unproctored mock cat 1 - solutions

8/6/2019 Unproctored Mock Cat 1 - Solutions

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Page1 Unproctored - Mock CAT 1MBATest PrepMBATest Prep

Unproctored - Mock CAT 1

Answers and Explanations

1 b 2 c 3 c 4 d 5 a 6 d 7 a 8 b 9 c 10 a

11 d 12 b 13 b 14 c 15 c 16 c 17 d 18 a 19 b 20 a

21 d 22 d 23 b 24 c 25 d 26 b 27 b 28 a 29 d 30 a

31 c 32 a 33 c 34 b 35 a 36 b 37 c 38 d 39 a 40 d

41 d 42 c 43 b 44 b 45 c 46 a 47 b 48 a 49 c 50 d

51 c 52 b 53 d 54 b 55 d 56 c 57 d 58 b 59 a 60 c


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1. b Option (a) is too specific to capture the implication of thecomment. Moreover, it does not talk about economists at whomthe comment is aimed. Option (c) is excessive as we cannotinfer from the comment that a well plumed bird wins in theend. All we can infer is that the behaviour of a typical economistis like a well-plumed bird. Option (d) is incorrect as the passagedoes not talk about putting down other economists. Yes, itdoes talk about the uncaring attitude. Hence Option (b) is aptas it talks about the behaviour of economists which is similarto well-plumed birds aiming to promote their own work.

2. c The lines in the first para Mr Leamer, an economist at theUniversity of California in Los Angeles, was frustrated byempirical economists emphasis on measures of correlationover underlying questions of cause and effect, such aswhether people who spend more years in school go on toearn more in later life reveal that the input variable is the timespent in school and the output is earnings.

Also refer to the lines in the third para some relevant variablesmay simply not be observable. For example, the time someonestays in school is probably influenced by his innate scholasticability, but this is very hard to measure. Leaving such variables

out can easily lead econometricians astray. So one can inferthat the left out variable is scholastic ability.

3. c Option (a) is incorrect as the passage does not examine therole of instrumental variables in causal literature. Indeed, thepassage mentions instrumental variables with context tocausal literature but then the passage moves on to discussthe influence of instrumental variables on economics. Option(b) leaves out instrumental variables which is the main topicof discussion in the passage. Option (d) leaves outeconomics which makes the choice too general and withouta context. Option (c) is correct as the author in the 2 nd

paragraph, in the lines The techniqueseducation, beginsto discuss the influence of instrumental variables on economics;the author further highlights this influence with the help ofexamples like Freakonomics.

4. d Option (a) is incorrect. Refer to the lines The techniques atthe heart of this literaturein particular, the use of so-calledinstrumental variables-have yielded insights into everythingfrom the link between abortion and crime to the economicreturn from education. But these methods are themselvesnow coming under attack. This makes it clear that thetechniques have not received a unanimous acceptance. Option(b) is incorrect as instrumental variables affect the outputthrough their influence only on the input variable. Refer topara 4. Option (c) cannot be inferred as the instrumentalvariable created by Joshua and Alan teases out schoolingstrue effect on wages. This means that the instrumental variablecarefully separates out schoolings true effect on wagesfrom a host of related factors or variables. This does not

mean that years of schooling have no effect on the wagesearned after schooling.

5. a In the question, filling the second blank holds a very importantkey. It says that in the process of throwing off the shackleswe are now exposed to the dangers of incipient theories andsolutions. On the basis of this, we can eliminate options (b)and (c). Now out of the remaining two options, we caneliminate option (d) on the basis of the first word-impervious(not allowing entrance or passage), which does not fit in thefirst blank.

6. d There should be a that or a which after companies torepresent the idea of a restrictive clause as the use ofsophisticated machinery and production of high qualityproducts is specific to some companies. Option (a) is incorrectbecause it places a comma before which and after products;in this case it seems as the production of high quality productsand use of sophisticated machinery are being indicated asadditional information about companies that understand the

needs. In case of the given sentence it is semanticallyincorrect. Option (b) contains a subject-verb agreement error.The subject companies is plural so the verb should beunderstand. Option (c) uses the -ing form of the verb useand does not use the same for produce. This leads to anerror of parallelism.

