- Common Admission Test 1994 (CAT 1994) - UPSCFEVER

# CAT 1994

## Section I

Ans .

c

1. Explanation :

C. should be the first sentence as it states that the logic presented in 1. is not true. A. and D. talk about the qualities of a good actor. B. talks about the author’s own plays and 6. continues with his observation in B.

Ans .

b

1. Explanation :

C. introduces the idea that some comedies have survived over many years. B. gives a reason for it and A. continues with the reason.

Ans .

a

1. Explanation :

B. introduces ‘an ally of the wind’, hinted at in 1. C. states that the author did not hear it and A. gives the reason for it.

Ans .

c

1. Explanation :

D. talks about the ‘power’ introduced in 1. A. states that if ‘it is an anchor in difficulties it should be remembered in good times too’. C. states the work done by some organizations and B. adds to it.

Ans .

d

1. Explanation :

A. suggests that seniors should help in showing the path. B. continues by referring to ‘the seniors’ mentioned in A. C. and D. state how one should accept the help provided by seniors.

Ans .

b

1. Explanation :

C. introduces the idea of making a will, A. gives a reason for doing so, B. and D. exemplify it through an example from author’s life.

Ans .

a

1. Explanation :

C. introduces the topic of the passage, A. states how India is doing what C. has warned against. B. compares India’s attitude with that of the smaller countries and D. refers to a specific case to prove the point.

Ans .

c

1. Explanation :

C. states a situation, A. contradicts by using ‘but’, D. states that as the trail continues one feels that one would soon see the plain, but B. shows that this hope is not fulfilled.

Ans .

a

1. Explanation :

D. introduces an idea of using something in tricks. C. gives an example of one such trick. B. talks of something entertainers would do and A. tells us about something that happened during one such show.

Ans .

d

1. Explanation :

B. introduces the author, D. says that he enjoys his profession, A. and C. continue with it.

Ans .

b

1. Explanation :

Privilege can be used in A., B. and D.

Ans .

c

1. Explanation :

Disaster can fit in A., C. and D.

Ans .

d

1. Explanation :

Depression fits in A., B. and D.

Ans .

b

1. Explanation :

Imagination fits in A. and D.

Ans .

a

1. Explanation :

State fits in A., B. and D.

Ans .

a

1. Explanation :

Perjury is deliberate, willful giving of false evidence under oath i.e. lying under oath.Similarly testimony is a statement given under oath.

Ans .

b

1. Explanation :

Medieval follows prehistoric, just as future follows present.

Ans .

d

1. Explanation :

Both the pairs are pairs of synonyms.

Ans .

d

1. Explanation :

C. should precede D. as D. uses ‘they’ to refer to ‘the evils of one’s own life’ mentioned in C.B. and A. logically follow.

Ans .

a

1. Explanation :

Only C. uses the noun ‘the writer’, which is referred to as ‘he’ in all other choices, hence C. should be the first one in the series. Also B should logically follow C. So this makes option (a) correct.

Ans .

b

1. Explanation :

The subject of the sentence has been introduced in A. as ‘the masterpiece’, so should be the first part of the sentence. A masterpiece cannot be a career, or untaught genius. Only D. can follow A.

Ans .

c

1. Explanation :

C. introduces the central point of the sentence as ‘the public being easily disillusioned’. It should be the first part in the series. B., D. and then A. logically follow.

Ans .

b

1. Explanation :

D. introduces the subject as ‘the roots of the riots’, B. states what the roots are related to, C. gives another point of relation, which has to logically precede A.

Ans .

b

1. Explanation :

Only ‘happened to be ’ or ‘wasn’t’ can grammatically fit here. ‘Wasn’t’ does not give the sentence the appropriate meaning.

Ans .

c

1. Explanation :

One ‘launches’ a product.

Ans .

d

1. Explanation :

‘Unexpected success’ goes best with ‘fortune was made’.

Ans .

a

1. Explanation :

The correct idiomatic usage is ‘smothering the flames’, which means to extinguish the flames.

Ans .

d

1. Explanation :

Because there is a reference of two peoples Sam and I, there is a need to use ‘Between’.

Ans .

b

1. Explanation :

‘Hinge upon’ means ‘depends upon’.

Ans .

a

1. Explanation :

Only ‘come in’ fits here, in the sense of “appear in”.

Ans .

c

1. Explanation :

C. and D both present facts and no other choice gives that as an option.

Ans .

a

1. Explanation :

A. presents a judgement on part of the author, B. and C. present facts and

Ans .

a

1. Explanation :

B. presents a fact and no other choice gives that as an option. C. Presents an inference based on a logical conclusion of the fact that the revenues are already dwindling.

Ans .

b

1. Explanation :

We can see that B. presents a fact and D. presents an inference.

Ans .

d

1. Explanation :

A. and C. clearly present facts. B. is an opinion of the author based on common sense .D. presents an inference.

Ans .

c

1. Explanation :

A. is based on common sense. B. is a well known fact. C. is a logical conclusion based on B.

Ans .

a

1. Explanation :

B. is a well known fact which logically leads to the inference drawn in C. Other two are opinions of the author and hence judgements.

