LR - Logical Connectives - Previous Year CAT/MBA Questions
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Based on the statement given below, identify which of the assumption/sis/are implicit:
Vikas says to Harry, "Refer to the Cambridge dictionary instead of Oxford dictionary to be good at English."
Assumption:
I. Harry wants to be good at English.
II. Vikas is a good advisor
- (a)
Only assumption I is implicit
- (b)
Only assumption II is implicit
- (c)
Both assumption I and II are implicit
- (d)
Neither assumption I nor II is implicit
Answer: Option A
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Text Explanation :
Only assumption I is implicit. We cannot comment on assumption II.
Answer is option A.
Workspace:
Answer the following question based on the information given below.
Richie invites three of his friends Sunny, Pinky, and Nancy for his birthday party organized at his home. As the party goes on till late in the night, Sunny, Pinky, and Nancy choose to stay at Richie's house. Being good friends they usually stay back at each other's house. Each of them including Richie stay either in the room painted blue or in the painted purple. They have adequate number of rooms of both colours. The preferences which need to be fulfilled are:
- If sunny stays in the room painted purple, then Pinky and Richie stay in the same room as Nancy.
- If Pinky stays in the room painted purple, then Sunny stays in the room in which Nancy and Richie don't stay.
- If Nancy stays in the room painted blue, then Sunny and Richie stay in the room which Pinky has chosen.
- If Richie stays in the room painted Blue then Sunny and Pinky do not stay in the same room as Nancy.
Under all possible combinations which of the two friends will always have their room colours unchanged.
- (a)
Richie & Sunny
- (b)
Pinky & Richie
- (c)
Nancy & Sunny
- (d)
Nancy & Pinky
Answer: Option C
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Text Explanation :
The following table can be made using the given 4 conditions :
Case 2a, 3a and 4a violates condition I, so these 3 cases are invalid.
Case 1a, 1b violates condition iii, so these cases are invalid.
Case 3b violates condition iv, so this case is invalid.
Finally we have the following two cases:
Nancy & Sunny.
Hence, option (c).
Workspace:
If Richie chose to stay in the room painted blue, then in which room does Pinky stay?
- (a)
Purple
- (b)
Blue
- (c)
Data Inadequate
- (d)
None of the above
Answer: Option A
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Text Explanation :
The following table can be made using the given 4 conditions :
Case 2a, 3a and 4a violates condition I, so these 3 cases are invalid.
Case 1a, 1b violates condition iii, so these cases are invalid.
Case 3b violates condition iv, so this case is invalid.
Finally we have the following two cases:
Purple
Hence, option (a).
Workspace:
If Pinky does not like to stay in the blue painted room, then where will Sunny stay?
- (a)
Blue
- (b)
Purple
- (c)
Data Inadequate
- (d)
None of the above
Answer: Option A
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Text Explanation :
The following table can be made using the given 4 conditions :
Case 2a, 3a and 4a violates condition I, so these 3 cases are invalid.
Case 1a, 1b violates condition iii, so these cases are invalid.
Case 3b violates condition iv, so this case is invalid.
Finally we have the following two cases:
Blue
Hence, option (a).
Workspace:
Based on the given statement, choose the right conclusion:‘If the breakfast doesn’t have eggs, I will not go for a walk and will not have lunch.’
- (a)
If I went for a walk and didn’t have lunch, the breakfast didn’t have eggs.
- (b)
If I went for a walk or I had lunch, the breakfast had eggs.
- (c)
If I went for a walk or I had no lunch, the breakfast had eggs.
- (d)
If I didn’t go for a walk and had lunch, the breakfast had eggs.
Answer: Option B
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Text Explanation :
Let,
A = The breakfast doesn't have eggs
B = I will not go for a walk and will not have lunch.
From the logical deductions,
AB = ~B~A
Also, and is replaced by or and vice versa.
So,
~A = The breakfast has eggs.
~B = I will go for a walk or will have lunch.
So, we get,
~B~A = I will go for a walk or will have lunch, the breakfast has eggs.
Hence, option (b).
Workspace:
Find the statement which is necessarily true according to the given information:
The Asatra Vriksh is an evergreen tree that grows in the Nilgiris. The Asatra Vriksh has a fleshy, poisonous fruit. Recently, Purol, a substance found in the bark of the Asatra Vriksh, was discovered to be a promising new antidepressant drug.
- (a)
Purol is poisonous when taken by healthy people.