7. a In the first sentence, faze means to disturb whereas phaserefers to a stage in a process of development or an aspect.Phased does not fit with the given sentence. The givensentence refers to the subjects refusal to be affected byinsulting remarks. In the second sentence, canon refers tolaws, principles whereas cannon is a part of artillery. Theword equitable means fair, impartial or just and equablemeans steady. The third sentence refers to the equal and fair

treatment given to all citizens by the law. The word reignmeans to rule whereas rein means to check or stop, control.The given sentence refers to lawlessness dominating thecity. Inflammable is used for something that can be easily seton fire whereas inflammatory refers to something thatprovokes anger or hostility. A communal discord can occurdue to inflammatory remarks.

8. b Taking up option (a), we can see that the purpose of scientificdata generated could not be to portend (to give an omen oranticipatory sign of). So option (a) cannot be the answer forthe question. Option (b) is the correct answer. The forestalling(Forestall means to prevent or hinder by doing somethingahead of time) of an inchoate rift makes proper sense. Becausethe data will not allow the rift to develop further. The rift is in anascent stage and the data from the satellites will stop the

development of the rift. Option (c) is not the correct choice, asdisturbances do not fit the second blank. Option (d) is not thecorrect answer. Schism means a separation or division intofactions. One can resolve factionalism but not faction. Thisexpression is incorrect.

9. c In Option (a), ... the better it solves them, creates a doubt:what does the pronoun them denote here? It is incorrect asit fails to pair with the last line of the paragraph; rather itfollows option (c). Option (b) can be easily annulled, as it isconvoluted and ambiguous due to the phrase, the seed of itsown negation. Here, we do not know whether the awarenessof the environment is subject to negation of the mind or theorganism itself is subject to negation. Option (c) is correct asit aptly forms a pair with the last line of the paragraph and

extends the discussion on the other factor: environment thenon-ego, which can be interpreted as a riddle; the brain-teaser to be understood and solved. Option (d) talks about theresolution of the oppositeness between ego and environmentalthough, there is no conflict between the ego and theenvironment apparent in the paragraph. One can see thatoption (d) may follow option (a) and does not follow the lastline of the paragraph.


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10. a Option (b) can be inferred from the line in Para 1 Instead, thatcountry is viewed either with ignorant disapproval or withuncritical admiration. Option (c) can be inferred from the linein Para 2 if only animals became aware of their strength, weshould have no power over them, and that men exploit animalsin much the same way as the rich exploit the proletariat. Thiscan be extended to the rich and proletariat. Option (d) can beinferred from the fact that Orwell has represented the

capitalists with Mr. Jones whose nature is self- indulgent anduncaring. But option (a) cannot be inferred as the statement isgeneralized. In the passage the statement is specific toEngland.

11. d An objective tone is seen when the author quotes whatOrwell has written. Narration is predominant throughout thepassage as the author relates what Orwell has written. Forexample, Orwell begins his book by criticizing thecapitalistsetc. The author also describes certain entities,for example Boxer, the overworked, incredibly strong, dumbhorse represents the common worker in Russia. But theauthor is not critical of anything. He is merely stating Orwellsopinion. The author does not take any particular side in thepassage. He objectively quotes, narrates or describes what

Orwell has written.

12. b C occurs first in sequence as seen in the first paragraphwhere the humans are seen to be the exploiters. B occursnext as seen in Para 1 where Old Major tells the otheranimals about his dream of animalism and the other animalsactually implement it. D occurs next as seen in the first line ofPara 2 where Napolean drives out Snowball. A occurs lastas the class that revolted (the pigs) acquires a resemblanceto humans.

13. b Secular means of or relating to the worldly or temporal.Mundane also means of, relating to, or typical of this world;secular. Preposterous means contrary to nature, reason, orcommon sense; absurd. Prudent means marked by wisdomor judiciousness. Fugacious and transient mean lasting for a

short time. Recalcitrant means obstinately defiant of authorityor restraint. Authoritative means having or proceeding fromauthority. Patent means open to public inspection.

14. c The question states that if the people are dissuaded fromusing petrol then they will use less petrol and this will earnless money for fertilizer subsidy. So if the objective of the firstis achieved then the objective of second will be jeopardized(due to lack of funds). Option (a) cannot be the answer. If thebooks are returned on time(which is the objective of sendingreminders), then there will be no need to send the reminders.So, success of first does not jeopardize the success of thesecond. Option (b) cannot be the answer as the achievementof the objective of the first will definitely lead to achievementof the objective of the second. Option (c) is the correct

answer. If people are dissuaded from using the metro service,then the funds for the expansion of metro services will be jeopardized. Hence, achievement of the objective of the firstwill lead to difficulty in achieving the objectives of the second.Option (d) cannot be the answer. The reasoning is similar tothat of option (a). If there is no litter, then there will be no needto pay overtime to the workers.