Ans .

b

1. Explanation :

B. and D. clearly present facts. C. presents an inference based on these facts

Ans .

c

1. Explanation :

A. and D. present facts, B. presents a logical conclusion based on these facts and C. presents a judgement on part of the author.

Ans .

d

1. Explanation :

A. is not a fact as it uses the phrase ‘it appears’. C. and D. clearly present facts.

Ans .

d

1. Explanation :

2. ś

Ans .

c

1. Explanation :

Ans .

a

1. Explanation :

Ans .

b

1. Explanation :

Ans .

d

1. Explanation :

Ans .

b

1. Explanation :

Ans .

c

1. Explanation :

Ans .

a

1. Explanation :

Ans .

b

1. Explanation :

Ans .

d

1. Explanation :

## Section II

Ans .

c

1. Explanation :

Let x be the number of votes not cast for Praja Party in the previous polls.
So the number of votes not cast for the party in this assembly polls would be 1.25x.
Margin of victory in the previous polls
= (260000 – x) – x = (260000 – 2x).
Margin of loss in this years polls
= 1.25x – (260000 – 1.25x)
= (2.5x – 260000).
As per the given information,
margin of loss this year = 2 × Margin of victory last year.
Therefore, (2.5x – 260000) = 2(260000 – 2x).
⇒ x = 120000.
So the number of votes cast for the party in assembly election = 260000 – 120000
= 140000.

Ans .

b

1. Explanation :

For questions 52 to 54: The data can be represented in the following Venn diagrams.
Number of persons in Dighoshpur who read only Ganashakti = 83.

Ans .

a

1. Explanation :

Refer venn diagram of Q52
Number of persons in Aghosh Colony who read both the newspapers = 13.

Ans .

c

1. Explanation :

Refer venn diagram of Q52
Number of persons in Aghosh Colony who read only 1 newspaper = 20+19 = 39.

Ans .

d

1. Explanation :

$$log_{7}log_{5}( \sqrt{x + 5}+ \sqrt{x}) = 0,$$
We know,
$$log_{a} = x ⇒ a^{x} = b$$
$$∴log_{5}( \sqrt{x + 5}+ \sqrt{x}) = 7^{0}$$
$$⇒log_{5}( \sqrt{x + 5}+ \sqrt{x}) = 1$$
$$⇒\sqrt{x + 5}+ \sqrt{x} = 5^{1}$$
$$⇒\sqrt{x + 5} = 5 - \sqrt{x}$$
Squaring both sides, we get,
$$⇒ x + 5 = 25 + x − 2×5\sqrt{x}$$
$$⇒ x + 5 = 25 + x − 10\sqrt{x}$$
$$⇒ 10\sqrt{x} = 20$$
$$⇒ \sqrt{x} = 2$$
$$⇒ (\sqrt{x})^{2} = (2)^{2}$$
⇒ x = 4 .

Ans .

a

1. Explanation :

Let the radius be r cm. Therefore, the height of the cone and cylinder will be 2r. ∴ The ratio $$\frac{1}{3}πr^{2}(2r) : πr^{2}(2r) : \frac{2}{3}πr^{3} = \frac{2}{3} : 2 : \frac{2}{3} = 2 : 6 : 2 = 1: 3: 1$$

Ans .

d

1. Explanation :

Hence, we find that the least expenditure will be incurred if the school is located in town B.
HINT : Students please note that since there are more number of students from Town B, to minimise the total expenditure the school should be located as closer to town B as possible.

Ans .

d

1. Explanation :

There are 18 men, 15 women and 6 children.
Working efficiency of man : woman : child = 6 : 3 : 1.
So the ratio of the work done in a day by 18 men, 15 women and 6 children
= (18 × 6) : (15 × 3) : (6 ×1) = 108 : 45 : 6.
Hence, the daily wage of Rs.1,113 should be divided in this ratio. That makes it, Rs.756 for men, Rs.315 for women and Rs.42 for children.
Hence, 6 children earn Rs.42 in a day.
So the daily wage of a child should be Rs.7

Ans .

b

1. Explanation :

Let the radius of the original cone be ‘r’.
∴ The volume of the original cone (V) = $$\frac{πr^{2}h}{3}$$
The height and radius of the smaller cone are $$\frac{2h}{3} and \frac{2r}{3}$$respectively.
So its volume = $$\frac{π}{3}×\left( \frac{2r}{3} \right)^{2} × \frac{2h}{3} = \frac{8V}{27}$$
∴ Volume of frustum = $$\left( V - \frac{8V}{27} \right) = \frac{19V}{27}$$
∴ Ratio of the volumes = 8 : 19.

