Logical Reasoning - Online Test

CAT Entrance Exams Data Interpretation and Logical Reasoning Logical Reasoning TEST : 10

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Q1.

Count the number of parallelogram in the given figure.

A. 8

B. 11

C. 12

D. 15

Answer : Option D
Explaination / Solution:

The figure may be labelled as shown.

The simplest parallelograms are LMHJ and BDFM i.e. 2 in number. The parallelograms composed of two components each are ABML and MFGH i.e. 2 in number.

The parallelograms composed of three components each are LBHI, LBEF, BDGH, DFLA, BCFH, KLFH, A6HJ and LFGJ i.e. 8 in number.

The parallelograms composed of six components each are LCFI, KBEH and ADGJ i.e. 3 in number.

Total number of parallelograms in the figure = 2 + 2 + 8 + 3 = 15.

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Q2.

Directions:Questions in the form of inference/conclusions are based on the passages given below. Each passage is followed by five inferences. You are required to examine each inference separately in the context of the passage and decide upon its degree of truth or falsity.

Passage:

Many intellectuals didn’t appreciate the sheer profusion of unsolicited American gifts. Simone de Beauvoir complained about the use in hotels of noisy vacuum cleaners, preferring the humble French broom, and Sartre found his beloved existentialism upstaged by the real choices available to rootless and mobile Americans. However, anti-Americanism proved to be a losing game because so much of American influence was inseparable from the wider world project of modernization.

In a downbeat coda, Conrad concludes that our world has become “so Americanized that we no longer need to venerate the United States”. I am not sure that I wholly agree. To be sure, the past decades have provided many grounds for rejecting the vision of the future supplied by the US, and these days the American constitution looks less admirable than it did when Luce heralded the new century. No shortage of those prepared to say that America’s global sway is at an end can be discerned.

Over the past few years, events and circumstances have reflected negatively upon the image of the United States. Give answer –

A. in the inference is probably true though not definitely true in the light of the facts given.

B. if the data are inadequate i.e., from the facts given you cannot say whether the inference is likely to be true or false

C. if the inference is probably false though not definitely false in the light of the facts given.

D. if the inference is definitely true, i.e., it properly follows from the statement of facts given.

E. if the inference is definitely false i.e., it cannot possibly be drawn from the facts given or it contradicts the given facts.

Answer : Option D
Explaination / Solution:
No Explaination.

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Q3.

Count the number of convex pentagons in the adjoining figure.

A. 16

B. 12

C. 8

D. 4

Answer : Option B
Explaination / Solution:

A convex pentagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.

The figure may be labelled as shown.

The pentagons in the figure, are ABDFH, CDFHB, EFHBD, GHBDF, ACDFG, CEFHA, EGHBC, GABDE, BDEGH, DFGAB, FHACD and HBCEF. Clearly, these are 12 in number.

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Q4.

Passage:

Due to the tarnished image of the USA, there has been a rise in the number of people criticizing the United States. Give answer –

A. if the inference is definitely true, i.e., it properly follows from the statement of facts given.

B. in the inference is probably true though not definitely true in the light of the facts given.

C. if the data are inadequate i.e., from the facts given you cannot say whether the inference is likely to be true or false.

D. if the inference is probably false though not definitely false in the light of the facts given.

E. if the inference is definitely false i.e., it cannot possibly be drawn from the facts given or it contradicts the given facts.

Answer : Option B
Explaination / Solution:
No Explaination.

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Q5.

Count the number of rectangles in the given figure.

A. 20

B. 18

C. 16

D. 15

Answer : Option A
Explaination / Solution:

The figure may be labelled as shown.

The rectangles composed of two components each are HIJE, EKJ,F, FMNG, GPQH, AEOH, EBFO, OFCG and HOGD i.e. 8 in number.

The rectangles composed of four components each are ABFH, BCGE, CDHF, DAEG and EFGH i.e. 5 in number.

The rectangles composed of six components each are IJFG, KLGH, MNHE and PQEF i.e. 4 in number.

The rectangles composed of eight components each are IJMN, KLPQ and ABCD i.e. 3 in number.

Thus, there are 8 + 5 + 4 + 3 = 20 rectangles in the given figure.

(Here note that the squares are also counted amongst rectangles)

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Q6.

Passage:

"Opening a retail business in Kosovo is not inadvisable, despite what critics of the plan may say. Eighteen years ago we opened a construction business in Beirut during an invasion, and that location has been generating profits ever since."

These questions are based on the information given above and the sentences labelled A., B., C., D., E. as given below.

A. The proposed retail store can make money despite being in the middle of a war zone.

B. Wars are profitable for retail.

C. Kosovo is not as politically unstable as Beirut.

D. Opponents of a new construction company in Kosovo are probably biased.

E. The proposed company in Kosovo will do better than the construction company in Beirut.

Which of the above is the author trying to imply?

A. All of the above

B. Only A

C. Only C

D. Both D and E

E. Only B

Answer : Option B
Explaination / Solution:

The author is using his prior experience to make a generalization. If he thought wars were profitable, he would be more encouraging of the venture instead of "not inadvisable." B. is a matter of degree; he is implying that war is not bad for business, but he is not arguing that war is good for business. B., that is statement A, is the correct answer.

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Q7.

Count the number of triangles and squares in the given figure.

A. 28 triangles, 10 squares

B. 28 triangles, 8 squares

C. 32 triangles, 10 squares

D. 32 triangles, 8 squares

Answer : Option C
Explaination / Solution:

The figure may be labelled as shown.