15. c Options (a) and (b) discuss the role of designs in everydaylife while the author has moved on to explain the obsession ofthe rich with the excesses of neo-classical designs. Hence,these options do not seem to be an appropriate ending for theparagraph. Option (c) is the best choice because the keywordsexcesses of neo-classical architecture and less is morerefer to the idea of grandeur associated with acceptabledesigns among the rich. This statement also reveals the motive

behind choosing excessive designs and hence is an aptchoice. Option (d) reiterates the bizarreness of populardesigns whereas the last sentence of the paragraph refersspecifically to the obsession of the rich with neo-classicaldesigns.

16. c Option (a) is incorrect because things is plural and countableand it should be preceded by many and not much. Also, thelast part of the sentence uses future continuous tensewhereas the sentence is in present tense. Option (b) containstwo errors. First, things is plural, so are should be used.Second, in the last part of the sentence must be finding isincorrect. Option (c) is the best choice because it does notcontain any error.In option (d) the adverb generally has been incorrectly placed

without a comma before the noun research.

17. d The question statement clearly mentions the word melancholy(depression of spirits). From this we can infer that the previousblank should be filled with an antonym of the word. So, blitheful,blissful and cheerful can be used. Fleetingness would fit thesecond blank as the profound melancholy can arise out of atransitory or fleeting nature of natural beauty and human glory.

18. a Option (a) is the correct answer. It can be seen that theprofessor is generalizing about all graduate students but hehas data only of his students. This is a major flaw in theargument. Option (b) makes an assumption that the argumentpertains to English language, which is incorrect. Option (c) isbeyond the scope of the argument. Option (d) is incorrect asthe argument does not pass any judgement on the capability

of the teacher.

19. b Formation means an arrangement of a body or group of peopleor things in some prescribed manner or for a particular purpose.Soldiers are arranged in a formation. Club means an associationof people for some common object usually jointly supportedand meeting periodically. A matrix consists of rows andcolumns but it is not a formation of columns; a matrix may bea formation of numbers or alphabets. Array means a numberof mathematical elements arranged in rows and columns. Aforest is a dense growth of trees, but not a formation of trees.

20. a Here, option (a) is the appropriate idiomatic expression. Inoption (c), raking over the coals which means to talk aboutunpleasant things from the past that other people would prefer

not to talk about, is out of context. In option (b), to take arunning jump which is an impolite way of telling someone togo away or that you will not give them something they want,is again unneeded and hence negated. In option (a), carryingcoals to Newcastle which means to take something to aplace or a person that has a lot of that thing already, does theneedful for the given sentence. In option (d), if you have arunning battle with someone, you have an argument thatcontinues over a long period of time. In the present context,no extended argument or conflict has been hinted at.


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21. d The passage clearly hints at a conflict or misunderstandingbetween the parents and the child. Refer to the last line,which states, I was learningbreaking. Option (a) makesan abrupt shift from this as it says our parents can easilyidentify. Options (b) and (c) are ruled out as these optionsfail to match with the tone of the last two lines of the paragraph,in which the speaker talks about his/her past experiences asa child. Refer to the lines, ... I was learning that parents

werent always right...we all go through at least a littlerebellion. Option (d) is better equipped than any other optiongiven. It reveals the speakers past experiences as a childcontrolling and steering its emotions, thoughts and energy.

22. d In the first line of the last paragraph, the author mentions that if turning away from the outer world is accepted as thedecisive case of the most conspicuous characteristics of ourdreams; this in no manner implies that turning away from theouter world leads to dreams. Option (c) cannot be inferredfrom the passage. Dissonance experienced with others canbe one of the sources of the reckless extravagances of ourjudgements, hopes and wishes in dreams and not a cause ofdreams. Even though, the passage states that lack of sensorystimuli leads to sleep we do not know what happens when a

sleeping mind is excited by sensory stimuli, thus even option(b) cannot be inferred.