Ans .

b

1. Explanation :

Assume some values of a, b and c such that sum of a, b and c is 0 where a ≠ b ≠ c,and find the value of the given expression.
Let a = 1, b = –1 and c = 0.
$$⇒ \frac{a^{2}}{2a^{2} + bc} + \frac{b^{2}}{2b^{2} + ac} + \frac{c^{2}}{2c^{2} + ab} = \frac{1}{2} + \frac{1}{2} + 0 = 1$$

Ans .

c

1. Explanation :

The harmonic mean of two numbers x and y is $$\frac{2xy}{(x + y)}$$and the geometric mean is $$\sqrt{xy} .$$
∴ $$\frac{\frac{2xy}{(x + y)}}{\sqrt{xy}} = \frac{12}{3} , ⇒ \frac{4xy}{(x + y)^{2}} = \frac{144}{169} .$$
Although this can be simplified to get the answer, the best way to proceed from here would be to look out for the answer choices and figure out which pair of x & y satisfies the above equation. You will find the answer is (c).
HINT : Students please note that this sum is a classic example of how you could have gone for intelligent guess work. Since we know that the denominator of the ratio is the geometric mean, which is $$\sqrt{xy}$$, the two numbers should be in such a ratio that their product should be a perfect square. The only pair from the answer choices that supports this is 4 & 9, as $$\sqrt{4 × 9} = \sqrt{36} = 6.$$

Ans .

a

1. Explanation :

If one root of $$x^{2} + px + 12 = 0$$ is 4, then $$4^{2} + 4p + 12 = 0$$, i.e. p = –7
$$x^{2} – 7x + q = 0$$ has equal roots
If both the roots are α , 2α = $$\frac{(−7)}{1} = 7$$ i.e. α =$$\frac{7}{2}, and q = α^{2} ⇒ q = \frac{49}{4}$$

Ans .

b

1. Explanation :

Ma[md(−2),mn(md(−3),−2),mn(6,md(−8))]
=Ma[2,mn(3,−2),mn(6,8)]
=Ma[2,-2,6]
=6

Ans .

a

1. Explanation :

For a > b, the given equation reduces to Ma[|a|,b ] = mn[ a,|a| ].
If b < a < 0, then |b| > |a| > 0 > a > b.
∴ Ma[|a|,b ] = |a| , and mn[ a,|a| ] = a.
Hence, option (a) is correct.

Ans .

b

1. Explanation :

Since a bucket holds 5 litres of water, water discharged in one minute by tap A, B and C is $$\frac{5}{6}$$ litres,$$\frac{2}{3}$$ litres and $$\frac{1}{2}$$ litres respectively
If A, B and C are all opened simultaneously, total discharge in one minute $$= \left( \frac{5}{6} + \frac{2}{3} + \frac{1}{2} \right) = 2$$ litres
So in 2 hours, the discharge would be 240 litres, that is the capacity of the tank.

Ans .

c

1. Explanation :

It is clear that the ratio of the distances between (DelhiChandigarh) : (Chandigarh-Shimla) = 3 : 4.
The ratio of the speeds between (Delhi-Chandigarh) : (Chandigarh-Shimla) = 3 : 2.
Let the distances be 3x and 4x respectively and speeds be 3y and 2y.
So the time taken will be $$\left( \frac{x}{y} \right)$$ and $$\left( \frac{2x}{y} \right)$$ respectively. Average speed $$= \frac{(Total Distance)}{(Total Time)} = \frac{(7x)}{ \left( \frac{x}{y} + \frac{2x}{y} \right) } = \frac{7y}{3} = 49$$
Hence, y = 21. So the average speed from Chandigarh to Shimla = 2y = 42 kmph.

Ans .

c

1. Explanation :

Middle term of an A.P. is average of all the terms in A.P.
Number of terms = 7
Middle term = Fourth term = 8
Therefore, sum of all the terms = 56.

Ans .

d

1. Explanation :

If a clock has to strike 4 or 4 times, there are 3 time intervals between the 4 strikes (Since the first strike happens at the zeroth second). So in 7 seconds the pendulum elapses 3 time intervals.To strike 11, there has to be 10 time intervals, which will take $$\frac{10 × 7}{3} = 23.33 seconds.$$

Ans .

d

1. Explanation :

Let the number of stones be ‘n’.
As the person covers 4.8 km, he covers 2.4 km on one side and 2.4 km on other side.
So total distance covered by him = 20 + 40 + 60 +…….
$$∴2400 = \frac{n}{2}[2x20 + (n-2)20 ] = 10n(n+1)$$
(Here n is the number of stones)
After solving, we get n = 15
∴Total number of stones = 15 + 15 + 1 = 31

Ans .

b

1. Explanation :

Required number = LCM (8, 11, 24) – 5 = 259.

Ans .

b

1. Explanation :

Since SP of spirit and solution water = Rs.75/l and there is a profit of 37.5%, CP of spirit and water solution $$=\frac{75}{1.375} = Rs.54.54/l$$
This should indeed be the weighted average of the costs of spirit and water. So if we alligate, we can get the ratio of spirit : water (assuming that cost of water is 0).

Ans .

a

1. Explanation :

Let x and y be the sides of the rectangle ABCD and z
be the length of AP.
Then CR = BP = x – z
By applying Pythagoras Theorem, we have
$$in ∆ APO,a^{2} = OP^{2} + z^{2} ... (i)$$
$$in ∆ BPO, b^{2} = OP^{2} + (x – z)^{2} ... (ii)$$
$$in ∆ CRO, d^{2} = OR^{2} + (x – z)^{2} ... (iii)$$
$$in ∆ DRO, c^{2} = OR^{2} + z^{2} ... (iv)$$
Solving above equation, we have $$a^{2} + d^{2} = b^{2} + c^{2}$$
∴ For any point inside a rectangle as shown, $$a^{2} + d^{2} = b^{2} + c^{2}$$
Pairing up the distance so that d is to be the maximum, we get $$40^{2} + d^{2} = 50^{2} + 60^{2}$$ ⇒ d = 67 m.