- (b)
Purol has cured people from various diseases.
- (c)
People should not eat the fruit of Asatra Vriksh.
- (d)
No treatment for depression was known till Purol was discovered.
Answer: Option C
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Text Explanation :
Option 1 is incorrect as the passage clearly mentions that the fruit of the tree is poisonous not Purol.
According to the passage, Purol only has anti-depressant properties. This eliminates option 2.
According to the passage, Purol is a “promising new drug”. This indicates that drugs treating depression existed prior to the discovery of Purol. This eliminates option 4.
Option 3 is necessarily true as according to the passage, “The Asatra Vriksha has a fleshy, poisonous fruit”.
Hence, the correct answer is option 3.
Workspace:
A research study recorded that the number of unemployed educated youth was equal to the number of unemployed uneducated youth. It was concluded by the researchers that being educated does not enhance the probability of being employed.
Which of the following information would be required to validate the above conclusion?
- (a)
The number unemployed educated and uneducated people in other age groups.
- (b)
The number of organisations employing youth.
- (c)
The percentage of unemployment in educated youth versus percentage of unemployment in uneducated youth.
- (d)
The percentage increase in number of educated youth versus last year.
Answer: Option C
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Text Explanation :
The passage is a comparison between the raw data resulting from a study. There were as many unemployed educated youth as unemployed uneducated youth. The conclusion being that education provided no guarantee in securing employment.
Option 1 is incorrect because these numbers are not really comparable as this data would not be able to either support or disqualify the findings of the study as option 1 does not pertain to youths.
Option 2 is incorrect as just this information would not suffice to prove the study findings.
Option 4 is incorrect because it only considers the increased number of educated youth. This is not complete information to support the study findings.
Option 3 is correct because the percentage figures would provide comparative data to validate the conclusion mentioned in the passage.
Hence, the correct answer is option 3.
Workspace:
Read the following instructions and answer the questions.
After the discussion at a high level meeting of government officers, the criteria for issuing of import / export licence to eligible business firms for the year 2011-12 were finalized as follows. The firms must –
- Have a Grade – ‘A’ certified unit for any products.
- Not have any legal dispute case against it.
- Possess minimum asset worth Rs. 40 lakhs.
- Submit an environment clearance certificate issued by the Pollution Control Board (PCB) of the state where the firm is located.
- Deposit the margin money of Rs. 1 lakh.
- Arrange for three guarantors with their personal identity cards (IDs).
However, if the firm satisfies all the above mentioned criteria except:
a. Criteria (I), but is a traditional handloom production unit, then the case may be referred to Development Commissioner, Handloom (DCH) of the state.
b. Criteria (IV), but is a local employment provider / thread (input) supplier / cloth supplier, the case may be referred to the Director, Department of Industry of the state.
c. Criteria (V) but can deposit at least Rs. 50000, the firm will be given import licence only and the case may be referred to the Deputy Director, Department of Industry of the state.
Based on the above criteria and information provided on each of the firms in the questions below, you have to decide which course of action should be taken against each firm. Without assuming anything regarding any applicant firm, the decision should be based on the information provided.
Mahalaxmi Weaving Center is a traditional handloom production unit. It has property worth more than Rs. 1 crore. It managed to get three guarantors with their personal IDs. No legal case is there against it. There is no problem submitting an environmental clearance, as the same is already issued to it by the State Pollution Control Board. It is also ready to deposit Rs. 1 lakh.
- (a)
Licence can be issued
- (b)
Licence not to be issued
- (c)
May be referred to the Development Commissioner, Handloom
- (d)
May be referred to the Director of Industry
Answer: Option C
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Text Explanation :
Mahalaxmi Weaving Centre has property worth Rs. 1 crore and is ready to submit Rs. 1 lakh. It also has managed to get three guarantors with personal IDs. Finally, it has no legal case against it and as obtained the environmental clearance issued by the State Pollution Control Board. Therefore, it satisfies conditions II, III, IV, V and VI.
Though nothing is mentioned about condition I, it is given that it is a traditional handloom production unit. Because there is no option marked “Data Insufficient”, sub-condition (a) becomes valid and the case may be referred to the Development Commissioner, Handloom.
Hence, option (c).
Workspace:
Ramayan Enterprise is a textiles firm which possesses assets worth Rs. 50 lakhs and is located in Surat where no firm having any legal dispute is permitted to operate. The firm agreed to deposit Rs. 1 lakh and give details of three guarantors with their personal details as required. It has got grade – A certificate and can submit an environment clearance certificate issued by the Pollution Control Board of the state.
