Comprehension
The table below presents the revenue (in million rupees) of four firms in three states. These firms, Honest Ltd., Aggressive Ltd., Truthful Ltd. and Profitable Ltd. are disguised in the table as A,B,C and D, in no particular order.
| States | Firm A | Firm B | Firm C | Firm D |
|---|---|---|---|---|
| U.P | 49 | 82 | 80 | 55 |
| Bihar | 69 | 72 | 70 | 65 |
| M.P | 72 | 63 | 72 | 65 |
Further, it is known that:
- In the state of MP, Truthful Ltd. has the highest market share.
- Aggressive Ltd.’s aggregate revenue differs from Honest Ltd.’s by Rs. 5 million.
Question: 1
What can be said regarding the following two statements?
Statement 1: Profitable Ltd. has the lowest share in MP market.
Statement 2: Honest Ltd.'s total revenue is more than Profitable Ltd.
What can be said regarding the following two statements?
Statement 1: Profitable Ltd. has the lowest share in MP market.
Statement 2: Honest Ltd.'s total revenue is more than Profitable Ltd.
Statement 1: Profitable Ltd. has the lowest share in MP market.
Statement 2: Honest Ltd.'s total revenue is more than Profitable Ltd.
Show Hint
Identify the two possible assignments of firms to names, then see which one makes Profitable the lowest in MP.
Updated On: Nov 4, 2026
- If Statement 1 is true then Statement 2 is necessarily false.
- If Statement 1 is true then Statement 2 is necessarily true.
- Both Statement 1 and Statement 2 are true.
- Neither Statement 1 nor Statement 2 is true.
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Totals and identification:
Totals: A \(=49+69+72=190\), B \(=82+72+63=217\), C \(=80+70+72=222\), D \(=55+65+65=185\).
Aggressive and Honest differ by 5: only the pairs {A, D} (190, 185) and {B, C} (217, 222) qualify.
Truthful has the highest MP share: A or C (both 72; B is 63, D is 65).
Case 1: Truthful \(=\) A, then {Honest, Aggressive} \(=\) {B, C} and Profitable \(=\) D.
Case 2: Truthful \(=\) C, then {Honest, Aggressive} \(=\) {A, D} and Profitable \(=\) B.
Step 2: Statement 1:
The lowest MP revenue is B (63). In Case 1, Profitable \(=\) D (65), so Statement 1 is false. In Case 2, Profitable \(=\) B (63), so Statement 1 is true. So Statement 1 true means Case 2.
Step 3: Statement 2 in Case 2:
Profitable \(=\) B (217), Honest is A (190) or D (185). Honest's total is less than Profitable's, so Statement 2 is false.
Thus, if Statement 1 is true, Statement 2 is necessarily false.
Final Answer:
The correct option is (1): If Statement 1 is true then Statement 2 is necessarily false.
Totals: A \(=49+69+72=190\), B \(=82+72+63=217\), C \(=80+70+72=222\), D \(=55+65+65=185\).
Aggressive and Honest differ by 5: only the pairs {A, D} (190, 185) and {B, C} (217, 222) qualify.
Truthful has the highest MP share: A or C (both 72; B is 63, D is 65).
Case 1: Truthful \(=\) A, then {Honest, Aggressive} \(=\) {B, C} and Profitable \(=\) D.
Case 2: Truthful \(=\) C, then {Honest, Aggressive} \(=\) {A, D} and Profitable \(=\) B.
Step 2: Statement 1:
The lowest MP revenue is B (63). In Case 1, Profitable \(=\) D (65), so Statement 1 is false. In Case 2, Profitable \(=\) B (63), so Statement 1 is true. So Statement 1 true means Case 2.
Step 3: Statement 2 in Case 2:
Profitable \(=\) B (217), Honest is A (190) or D (185). Honest's total is less than Profitable's, so Statement 2 is false.
Thus, if Statement 1 is true, Statement 2 is necessarily false.