Ans .

b

1. Explanation :

Let they meet at a distance x km from X.
So the total distance travelled by A = x.
Total distance travelled by B = 27 + (27 – x) = (54 – x).
Time taken by A = $$\frac{x}{5}$$.
Time taken by B = $$\frac{(54 – x)}{7}$$.
Since they have met at the same time, they would have travelled for the same time.
Hence $$\frac{x}{5} = \frac{(54 – x)}{7}$$ or x = 22.5 kms.

Ans .

d

1. Explanation :

Let us assume that Alphonso’s total property was of Rs.x. Since Alphonso’s wife is also the mother of Dave, the total share of this lady would be $$\left( \frac{x}{2} + \frac{15x}{96} = \frac{63x}{96} \right)$$.
And since, $$\frac{63x}{96} = 1,575000$$
⇒ x = Rs.24 lakhs.

Ans .

a

1. Explanation :

Refer Diagram of answer 74 Carl’s original share was $$\frac{x}{6} = \frac{24}{6}$$= Rs.4 lakhs.

Ans .

b

1. Explanation :

Refer Diagram of answer 74 The ratio’s of the property owned by the widows of the 3 sons $$= \left( \frac{1}{`2} : \frac{5}{48} : \frac{15}{96} \right) = 8 : 10 : 15.$$

Ans .

c

1. Explanation :

Let $$log_{6}216\sqrt{6} = x.$$
Then by rule, $$log_{b}a = x ⇒ b^{x} = a$$ we have,
$$6^{x} = 216\sqrt{6}$$
$$6^{x} = 6^{3} x 6^{\frac{1}{2}}$$
⇒ $$6^{x} = 6^{\frac{7}{2}}$$
∴ = $$\frac{7}{2}$$

Ans .

c

1. Explanation :

Since the leak can empty the tank in 8 hours, the rate of leak = $$\frac{1}{8}$$
And since the leak along with the tap can empty it in 12 hours, the equation can be rewritten as:
$$\frac{1}{x} -\frac{1}{8} = - \frac{1}{12}$$ (where x is the time taken by the tap to fill the tank).
Simplifying we get, $$\frac{1}{x} = \frac{1}{24}$$ or x = 24.
This means that the tap can fill the tank in 24 hours.
Since the tap admits 6 litres per hour, it will admit (6 × 24) = 144 litres in 24 hours, which should be the capacity of the tank.

Ans .

d

1. Explanation :

The LCM of 7, 12 and 16 is 336. The closest multiple of 336 to 1856 is 1680. So 1684 when divided by 7, 12 and 16 leaves a remainder of 4. This is the closest such number, less than 1856.
Hence, the number to be subtracted from 1856 to get 1684, must be the least such number. So the answer is (1856 – 1684) = 172.
Alternate method:
Subtract options from 1856 and check.

Ans .

a

1. Explanation :

16 articles sold at priced 12 articles, is equivalent to discount of $$\left[ \left( \frac{16 - 12}{16} \right) x100 \right] = 25%$$
Hence, shop keepers offer two discounts of 20% and 25% respectively and still makes a profit of 20%.
If c is the cost price of an article and m is the marked price, then 1.2 × c $$= m × \frac{3}{4} × \frac{4}{5}$$
⇒ m = 2c.
This means that he had marked his goods 100% above his cost price.

Ans .

d

1. Explanation :

Since the ages of none of them is mentioned and we have two equations and three unknowns.
Hence, we cannot say anything about the ages of any of them.

Ans .

c

1. Explanation :

Since ∠C = ∠2E , therefore ∠BCA = 60°.
Also since ABCD is a parallelogram,
AB = CD and AD = BC = AC.
Hence, ∆ABC and ∆ACD are equilateral triangles.
Hence, area of this triangle $$\frac{s^{2}}{4} \sqrt{3}$$,
where s is the side of the triangle = AB = AD = DC = BC
∴ Area of the parallelogram is twice this area = $$\frac{s^{2}}{2} \sqrt{3}$$
Since ∠CAD = 60°, ∠DAE = 90°, so ∆EAD is a right triangle with side AD = s. Since it is a 30°-60°-90° triangle, hence side AE $$= s\sqrt{3}.$$
∴ Area of this triangle $$= \frac{s × s\sqrt{3}}{2} = \frac{s^{2}\sqrt{3}}{2}$$
Hence, the required two areas are equal or I = II

Ans .

a

1. Explanation :

Miguel’s income = 5 + (0.02 × 25) + (0.03 × 25) + (0.04 × 50) = $8.25. Martin’s commission =$10.
Hence, obviously I > II.

Ans .

c

1. Explanation :

Since the lines are parallel,$$\frac{AB}{BC} = \frac{DE}{EF}$$ i.e. AB × EF = BC × DE.
Hence I = II.

Ans .

b

1. Explanation :

53 Sundays can occur in a non-leap year, if 1st January is either a Saturday or a Sunday. But 54 Sundays can never occur.
Hence, I < II.