Triangles :

The simplest triangles are IJQ, JKQ, KLQ, LMQ, MNQ, NOQ, OPQ and PIQ i.e. 8 in number. The triangles composed of two components each are ABQ, BCQ, CDQ, DEQ, EFQ, FGQ, GHQ, HAQ, IKQ, KMQ, MOQ and OIQ i.e. 12 in number.

The triangles composed of four components each are ACQ, CEQ, EGQ, GAQ, IKM, KMO, MOI and OIK i.e. 8 in number.

The triangles composed of eight components each are ACE, CEG, EGA and GAC i.e. 4 in number.

Total number of triangles in the figure = 8 + 12 + 8 + 4 = 32.

Squares :

The squares composed of two components each are IJQP, JKLQ, QLMN and PQNO i.e. 4 in number.

The squares composed of four components each are ABQH, BCDQ, QDEF and HQFG i.e. 4 in number.

There is only one square i.e. IKMO composed of eight components.

There is only one square i.e. ACEG composed of sixteen components.

Thus, there are 4 + 4 + 1 + 1= 10 squares in the given figure.

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Q8.

Passage:

These questions are based on the information given above and the sentences labelled A., B., C., D., E. as given below.

A. The proposed retail store can make money despite being in the middle of a war zone.

B. Wars are profitable for retail.

C. Kosovo is not as politically unstable as Beirut.

D. Opponents of a new construction company in Kosovo are probably biased.

E. The proposed company in Kosovo will do better than the construction company in Beirut.

Which of the above, if true, most strengthens the argument?

A. Only E

B. Only C

C. Only B

D. Both B and E

E. All of the above

Answer : Option D
Explaination / Solution:

Both B and E statements, when used in relation to the given information, make strong points for the construction of the said business.

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Q9.

Determine the number of rectangles and hexagons in the given figure.

A. 30, 5

B. 32, 3

C. 28, 5

D. 30, 3

Answer : Option A
Explaination / Solution:

The figure may be labelled as shown.

Rectangles:

The simplest rectangles are CVSR, VETS, RSWM and STKW i.e. 4 in number.

The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e. 4 in number.

The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e. 4 in number.

The rectangles composed of four components each are CEKM, AVSP,PSWO, VGHS and SHIW i.e. 5 in number.

The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e. 4 in number.

The rectangles composed of six components each are ACMO and EGIK i.e. 2 in number.

The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e. 4 in number.

The rectangles composed of ten components each are AEKO and CGIM i.e. 2 in number.

AGIO is the only rectangle having sixteen components.

Total number of rectangles in the given figure

= 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30.

Hexagons:

The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP.

So, there are 5 hexagons in the given figure.

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Q10.

Directions: Study the following information carefully and answer the questions given below:

There are 9 managers namely-A, B, C, D, E, F, G, H and I come to play UEFA Champions League, Staying in a hotel on a different floors of the building. Each of them owns a different football club team among Barcelona, Arsenal, Dortmund, Napoli, Monaco, Real Madrid, Bayern, Sevilla and Manchester City but not in order. The ground floor is numbered 1, the floor above it is numbered 2 and so on until the topmost floor is numbered 9.

a) There is just one floor between the floors on which E and the floor on which G stay. A’s floor is not below E’s floor.

b) D stay on a floor immediately above B’s floor. The one who owns Real Madrid stays on the topmost floor. E does not stay on first floor.

c) H owns Manchester City and there are three floors between the floor on which H stay and the floor on which G stay.

d) C stays on the 2nd floor and owns Monaco. F does not own Barcelona team.

e) The one who owns Dortmund stays on the 3rd floor. The floor on which D lives is immediately adjacent to the floor on which, the person having Bayern team lives.

f) I stays on an even numbered floor and owns Napoli. The one who owns Sevilla stays on 4th floor.

g) The person having Barcelona does not live on the floor, which is immediately above the floor of the person, who is having Napoli. If A has Barcelona then E can never have Arsenal.

h) E’s floor is above G’s floor. B does not own Bayern Team.

Who owns Napoli Team?

A. I

B. C

C. D

D. F

E. B

Answer : Option A
Explaination / Solution:

From (a), (c), (g), (h) we get that H cannot be on 9th or 3rd floor as he owns Manchester City. H and G can also not be on 8th and 4th floors respectively as E will not be able to live anywhere. As E doesn’t live on 1st floor, H and G cannot be on 7th and 3rd floors respectively. Thus, H, G and E can live on (1,5,7), (7,5,3), (8,4,6), (5,1,3) respectively. D lives immediately above B and B doesn’t own Bayern. The one having Bayern lives on adjacent floor to D’s floor. Thus, D can never be on top floor. When H, G and E can live on (7,5,3) or (8,4,6) floors respectively then D and B won’t be able to live anywhere. When H, G and E can live on (5,1,3) respectively then D and B can only be on (7,6) floors respectively. Now, I who owns Napoli and lives on even numbered floor cannot live anywhere. Thus, H, G and E can only live on (1,5,7) floors respectively. From (f), I can stay on 6th or 8th floors. Therefore, we have two cases-

Case1: I lives on 8th floor. from (b) D, B can only live on (4,3) floors. From (e), the person on 5th floor has to have Bayern. As A’s floor is not below E’s floor, A lives on 9th floor and F lives on 6th floor. As F does not have Barcelona, E has Barcelona and F has Arsenal. So this case is valid and final.

Final Table will be like this-

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CAT Entrance Exams Data Interpretation and Logical Reasoning Logical Reasoning TEST : 10