23. b Statement A is given in the passage. Refer to the lines, Hestates the first distinguishing mark of dreamsperceptionsin the first paragraph. Statement B is also shown to be linkedto mistaking hallucinations for objective perceptions in dreams.Refer to the following lines in the first paragraph, Theseactivities too, ..during sleep. Statement C is mentioned in adifferent context and talks about a new idea.

24. c Option (a) is inappropriate as the author just discussesHaffners explanation. He does not show how Haffnersexplanation is different from Delboeufs. The author moves onto give more clarity and also to moderate the deductions made.Option (b) is also narrow. It does not talk about Burdach or

the author attempting to give more clarity in the latter part ofthe passage. Option (d) is also incomplete as it only talksabout moderation as the aim in moving to Burdachsobservations. Only option (c) represents without an errorhow the author develops the passage.

25. d In option (a), Old heave-hos is the act of throwing someoneout; dismissal from ones job or from ones position. An opensesame is a very successful way of achieving something. Inoption (c), old flame is a person that you loved or had aromantic relationship with in the past. Thus, for the givensentence options (a), (b) and (c) are unsuitable. The correctanswer choice is (d). Eat carrots for better eyesight is anold wives tale- an often traditional belief that is not based onfact.

26. b Let us write first 260 natural numbers. Our task is to findthose numbers that are either squares or cubes of a naturalnumber and eliminate them from the series.

There will be = 260 16 perfect squares and

3 260 = 6

perfect cubes, ([ ] is the greatest integer function.)Also, there are two numbers (1 and 64), that are both aperfect square and a perfect cube. So, altogether 16 + 62or 20 numbers will get eliminated. Hence, 260 will be 26020= 240th term of the set S.

27. b66 66 66 3 22

2 2 2

13 23 13 23 13 122 (13 ) 1 22

183 13 13 1 13 13 1 13 13 1

= = =

+ + + + + +

3 22 3 22

2 3

(131) (13 ) 122 (131) (13 ) 122

(131)(13 13 1) (13 1)

=

+ +

[(133)221 is divisible by 1331.]Therefore, the net remainder = 18322 = 161.

Alternative method:

Dividend 136623 is of the form 3k + 2 (where k is a naturalnumber) and the divisor 183 is a multiple of 3. Therefore, theremainder has to be of the form 3N + 2 (where N is a naturalnumber) and of the given options only 161 is of such a form.

28. a We obtain the sum of all the coefficients of a polynomial byequating all the variables to 1. Here by putting x = 1 in thepolynomial, the required sum comes out to be zero.

29. d It is given that, a = b3/2 and c = d5/4

As a and c are positive integers, b has to be a perfect squareand d has to be fourth power of a natural number.

Let, b = x2

and d = y4

, where x, y are positive integers.bd = x2y4 = (xy2) (x + y2) = 9. (xy2), (x + y2) = 1, 9i.e. x = 5, y = 2or ac = x3y5 = 12532 = 93.

30. a As we have only 3-digit and 4-digit numbers in the set G, aparticular category can have either 1 digit or 2 digits or 3 digitsor at the most 4 distinct digits. Number of categories of 1 digit= 9C

1= 9 (we cannot consider zero in this case).

Number of categories of 2 digits, 3 digits and 4 digits would be10C

2, 10C

3and 10C

4respectively. Therefore the required answer

is 9C1+ 10C

2+ 10C

3+ 10C

4= 384.

31. c (7a) (7b) (7c) (7d) (7e) = 28.Since, (7a), (7b), (7c), (7d), (7e) are all distinctintegers, 28 can be written as 1 2 7 (2) (1).Hence, the values that a, b, c, d and e can take, are 6, 5, 0, 9and 8 in any particular order.But for each of these cases the sum a + b + c + d + e isalways 28.

32. a Let each worker put in 1 unit of work per hour. Let, it take a, band c units of work to produce one unit of the products A, B

and C respectively.

So, 100 = 80 a + 160 b + 120 c ...(i)150 = 125 a + 140 b + 180 c ...(ii)450 = 150a + X b + 540 c ...(iii)Solving for (1.5 (i)(ii)) gives the relation, A = 20 B.Substituting, a = 20 b in (3 (ii)(iii))

We get X = 4920.

33. c The probability of getting an odd or even result on rolling a die

is the same and it is1

2.