- (a)
Licence can be issued
- (b)
Licence not to be issued
- (c)
May be referred to the Development Commissioner, Handloom
- (d)
May be referred to Deputy Director of Industry
Answer: Option A
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Text Explanation :
Ramayan Enterprise satisfies all the given conditions as explicitly mentioned in the question. Condition II gets satisfied because it is given that the firm is located in Surat, where no firm having a legal dispute is permitted to operate. Therefore, it can be inferred that Ramayan Enterprise does not have legal dispute against it. Since it satisfies all 6 conditions, the license can be issued to it.
Hence, option (a).
Workspace:
Hirabhai Handlooms is a Vadodara based traditional Gujarati handloom firm keen to get an export licence. It is ready to pay the required security amount and possesses assets of Rs. 55 lakhs. Hirabhai Chamanlal is the owner of the firm as well as the President of State Handloom Association. Hence getting more than three guarantors with their IDs is not a problem. The firm possesses the environmental clearance certificate from the State Pollution Control Board after it was made mandatory for all handloom firms in the state.
- (a)
Licence can be issued
- (b)
Licence not to be issued
- (c)
May be referred to the Development Commissioner, Handloom
- (d)
May be referred to the Director of Industry
Answer: Option B
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Text Explanation :
Hirabhai Handlooms possesses assets of Rs. 55 lakhs and is ready to pay the security deposit. It has the environmental clearance and can get three guarantors with personal IDs. Therefore, it satisfies conditions III, IV, V and VI. There is no data for conditions I and II. As far as condition I is concerned, sub-condition (a) gets satisfies because it is given that it is a traditional handloom firm. However, condition II has no sub-condition associated with it and there is no data given. Finally, there is no option marked “Data Insufficient”. In such a case, the only option action that can be taken is that the license cannot be issued.
Hence, option (b).
Workspace:
A Retail chain has seven branches in a city namely R1, R2, R3, R4, R5, R6, R7 and a central distribution center (DC). The nearest branch to the DC is R6 which is in the south of DC and is 9 Km away from DC. R2 is 17 Km away from DC in the west. The branch R1 is 11 Km away R2 further in the west. The branch R3 is 11 Km in the north east of R1. R4 is 13 Km from R3 in the east. R5 is 11 Km in the north east of the distribution center. In the north east of R6 is R7 and distance between them is 15 Km. The distance between R1 and R6, R2 and R6, R6 and R5 is 23 Km, 19 Km, 13 Km respectively. R3 is 14 Km away from the DC in the north west direction, while R2 is also 14 Km away from R4 in the north east direction of R2. A truck carrying some goods starts from the distribution center and has to cover at least four stores in a single trip. There is an essential good that has to be delivered in the store R7, but the delivery at R7 has to be done in the end, so what is the shortest distance the truck would travel?
- (a)
55
- (b)
56
- (c)
63
- (d)
66
Answer: Option C
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Text Explanation :
According to the given conditions, the relative position of each city is as shown in the figure below:
The shortest route for the truck would be DC - R3 - R1 - R6 - R7.
Thus, the total distance travelled would be 14 + 11 + 23 + 15 = 63 km
Hence, option (c).
Workspace:
ABCDE play a game of cards. ‘A’ tells ‘B’ that if ‘B’ gives him five cards ‘A’ will have as many cards as ‘E’ has. However if A gives five cards to ‘B’ then ‘B’ will have as many cards as ‘D’. A and B together has 20 cards more than what D and E have together. B has four cards more than what C has and total number of cards are 201. How many cards B have?
- (a)
185
- (b)
37
- (c)
175
- (d)
27
Answer: Option A
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Text Explanation :
Data given in the question is not correct.
Let a, b, c, d and e be the number of cards with A, B, C, D and E.
If B gives A five cards, A will have as many cards as E.
∴ e = a + 5 …(i)
If A gives B five cards, B will have as many cards as D.
∴ d = b + 5 …(ii)
A and B together have 20 cards more than what D and E have together.
∴ a + b = e + d + 20 …(iii)
It is also given that B has four cards more than what C has and the total number of cards are 201.
∴ b = c + 4 and …(iv)
a + b + c + d + e = 201 …(v)
Adding (i) and (ii) we get e + d = a + b + 10 which contradicts equation (iii)
∴ The data given in the question is not correct.
Workspace:
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