Ans .

c

1. Explanation :

Since it is a relay race, all the runners ran the same distance.
Hence, for a same distance,
ratio of times =$$\frac{1}{ratio of speeds}$$.
Hence, ratio of times taken by B & D = 18 : 16 = 9 : 8.

Ans .

b

1. Explanation :

Let $$g(x) = \frac{x - 3}{2}$$ be y.So, fog(x) = f(y) = 2y + 3.
Substituting y = $$\frac{x - 3}{2}$$ we get
$$fog(x) = (x – 3) + 3 = x = \frac{[(2x + 3) – 3]}{2} = gof(x)$$

Ans .

c

1. Explanation :

If 2x + 3 = $$\frac{[(x-3)-3]}{2}$$, then x = -4

Ans .

b

1. Explanation :

From Question 87, fog(x) = gof(x) = x, you will realise that if you were to form a chain of these functions for even number of times, you would still end up getting x.
E.g. fogofog(x) = fog(x) = x. Since both the brackets have the functions repeated for even number of times, each of their value will be x and their product will be $$x^{2}$$.

Ans .

c

1. Explanation :

From question 87, gof(x) = fog(x) = x.
fo(fog)o(gof)(x) = fo(fog)(x) = f(x) = 2x + 3.

Ans .

c

1. Explanation :

Statement I tells us that the time taken to cover both distances is the same, but it does not tell us anything about the speeds at which these are covered. The information is given in second statement, says the speed from cinema hall to home is less than that between home to the office.
Hence, by using both the statements we can say that the distance between cinema hall to home is less than that between home to the office.

Ans .

a

1. Explanation :

If the total work is one unit, work done by A and B in one day will be $$\frac{1}{a}$$ unit and $$\frac{1}{b}$$ unit respectively.
Using statement I: $$\frac{n}{a} + \frac{n}{b} =1$$
Since ‘n’ is an integer, if both A and B work for n days, work will be completed no matter who starts a work.
Using statement II, nothing can be concluded as total amount of work is not known.

Ans .

b

1. Explanation :

2g + 3b = 20.
Since b & g should be integers the values that satisfy this equation are (g = 10 & b = 0), (g = 7 and b = 2), (g = 4 & b = 4), and (g = 1 and b = 6).
From the statement I, we can shortlist the last two possibilities i.e. g =4 or g = 1, but cannot get a unique answer.
The statement II suggests that the number of girls and boys have to be equal. Hence, we get a unique answer viz. g = 4 & b = 4. Only statement II is required to answer the question.

Ans .

b

1. Explanation :

P = (SP – CP) x Sales. From the data given in the question we can figure out that P1 = (1.1SP – CP) x 0.9Sales. Hence, $$\frac{P}{P1} = \frac{1.11(SP – CP)}{(1.1SP – CP)}$$ .To find this ratio we need to eliminate the variables CP & SP. This can only be done if in the denominator, CP is replaced by 1.1CP. In other words, if the CP increases by 10%, as in that case our ratio will be $$\frac{1.11}{1.1} = 1.01.$$
Hence,only statement II is required to answer the question.

Ans .

d

1. Explanation :

As neither average weight of the original members is not mentioned nor the number of members in original team, question cannot be answered.

Ans .

c

1. Explanation :

None of the statement alone is sufficient to answer the question.
Using both statements together:
PQ = PB + BQ and RS = RE + ES
If BQ = ES and PB > RE, PQ > PS.

Ans .

b

1. Explanation :

Let the number of toffees with the first, second and third boy be x, (x+4) and (x+8) respectively.
Hence, total number of toffees = (3x+12).
The statement I merely suggests that (3x+12) is a multiple of 2, which means that x is a multiple of 2. Nothing concrete can be concluded on the basis of this statement.
The statement II suggests that (x – 4 + 2 ), (x + 4 – 6 + 2) and (x + 8 – 4) are in GP or (x-2), x and (x+4) is in GP.
$$∴ x^{2} = (x + 4)(x − 2)$$
⇒ x = 4
⇒ (3x + 12) = 24
Question can be answered using statement II alone.

Ans .

c

1. Explanation :

The statement I suggests that the number of sheep had increased by 20% last year over the previous year. But it does not suggest whether the rate of increase is annual or not.
For eg. 20% increase in a year can also be obtained by 9.5% increase over 6 months. i.e. 1.095 x 1.095 = 1.20.
The statement II however suggests that the increase is compounded annually.
Hence, now we can find the answer.
If the number of sheep last year was x,
then $$x + 400 = x(1.2)^{2}$$
Hence, x = 909.
Thus, we require both statements to answer the question.

Ans .

d

1. Explanation :

From the statement I, we can find out the area that needs to be bordered. And from the statement II, we can find out the cost of each tile. But to find the total cost, we require the total number of tiles and to find this we require the dimension of each tile. Since this is not known, we cannot answer the question using either statements.

Ans .

d

1. Explanation :

From the statement I, we can only find the number of mangoes stolen by 4 of the 10 boys.
The statement II suggests that the number of mangoes stolen by each of the remaining six boys is more than 4 and less than 40. Although from the two statements that are given it is tempting to assume that the number of mangoes stolen by the boys must be in AP, since it is not mentioned explicitly we cannot answer the question.