Let O = Odd, E = even.Following are the possible cases:

I. When we have 2 even and 2 odd resultsNumber of red balls taken out = 3 + 3 + 1 + 1 = 8.Number of blue balls taken out = 1 + 1 + 2 + 2 = 6.

This satisfies our requirement and this is possible in4

2 2

= 6 cases.


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The cases are: (OOEE), (OEOE), (EEOO), (EOEO), (OEEO)and (EOOE).

II. When we have 3 even and 1 odd result, total cases

=4!

3!= 4.

III. When we have 4 even and 0 odd results, total cases

=4!

4!= 1.

Total number of cases satisfying the criteria = 6 + 4 + 1= 11.Total number of cases = 24 = 16.

11Required probability = .

16

34. b Let T1

m3 and T2

m3 be the capacities of the two tanks andP

1m3/hour and P

2m3/hour be the flow rates of the two pipes P

1

and P2.

1 2

1

T T12,

P

=

1 2

2

T T24,

P

=

1 2 1 21 2

(T T ) (T T )P P

12 24 + = +

Required answer( ) ( )

1 2 1 2

1 2 1 2 1 2

T T (T T )

P P P P (P P )

= =

+ + +

18 hours.

1 1

12 24

= =+

35. a Since, pq pr = pqr pq pr = 10 pq + r pq(10pr) + r = 0Here, there are two possibilities.I. pq(10pr) =r

3 r is single digit number and pq is a two-digit number,

this is impossible if r 0 .

II. pq(10pr) = r = 0

pq(10pr) = 0, pr = 10 (as pq 0 ).

p = 1, The required remainder is the number which we getas the remainder when q1 1001 is divided by 11.

36. b

Q

M

O

P

S3

S2

S1

Join MO.Area of the quadrilateral OPMQ is equal to the sum of the

areas of OPM and OQM .

Since, PM is a tangent, therefore OPM 90 =

So, ( ) ( )2 22 2PM OM OP or 4r 2r or 2 3 r units= .

Area of21 1OPM PM OP 2 3r 2r 2 3r

2 2 = = = square units.

Similarly, MQ is a tangent to the semicircle S1.

So, OQM 90

= .

Area of 215

OQM r2

= square units.

Hence, area of quadrilateral OPMQ=( ) 215 4 3 r

2

+square

units.

For questions 37 and 38:

Let, the number of candidates who passed in the examination be 'p'and the number of candidates who failed in the examination be f.

60p 25f43 49

p f

+ < +

<


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39. a Extend AB and DC to intersect at the point S.Let the radius of the circle be r units.

A D

O

P R

C

Q

B

S

CBS 180 120 60 and BCS 180 150 30 = = = = .

BSC 180 (60 30 ) 90 = + = .

PSR SPO POR SRO 90 and OP OR = = = = = . PSRO is a square.

BS 1sin30 BS

BC 2= = .

1BP r

2 = .

In PBO : PBO 60 = ( OPB and OQB are congruent.) 3

POtan60 3

PB= =

+ = =

r 3 33 r .

1 4r

2

40. d A

S

R

CP Y

X

B

Q

W

Lets draw WS parallel to QR and then WX parallel to SR.Also extend SR to meet BC at Y.

Statement I:

2 < AB 2 + PQ 2 < 6 and lengths of sides AB and PQ (in cms)are integers.

AB = 1 or 2But if AB = 1 cm then PQ is definitely less than 1 and AB2 +PQ2 < 2 which goes against the statement.So, AB = 2 cm.Subsequently PQ can only be 1 cm.As no relation between PQ , QR and SR is provided, we cansay that there are many cases that may satisfy the abovecondition. And hence many distinct locations of point R arepossible.So, statement I alone is insufficient.

Statement II:

PQ = 1So, in triangle QBP

PQ 2QB = =

sin60 3

Also WX = SR = PQ = 1So, in triangle WQX

WX 2WQ = =

sin 60 3

andWX 1

QX = =tan60 3

.

Also,( )3 1

WS XR QR QX AW3

= = = = (as WS is

parallel to QR and hence BC, AWS must also be anequilateral triangle).So, AB = BQ + QW + WA

( )3 12 23 1

3 3 3

= + + = +

( ) ( ) ( )( )2 22 2CR CY RY BC BY PQ= + = +

( ) ( )( ) ( ) ( )( )2 2 2 2AB BY PQ AB PY BP PQ= + = +

( ) ( )( )2 2AB QR BP PQ= +

= + + =

221 73 1 1 1 .