Final Answer:
The correct option is (1): If Statement 1 is true then Statement 2 is necessarily false.
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Question: 2
What can be said regarding the following two statements?
Statement 1: Aggressive Ltd.'s lowest revenues are from MP.
Statement 2: Honest Ltd.'s lowest revenues are from Bihar.
What can be said regarding the following two statements?
Statement 1: Aggressive Ltd.'s lowest revenues are from MP.
Statement 2: Honest Ltd.'s lowest revenues are from Bihar.
Statement 1: Aggressive Ltd.'s lowest revenues are from MP.
Statement 2: Honest Ltd.'s lowest revenues are from Bihar.
Show Hint
List the four possible (Honest, Aggressive) assignments and check, for each, the state in which each firm has its lowest revenue.
Updated On: Nov 4, 2026
- If Statement 2 is true then Statement 1 is necessarily false.
- If Statement 1 is false then Statement 2 is necessarily true.
- None of the above.
- If Statement 1 is true then Statement 2 is necessarily true.
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Totals and identification:
Totals: A \(=49+69+72=190\), B \(=82+72+63=217\), C \(=80+70+72=222\), D \(=55+65+65=185\).
Aggressive and Honest differ by 5: only the pairs {A, D} (190, 185) and {B, C} (217, 222) qualify.
Truthful has the highest MP share: A or C (both 72; B is 63, D is 65).
Case 1: Truthful \(=\) A, then {Honest, Aggressive} \(=\) {B, C} and Profitable \(=\) D.
Case 2: Truthful \(=\) C, then {Honest, Aggressive} \(=\) {A, D} and Profitable \(=\) B.
Step 2: The four possible assignments:
Lowest revenues: A in UP (49), B in MP (63), C in Bihar (70), D in UP (55).
(a) Honest \(=\) C, Aggressive \(=\) B: Statement 1 true (B lowest in MP), Statement 2 true (C lowest in Bihar).
(b) Honest \(=\) B, Aggressive \(=\) C: Statement 1 false (C lowest in Bihar), Statement 2 false (B lowest in MP).
(c) Honest \(=\) A, Aggressive \(=\) D: Statement 1 false, Statement 2 false (both lowest in UP).
(d) Honest \(=\) D, Aggressive \(=\) A: Statement 1 false, Statement 2 false.
Step 3: Test the options:
Option 1: Statement 2 true occurs only in (a), where Statement 1 is true. So it is not 'necessarily false'.
Option 2: Statement 1 false occurs in (b), (c), (d), where Statement 2 is false. So it is not 'necessarily true'.
Option 4: Statement 1 true occurs only in (a), where Statement 2 is true. So it is necessarily true.
Final Answer:
The correct option is (4): If Statement 1 is true then Statement 2 is necessarily true.
Totals: A \(=49+69+72=190\), B \(=82+72+63=217\), C \(=80+70+72=222\), D \(=55+65+65=185\).
Aggressive and Honest differ by 5: only the pairs {A, D} (190, 185) and {B, C} (217, 222) qualify.
Truthful has the highest MP share: A or C (both 72; B is 63, D is 65).
Case 1: Truthful \(=\) A, then {Honest, Aggressive} \(=\) {B, C} and Profitable \(=\) D.
Case 2: Truthful \(=\) C, then {Honest, Aggressive} \(=\) {A, D} and Profitable \(=\) B.
Step 2: The four possible assignments:
Lowest revenues: A in UP (49), B in MP (63), C in Bihar (70), D in UP (55).
(a) Honest \(=\) C, Aggressive \(=\) B: Statement 1 true (B lowest in MP), Statement 2 true (C lowest in Bihar).
(b) Honest \(=\) B, Aggressive \(=\) C: Statement 1 false (C lowest in Bihar), Statement 2 false (B lowest in MP).
(c) Honest \(=\) A, Aggressive \(=\) D: Statement 1 false, Statement 2 false (both lowest in UP).