## Section III

Ans .

d

1. Explanation :

The passage is basically about how ants communicate.

Ans .

c

1. Explanation :

Ants attack strangers who might belong to the same species.

Ans .

d

1. Explanation :

If they did so they would have been unable to communicate with the drunken ants.

Ans .

d

1. Explanation :

Chloroform killed the ants.

Ans .

b

1. Explanation :

The author has a playful, whimsical way of writing.

Ans .

b

1. Explanation :

All others can pass through the atmospheric windows without distortion.

Ans .

d

1. Explanation :

Clouds from volcanic eruptions do not find a mention in the passage.

Ans .

d

1. Explanation :

Telescope mounting is used to neutralize the Earth’s rotation relative to the stars.

Ans .

d

1. Explanation :

The precession period of the Earth is 26,000 years

Ans .

c

1. Explanation :

The diurnal spinning is the spinning of the Earth on its own axis, having no relation to the gravitational force of the Sun or the Moon.

Ans .

b

1. Explanation :

The last passage states that there can be uncertainty in the rate of orbital motion of the Earth.

Ans .

c

1. Explanation :

Man made signals can interfere with the radio wavelengths between 1cm. And 20m. implying that they also fall in the same range.

Ans .

b

1. Explanation :

US was more concerned with ‘order’ than with reforms of any kind.

Ans .

d

1. Explanation :

Latin Americans regarded it as economic imperialism.

Ans .

a

1. Explanation :

The Act of Bogota was most closely related to the Marshall Plan or Latin America.

Ans .

c

1. Explanation :

US preferred dictatorship to the spread of communism in Latin America.

Ans .

b

1. Explanation :

The President’s initiative to present financial economic aid to Latin America has been presented as an example of his efforts to mend his ‘Latin Ameriacn fences’. Thus he was not acting to continue to keep communism from intruding the country.

Ans .

a

1. Explanation :

The passage states that speeding up social reforms implied a risk of revolt, which could be avoided by maintaining status quo.

Ans .

b

1. Explanation :

The examination system was the traditional avenue of selecting the officials.

Ans .

a

1. Explanation :

The Restoration statesmen tried to restore the society, and not create a new one. They tried to stretch the traditional ideology in order to make the Confucian system under the new conditions.

Ans .

a

1. Explanation :

The only similarity was their intent to conserve.

Ans .

d

1. Explanation :

None of these philosophers has been mentioned in the passage.

Ans .

c

1. Explanation :

The aim of the Restoration was to restore to their original vitality the best of the ancient institutes.

Ans .

c

1. Explanation :

Western conservatism distrusted cosmopolitanism.

Ans .

b

1. Explanation :

The passage is basically about Chinese Conservatism.

Ans .

b

1. Explanation :

India has the lengthiest constitution in the world.

Ans .

c

1. Explanation :

Israel does not have a written constitution.

Ans .

b

1. Explanation :

Presidential cabinet is not even mentioned in the American constitution.

Ans .

b

1. Explanation :

The constitutions of new states in the US are very concise.

Ans .

b

1. Explanation :

A normative constitution has the status of supreme law and is fully activate and effective.

Ans .

d

1. Explanation :

Where the written constitution is only nominal, behind the verbal façade will be found the real constitution containing the basic principles according to which power is exercised in actual fact

Ans .

c

1. Explanation :

Since a long constitution says too many things, on too many subjects, it has to be amended often.

Ans .

b

1. Explanation :

The presence or absence of a written constitution makes a difference, but only of a degree.

Ans .

a

1. Explanation :

The author is concerned about the books and is also well informed about the topic.

Ans .

c

1. Explanation :

The paper of ‘archival quality’ refers to a long lasting paper.

Ans .

a

1. Explanation :

Wood pulp helped in producing large quantities of paper

Ans .

b

1. Explanation :

Paper that is acidic is highly unstable.

Ans .

c

1. Explanation :

This is not a reason mentioned in the passage, for producing long lasting paper.

Ans .

a

1. Explanation :

Reduction in government funding has not been mentioned as a reason for curtailing purchase of new books.

Ans .

d

1. Explanation :

The continued use of wood pulp will not have any effect on the governments.

Ans .

c

1. Explanation :

Lignin is a major factor that causes paper to discolour.

Ans .

d

1. Explanation :

Eisaku Sato was the Prime Minister for eight years.

Ans .

b

1. Explanation :

Hirohito has been said to be on throne for 61 years at the time of writing of the passage, which was in 1987.

Ans .

c

1. Explanation :

Mr. Tanaka was involved in a bribe scandal.

Ans .

b

1. Explanation :

The passage says that Mr. Yasuhiro Nakasone is ‘now bowing out’.

Ans .

c

1. Explanation :

He has proved himself more skillful in the game of factional politics and thus his hopes are stronger.

Ans .

c

1. Explanation :

The author states that how Mr. Takeshita will fare after taking over the reins of the government is not certain, and reasons about this in an objective manner.

Ans .

d

1. Explanation :

The quick turnover of Prime Ministers has led to factionalism in LDP.

Ans .

c

1. Explanation :

Mr. Takeshita will be the first Prime Minister with humble rural origins.