3 3

So, Statement II alone is sufficient.

41. d From Statement A:

Let a and a + 1 be the real and distinct roots of the givenequation.

Sum of the roots = a + a + 1 = P;Product of the roots = (a) x (a + 1) = QOnly possible value Q can take such that the roots of theequation are consecutive positive integers is 2 (otherwise Qwill become greater than or equal to 6), where the roots of theequation are 1 and 2.Hence, P = 3 and Q =2.Therefore, (2P + 3Q) = 12.Statement A alone is sufficient to answer the question.

From Statement B:Let b and b + 1 be the real and distinct roots of the givenequation.Sum of the roots = b + b + 1 = 2b + 1 = PProduct of the roots = b (b + 1) = QOnly possible value Q can take such that the roots of theequation are consecutive non-zero integers is 2 (otherwiseQ will become greater than or equal to 6); where the rootsof the equation can be (1,2) or (1, 2).If the roots of the equation are (1,2) thenP =3 and Q = 2 and 2P + 3Q = 6 + 6 = 0.If the roots of the equation are (1, 2) thenP = 3 and Q = 2 and 2P + 3Q = 6 + 6 = 12.Hence statement B alone is not sufficient to answer thequestion.


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42. c The remainder when a five-digit number PQRSR is divided by125 is same as when a three-digit number RSR is divided by125.So, if we can find unique values of R and S, we can find theanswer to the question.

From Statement A:

A = 25K + 13 (K is a natural number.)

PQSR = 4A = 4 (25K + 13) = 100K + 52.

S = 5 and R = 2.Hence statement A alone is sufficient to answer the question.

From Statement B:

QR leaves a remainder greater than 3, when divided by 10.So, R has to be greater than 3.Also, given that RS = SR, so the values of R and S have to be4 and 2 respectively.Hence, the remainder can be found.Hence, statement B alone is also sufficient to answer thequestion.

43. b From Statement A:

Let the savings of S and A be s and a respectively.

So, S must have given1

s3

to A and1 2

s3 3

to G.

1 2 1s s s a s

3 9 3

+ = +

sa

9 =

Nothing can be said about the savings of S. So, this statementalone is not sufficient to answer the question.

From Statement B:Let the savings of S and G be s and g respectively.

So, S must have given1

s4

to G and1 3

s4 4

to A.

1 3s s s 17000 g

4 16

+ = +

9s g 17000

16 =

Nothing can be said about the savings of S. Hence, thisstatement alone is also not sufficient to answer the question.

Combining both the statements together:

Since, it is known that the ratio of savings of A and G is 1 : 2.Hence, a : g :: 1 : 2 or g = 2a ...(i)

From Statement (B), we get =9

s g 1700016

...(ii)

9s 2a 17000

16 =

From statement A, we gets

a9

=

9 2s s 17000

16 9 =

17000 144s

49

=

1 17000 16a s

9 49

= =

Hence, the question can be answered by using both thestatements together.

44. b P

RQ

M

NO

L

Triangles QOL and POM are similar. Since, POM = QOL and

OLQ = OMP.

Therefore, we get:QO OL

PO OM=

QO OM = PO OL QO + (QMQO) = PO (PLPO) 6 (QM6) = 9 (109)

QM = 7.5 units.

45. c 8 64 5122log x + 4log y + 6log z 23

2 2 28 8 8log x + log y + log z 2

( )2

8log xyz 2

(xyz)2 64

(xyz) 8 ( (xyz) is positive.)3 (xyz)3 512

( ) ( ) ( )2 2 2x y y z z x 8.8.8.

Applying AM GM, we get that

( )+ +

12 2 2

2 2 2 3x y y z z x

x y y z z x3

2 2 2x y y z x z 24 + + Minimum possible value of (x2 y + y2 z + z2 x) = 24.

46. a The total worth (in Rs. crores) of Property, Jewellery andShares are

( ) ( ) ( ) = =

4 2 125 = 10 , 25 5 and 25 2.5

10 10 10

Me m bers Total w orth of ass et (Excluding cash)

A Rs.2.625 croresB Rs.4.3 crores

C Rs.1.8 crores

D Rs.2.95 crores

E Rs.1.95 crores

F Rs.3.875 crores

Of course, the required worth was the second highest forF.


