not taken into account the mechanization.

Refer to the following lines:"The labour movements arose largely as a revolt against the conception of workers as commodities to be bought and sold without regard to their needs as human beings."

Option C is clearly mentioned in these lines.

Refer to the following lines:"In the earlier and more ruthless days of capitalism the duty of the economic system to provide work was overlooked The purpose of competitive enterprise was to realize a profit. When profit ceased or was curtailed, production also ceased or was curtailed"

Option D is clearly mentioned in these lines.

Refer to the following lines:"When, therefore, we look ahead to the situation likely to be produced by the continued rapid extension of machine production, we should think not so much about providing occupation for leisure as about limiting the amount of leisure to that which can be profitably used."

Option C is clearly stated in these lines.

Refer to the following lines:"There are forms of work, of course, which since external compulsion is reduced to a minimum, are hardly to be differentiated from occupation. The artist, the imaginative writer, the scientist, the social worker, for instance, find their pleasure in the constant spontaneous exercise o creative energy and the essential reward of their work is in the doing of it. " Option B is stated in these lines.

Refer to the following lines:"There are forms of work, of course, which since external compulsion is reduced to a minimum, are hardly to be differentiated from occupation."

Here the author clearly states that some works can be hardy differentiated from occupation which is contrary to what is mentioned in D.

Refer to the following lines of the passage:"Occupation absorbs time and energy so long as we choose to give them; it demands constant initiative, and it is its own reward." " But for most people the pleasure of occupation needs the addition of the necessity provided in work. "

Option D correctly summarizes the answer as the occupation is a desire to do something which requires initiative and will.

Refer to the following lines:"Work has for him obvious utility, and it bring the satisfaction of tangible rewards. Where as occupation is an end in itself, and we therefore demand that it shall be agreeable, work is usually the means to other ends." Option C clearly mentions the aspects present in these lines.

Although articulate refers to the person having clarity of thought but in this case it is contextually incorrect. Here the author wants to mention those persons who are well educated and can form a coherent class. Option C mentions the meaning in the correct context.

Refer to the following lines:"Far from oppressing the cultured minority, or any other minorities, democracy gives more of them more scope to have their way than any other system does." The author clearly mentions that the minorities are given more voice in a democracy which is mentioned in C.

Refer to the following lines:"This is the lesson of experience. It might also have been derived from an analysis of the concept of democracy, if the concept had been accurately analyzed." Here the author mentions the proven record of democracy when he mentions his experience. Option C correctly states the fact.

Refer to the following lines:"It might also have been derived from an analysis of the concept of democracy, if the concept had been accurately analyzed." Here the author states that if the concepts of democracy are analysed properly then its wide scope can be deciphered.

In the whole passage, the author seems to favor democracy over the rule of the minority. He offers various context in this support and concludes that democracy is better in terms of taking care of minority.

Refer to the following lines:"If the more articulate members of a community formed a coherent and united class with a common interest, democracy would probably replace in to the rule of that intelligent, educated minority; " Here the author mentions the present context where the rule is of educated minority whicha an be removed by a coherent and united class. Option D mentions this aspect of the answer.

Refer to the following lines:"I think it is the duty of science . I do not say of every individual man of science, to study the means by which we can adapt ourselves to the new world." Here the author states that a man of science has to study the means by which we can adapt ourselves to the new world.

Refer to the following lines:"To come to more recent times, Archimedes was respected for his scientific defense of Syracuse against the Romans; Leonardo obtained employment under the Duke of Milan because of his skill in fortification, though he did mention in a postscript that he could also paint a bit. Galileo similarly derived an income from the Grant Duke of Tuscany because of his skill in calculating the trajectories of projectiles. In the French Revolution those scientists who were not guillotined devoted themselves to making new explosives. "

In this paragraph, the author mentions the relation between the aspects of science and war by taking the examples of Syracuse vs Romans, fortification and trajectories of projectiles. The author wants to state the intimacy between science and war.

Refer to the following lines:"We do not so readily apprehend a similar failure of duty on our own side. I do not wish to be thought to suggest treachery, since that is only a transference of loyalty to another national state. I am suggesting a very different thing; that scientists the world over should join in enlightening mankind as to the perils of a great war and in devising methods for its prevention. I urge with all the emphasis at my disposal that this is the duty of scientists in East and West alike."

In this passage the author requests the scientists to enlighten the people in perils of great war as the science is intimately associated with war. This is substantiated by providing the examples of Galileo, Leonardo and Archimedes. Option B is the correct answer

This fact is mentioned in the first sentence of the passage:"A difficult readjustment in the scientist's conception of duty is imperatively necessary."

Refer to the following lines:"Loyalty to the human race must take its place. Everyone in the West will at once admit this as regards Soviet scientists. We are shocked that Kapitza who was Rutherford's favourite pupil, was willing when the Soviet government refused him permission to return to Cambridge, to place his scientific skill at the disposal of those who wished to spread communism by means of H-bombs." From this we can see that Kapitza agreed to help Soviet Union when they did not permit him to return to Cambridge. The Soviet Union could do so because he was a citizen of the Soviet Union. 

From this we can infer that firstly, the author is shocked that Kapitza agreed to help his own state of Soviet Union even when their actions were against humanity and secondly, the author feels that the example of Kapitza shows that we should be loyal to humanity and not individual countries. Hence, the example of Kapitza is used to show that current system of loyalty to home country is a wrong one. Hence, option C is the right answer.