Ans .

b

1. Explanation :

The three Prime Ministers mentioned by name here are Mr. Nakasone, Mr. Eisaku Sato and Mr. Kakue Tanaka.

## Section IV

Ans .

c

1. Explanation :

Hence (c) is the correct answer.

Ans .

c

1. Explanation :

At 30oC, solubility of potassium nitrate is 0.38 kg./lt. Hence in 10 litres 3.8 kg.( ≈ 4 kg) of potassium nitrate can be dissolved.

Ans .

d

1. Explanation :

Percentage increase in solubility of potassium chlorate
$$= \frac{(0.4 – 0.1) ×100}{0.1} = 300%$$

Ans .

d

1. Explanation :

Solubility of potassium chloride at 36°C = 0.4 kg./lt. Hence the amount of Potassium chloride that can be dissolved in 100 lt. at 36°C = 40 kg.
Number of moles $$\frac{40}{0.07456} = \frac{40}{0.075} = 533.$$
As we have approximated 0.07456 as 0.075 and 540 is closest to 533, it should be correct answer.

Ans .

c

1. Explanation :

From the graph it can be seen that between 15°C & 25°C, solubility of sodium nitrate, potassium chloride, sodium chloride, is almost constant. It can clearly seen from graph that solubility of sodium chlorate is maximum.

Ans .

c

1. Explanation :

The correct seating arrangement can be depicted as shown below: Jackie is the host and also sitting on Shobha’s right. Hence (c) is the correct answer.

Ans .

d

1. Explanation :

Shobha is sitting next to Jackie and Dhirubhai. So she is the only person who is not seated next to a person of the same sex.

Ans .

a

1. Explanation :

If Ratan would have exchanged seat with a person four places to his left, which is Shobha, the following arrangement would exist. The first statement is hence true, since no man is sitting between two woman and no woman is sitting between two man. However statements II and III are not true. Hence the answer is (a).

Ans .

a

1. Explanation :

Among the given choices, only Ratan & Monisha are sitting opposite to each other and hence they must be married.

Ans .

d

1. Explanation :

From the data that is given we can find the following data: (the explanation of how the following values were arrived, is given after the table). Food related exports in 1985-86 = 0.23x25800 = 5934. So food related exports in 1984-95 = (5934 – 1006) = 4928.
Hence, percentage of food related exports in 1984-85
$$= \frac{4928}{22400}×100 = 22%.$$

Ans .

b

1. Explanation :

In 1984-85, Value of Manufactured articles & Raw materials exports = (22400 – 4928) = Rs.17472 crores. Since Export of manufactured goods is twice that of raw materials, Rs.17472 has to be divided in the ratio 2:1.
Therefore, export of manufactured goods = Rs.11648 crores and Raw materials = Rs.5824 crores. Hence, the difference between raw material and food = (5824 – 4928) = Rs.896 crores.

Ans .

d

1. Explanation :

In 1985-86, the combined percentage of Manufactured articles and Raw materials = 77% and this is in the ratio 4 : 3.
Hence, percentage of Manufactured articles export is 44% and that of Raw materials export is 33%. Hence, value of manufactured = 0.44 × 25800 = Rs.11352 crores and the value of Raw materials = Rs.8514 crores. Hence, percentage difference between the value of Raw materials between 1984-85 and 1985-86
$$= \frac{(8514 – 5824)}{8514} × 100 = 31.6%.$$

Ans .

a

1. Explanation :

The change in the value of exports from 1984-85 to 1985-86 = (11648 – 11352) = Rs.296 crores.

Ans .

b

1. Explanation :

From the given conditions, the only possible arrangements are If Aishwarya is standing at the extreme left, case II holds good. Hence Sushmita is standing in the middle.

Ans .

d

1. Explanation :

Again Case II holds good. So the girl who is standing second from left is Manpreet.

Ans .

d

1. Explanation :

Under the given conditions, the following arrangement is possible: Hence, Rachel is standing at the extreme right.

Ans .

c

1. Explanation :

The skin & muscular protein totally constitutes 33% of the total proteins. The total proteins itself is 15% of the total body weight. Hence the percentage of skin & muscular protein as a fraction of the total body weight
$$= 33% of 15% ≈ 5% = \frac{1}{20}.$$

Ans .

a

1. Explanation :

Required Ratio = 25 : 8 ≈ 3 : 1

Ans .

d

1. Explanation :

We can determine only the percentage of skin protein in Ghosh Babu’s total body weight. But there is no data given about the percentage of skin in Ghosh Babu’s body. Hence the answer is (d).

Ans .

a

1. Explanation :

Proportion of material other than water & protein in Ghosh Babu’s body is
$$\frac{15}{100} = \frac{3}{20}.$$

Ans .

b

1. Explanation :

The first statement suggests : B is now as old as C was in the past. Therefore, B < C. Also sometime in the past, A was twice as old as D. So A > D. C will be as old as E in future. Hence C < E.
The second statement suggests : A > F. A was as old as G in the past. Therefore, A > G. D will be as old as F in future. So F > D. F will be as old as G now in future. This implies G > F. G was as old as B, when A was as old as G. Hence, A = B.
Combining both the results, we get : E > C > B = A > G > F > D (Note by A = B, it is meant that they are of similar age group, not necessarily the same).
It could be figured out that E is the eldest brother.