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47. b Let the total worth (in Rs. crores) of Property and Shares beP and S respectively.Given that, 15% of P = 25% of S

=S

0.6P

Let M denote the ratio of the total worth (in Rs. crores) ofShares and Property held by each member of the family.

The value of M for B, C, D, E and F are

12 10 20 18 150.6 , 0.6 , 0.6 , 0.6 and 0.6

35 8 12 5 25

respectively.Therefore, the value of M is less than 1 for the members B, Cand F.

For questions 48 and 49:The total increase in the worth of all the forms of assets held by themembers of the family = Rs. 20 lakhs.The decrease in the worth (in Rs. crores) of the Property and theincrease in the worth (in Rs. crores) of the Shares held by B in theyear 2009 as compared to the year 2008 are 0.1 0.35P and0.08 0.12S respectively.

So, we can say that 0.08 0.12S > 0.1 0.35P.

( ) > > =S 175

96S 350P 3.65 .P 48

48. a In 2008, the worth ( in Rs. crores) of the Shares is greaterthan that of the Property for all the members of the family.

49. c Since, it is given that0.08 0.12S0.1 0.35P = 0.2 (in Rs. crores)

48S175P = 1000

= + = +1000 175P

S 20.83 3.65P48 48

Only possible value P can take = Rs.1 crore(as otherwise the value of S will go beyond Rs. 25 crores).

S = 20.83 + 3.65 = 24.48 crores.But in this case S + P = 24.48 + 1 = 25.48But 25.48 is greater than 25 and this is impossible (as the totalworth of assets in 2008 was 25 crores).Hence, P cannot be a multiple of a crore.

For questions 50 to 53:

The maximum possible sum of ratings received by a character(considering only statement 1) could be when he/she would havereceived ratings 3, 4, 5 and 6 from the four judges.Hence, the maximum possible sum = 3 + 4 + 5 + 6 = 18.The minimum possible sum could have been, ( considering onlystatement 1) when a character would have received ratings 1, 2, 3and 4 from the four judges.Hence, the minimum possible sum = 1 + 2 + 3 + 4 = 10

Hence, maximum possible difference between the sum of ratings thatcan be received by any two characters =18 10 = 8.

From statements 2 and 3:

The sum of ratings received by Chandler, Monica and Rachel must be10, 14 and 18(not necessarily in that order) as no other values cansatisfy the above conclusion.Since, the four ratings for each of Chandler, Monica and Rachel werein A.P., sum of 14 can be obtained by 2 + 3 + 4 + 5.But, Chandler received rating 6 from J1 and Monica received rating 1from J1.So, the sum of ratings for Chandler must be 18 (as only 18 can havea 6 in it) and, the sum of ratings for Monica must be 10 (as only 10 canhave a 1 in it).

Hence, the sum of ratings for Rachel was 14.It is to be noted that, these three have ratings 4 and 3 in common.

From Statement 5:The ratings received by Chandler from J2, Monica from J4 and Rachelfrom J3 must be equal to 3 as rating received by Chandler from J4 isequal to 4.Also, Statement 6 means that the ratings received by Monica from J3

and J2 must be equal to 4 and 2 respectively.From all the above conclusions, the rating received by Chandler, Racheland Monica from all the four judges can be concluded as below.The other possible unknown values are also represented below:

J1 J2 J3 J4

Chandler 6 3 5 4

Joey 3 1 or 4 or 6 1 or 2 or 6 5

Monica 1 2 4 3

Pheobe 2 1 or 4 or 6 1 or 6 1 or 6

Rachael 4 5 3 2

Ross 5 1 or 4 or 6 1 or 2 or 6 1 or 6

From Statement 4:Let, the sum of four ratings received by Joey, Phoebe and Ross be(x1), x and (x + 1) (not necessarily in that order).So, (x1 + x + x + 1) = 3x.= (Total sum of ratings) (Sum of the ratings received by Rachel,Chandler and Monica) = 4(1 + 2 + 3 + 4 + 5 + 6)(10 + 14 + 18) = 42.So, x = 14 and the ratings = 13, 14 and 15.It can be seen that Ross could not have received rating 4 from J2 as,his/her sum of ratings could never be 13, 14 or 15.

This is explained below:If Ross would have received rating 4 from J2, then possible pair ofratings from J3 and J4: (1,6) or (2,6) or (2,1) or (6,1). So, sum wouldhave been 16, 17, 12 or 16.So, Ross received either rating 1 or 6 from J2 and J4 in any order.Hence, he received the rating 2 from J3.

Ross sum of ratings = 5 + 2 + 1 + 6 = 14.Phoebe received 4 as rating from J2 as she received ratings 1 and 6from J3 and J4 (not necessarily in that order).Phoebes sum of ratings = 2 + 4 + 1 + 6 = 13.So, Joeys sum of Ratings = 15.It can be concluded that Joey received rating 1 and 6 from J2 and J3(not necessarily in that order).The final representation can be as follows:

J1 J2 J3 J4

Chandler 6 3 5 4

Joey 3 1,6 6,1 5

Monica 1 2 4 3

Phoebe 2 4 1,6 6,1

Rachel 4 5 3 2

Ross 5 6,1 2 1,6

50. d Chandler received 18.

51. c Ross got 5 + 2 + 6 + 1 = 14.

52. b

53. d Joey received either of the two ratings 1 or 6 from J2.


9/9


For questions 54 to 56:

Against Australia, Yuvraj played 18 ODIs and Gambhir played 11 Tests.So, India played at least 18 + 11 = 29 matches against Australia.Similarly we can say that India played at least 24 + 12 = 36 matchesagainst South Africa, at least 14 + 18 = 32 matches against England, atleast 12 + 11 = 23 matches against Pakistan and at least 19 + 32 = 51matches against the West Indies.Let the total number of matches played by Indian cricket team in 2008

be x.

India playedx

4matches with Australia,

x

5matches with South

Africa,3x

20matches with England,

x

10matches with Pakistan and

3x

10matches with the West Indies.

x should be a multiple of 4, 5, 10 and 20. x should be a multiple of 20.As India played at least 29 matches against Australia (against whomit played 25% of all its matches in 2008)

x

29 or, x 116.4

Similarly x

36 o r, x 180,5

3x

32 or, x 213.33,20

x23 or, x 230 and

10

3x51 or, x 170.

10

But x has to be an integral multiple of 20 and hence the least possiblevalue of x is 240.

54. b

55. d India played at least =3

240 7210

matches against the West

Indies in 2008, out of which Yuvraj played 32 + 19 = 51

matches.

Yuvraj definitely did not play in at least 7251 = 21 matchesagainst the West Indies in 2008.

56. c Since Raina played all the ODIs against England in 2008,therefore India played a total of 14 ODIs against England in

2008. As we know that India played at least =3

240 3620

matches against England that year, it must have played atleast 3614 = 22 Test matches against England.

For questions 57 to 60:From additional information (I), we can conclude that Johnny ate icecream having flavour L on Sunday, Wednesday and Saturday.From additional information (II) and (IV), we can conclude that he ateice creams having flavours L, S and BC on Sunday, Wednesdayand Saturday.

The table looks like:

Days

Sunday L BC S

Monday

Tuesday

Wednesday L BC S

Thursday

Friday

Saturday L BC S

Flavours

From statement V:

It is obvious that, BS was eaten on Monday, Tuesday and Thursday.Flavour O was eaten on Friday.

Johnny could not eat ice creams of flavours L, BC, S and BS on Fridayas they were all exhausted on the other days.

Therefore, on Friday Johnny ate ice creams of flavours O, M and C.

Following are the cases possible:

Case I:Flavours O and M on Tuesday and Friday.

Days

Sunday L BC S

Monday C BS M/O

Tuesday O M BS

Wednesday L BC S

Thursday C BS O/M

Friday O M C

Saturday L BC S

Flavours

Case II:

Flavours O and M on Monday and Friday.

Days

Sunday L BC S

Monday O M BS

Tuesday C BS M/O

Wednesday L BC S

Thursday C BS O/M

Friday O M C

Saturday L BC S

Flavours

57. d

58. b

59. a As we can observe in cases I and II, we can uniquelydetermine the flavours for Sunday, Wednesday, Friday andSaturday.

60. c Given that he did not eat ice cream having flavour O onMonday. So, the only possibility is given below.

Days

Sunday L BC S

Monday C BS MTuesday O M BS

Wednesday L BC S

Thursday C BS O

Friday O M C

Saturday L BC S

Flavours

unproctored mock cat 1 - solutions

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