Ans .

b

1. Explanation :

D is the youngest brother.

Ans .

c

1. Explanation :

Only A and B could probably be twins.

Ans .

c

1. Explanation :

It could be figured out that only statement (c) is false as B has only 2 elder brothers and not 3.

Ans .

c

1. Explanation :

Required percentage growth
$$= \frac{(68718 – 42137) × 100}{42137}$$
Students please note that to calculate the exact value of this expression, we need calculator. Since, options given are not very close to each other so we can approximate values. And using approximations we get the value of required ratio
$$= \frac{(68600 – 42000) ×100}{42000} = \frac{2650}{42} = 63%.$$

Ans .

c

1. Explanation :

Hence, percentage growth is least for higher secondary books viz.26%.

Ans .

b

1. Explanation :

Again referring to the above table we can see that the percentage growth rate is maximum for secondary level books viz.125%.

Ans .

d

1. Explanation :

It can be seen from the given table that though primary level books have shown a consistent growth, it has declined in the year 1978. On the other hand even Secondary and Higher secondary level books have shown a consistent increase except for the year 1977 when it had declined. But the graduate level books have shown a consistent growth over the period.

Ans .

d

1. Explanation :

The data given the graph can be tabulated as given below : Total number of students in 1989–90 = (180 + 130 + 70 + 40) × 100 = 42000.

Ans .

c

1. Explanation :

Growth rate in number of students in Govt. Engg.
College $$= \frac{(120 – 80)}{80} = 50%.$$
Growth rate in number of students in Private Engg.
College $$= \frac{(180 – 120)}{120} = 50%.$$
Hence the growth rate is equal.

Ans .

d

1. Explanation :

Total number of students in 1990–91 = (250 + 130 + 100 + 80) 100 = 56000
Hence the total number of students in 1991-92 = 0.9 × 56000 = 50400. Hence (d) is the correct answer

Ans .

c

1. Explanation :

Percentage of IIT students in 1990 – 91
$$= \frac{80}{560} = \frac{1}{7} = 14.28%.$$

Ans .

b

1. Explanation :

All the sentences are possible except (b) as Grumbs have to be used with Ihavitoo and Grumbs cannot be used in any other type but Bingoes.

Ans .

d

1. Explanation :

Since Grumbs and Harrumphs are the Bingoes and Grumbs has to always go with Ihavitoo, so we will have to use Ihavitoo as the Cingo. Since statement I is true, the answer can only be (a) or (d). So we will only evaluate the option (d). Since we have not used Koolodo as Cingo, we can use either Lovitoo or Metoo or both as Dingos. Hence, statement III is also true, so the answer is (d).

Ans .

a

1. Explanation :

Option (b) uses two Cingo’s instead of one, hence grammatically incorrect. Option (c) violates the same rule again and in addition it uses ihavitoo without using Grumbs. Option (d) again uses two Cingo’s instead of one. Hence, the only option that is grammatically correct is (a).

Ans .

b

1. Explanation :

If Grumps is the Bingo, then Ihavitoo must also be used. And since Ihavitoo is common to Bingo and Cingo, Ihavitoo must be used as a Cingo . Also no other Cingo can be used. So obviously Harrumphs must also be used as a Bingo. And since we are not using Koolodo as Cingo, we can use Lovitoo as Dingo. So (a), (c) and (d) can all be true. So (b) cannot be true.

Ans .

b

1. Explanation :

From the first week data we can arrive at the following work pattern of Bankatlal for the 1st month.
First Month : Thus his total wage = (600+120+600+120) = Rs.1440

Ans .

c

1. Explanation :

Let us compile the data for 2nd, 3rd and 4th month.
Second Month : Third Month : Fourth Month : Total wage for 1st month = Rs.1440
Total wage for 2nd month = (840 +180 +840 +180) = Rs.2040
Total wage for 3rd month = (720 + 240 + 720 + 240) = Rs.1920
Total wage for 4th month = (960+960) = Rs.1920
Total wage for the 4 months = (1440+2040+1920+1920) = 7320
Hence the average salary $$= \frac{7320}{4} = Rs.1830.$$

Ans .

d

1. Explanation :

Using the above data, we can revise the wage compilation for the third month as given below:
Third Month : So now his third month age = (780+120+780+120) = Rs.1800.
Previously he used to earn Rs.1920 in the third month.
Hence change in Bankatlal’s salary for the 3rd month = (1920 – 1800) = Rs.120.

Ans .

d

1. Explanation :

For the fourth month, the new wage compilation will be as given below :
Fourth Month So now his total wage for the 4th month = (2400 + 2400 – 240 – 240) = Rs.4320.
Since the calculations for the first two months are made as per the old scheme of things, this has already been computed.
Total wage for 1st month = Rs.1440
Total wage for 2nd month = Rs.2040
Calculation for the third and fourth month are as per new calculations and they are :
Total wage for 3rd month = Rs.1800
Total wage for 4th month = Rs.4320
Therefore, total salary for the four months = (1440 + 2040 + 1800 + 4320) = Rs.9600.