(d) Honest \(=\) D, Aggressive \(=\) A: Statement 1 false, Statement 2 false.
Step 3: Test the options:
Option 1: Statement 2 true occurs only in (a), where Statement 1 is true. So it is not 'necessarily false'.
Option 2: Statement 1 false occurs in (b), (c), (d), where Statement 2 is false. So it is not 'necessarily true'.
Option 4: Statement 1 true occurs only in (a), where Statement 2 is true. So it is necessarily true.
Final Answer:
The correct option is (4): If Statement 1 is true then Statement 2 is necessarily true.
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Question: 3
What can be said regarding the following two statements?
Statement 1: Honest Ltd. has the highest share in the UP market.
Statement 2: Aggressive Ltd. has the highest share in the Bihar market.
What can be said regarding the following two statements?
Statement 1: Honest Ltd. has the highest share in the UP market.
Statement 2: Aggressive Ltd. has the highest share in the Bihar market.
Statement 1: Honest Ltd. has the highest share in the UP market.
Statement 2: Aggressive Ltd. has the highest share in the Bihar market.
Show Hint
Find which firm has the highest revenue in UP and which in Bihar; then see whether one firm would have to be both Honest and Aggressive.
Updated On: Nov 4, 2026
- At most one of the statements is true.
- At least one of the statements must be true.
- Both statements could be true.
- None of the above.
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Highest revenues:
UP: B has 82 (the highest). Bihar: B has 72 (the highest).
Step 2: Statements:
Statement 1 is true only if Honest \(=\) B. Statement 2 is true only if Aggressive \(=\) B. One firm cannot be both Honest and Aggressive, so both statements cannot be true together. Hence at most one of the statements is true.
Step 3: Check the other options:
Option 3 is false (both cannot be true). Option 2 would need B to be Honest or Aggressive; but in Case 2 (Truthful \(=\) C, Profitable \(=\) B, {Honest, Aggressive} \(=\) {A, D}) both statements are false. So neither must be true.
Final Answer:
The correct option is (1): At most one of the statements is true.
UP: B has 82 (the highest). Bihar: B has 72 (the highest).
Step 2: Statements:
Statement 1 is true only if Honest \(=\) B. Statement 2 is true only if Aggressive \(=\) B. One firm cannot be both Honest and Aggressive, so both statements cannot be true together. Hence at most one of the statements is true.
Step 3: Check the other options:
Option 3 is false (both cannot be true). Option 2 would need B to be Honest or Aggressive; but in Case 2 (Truthful \(=\) C, Profitable \(=\) B, {Honest, Aggressive} \(=\) {A, D}) both statements are false. So neither must be true.
Final Answer:
The correct option is (1): At most one of the statements is true.
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Question: 4
If Profitable Ltd.'s lowest revenue is from UP, then which of the following is true?
If Profitable Ltd.'s lowest revenue is from UP, then which of the following is true?
Show Hint
Check in which of the two cases Profitable's lowest revenue is in UP, and then read off Truthful's lowest state.
Updated On: Nov 4, 2026
- Truthful Ltd.'s lowest revenues are from MP.
- Truthful Ltd.'s lowest revenues are from Bihar.
- No definite conclusion is possible.
- Truthful Ltd.'s lowest revenues are from UP.
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Totals and identification:
Totals: A \(=49+69+72=190\), B \(=82+72+63=217\), C \(=80+70+72=222\), D \(=55+65+65=185\).
Aggressive and Honest differ by 5: only the pairs {A, D} (190, 185) and {B, C} (217, 222) qualify.
Truthful has the highest MP share: A or C (both 72; B is 63, D is 65).
Case 1: Truthful \(=\) A, then {Honest, Aggressive} \(=\) {B, C} and Profitable \(=\) D.
Case 2: Truthful \(=\) C, then {Honest, Aggressive} \(=\) {A, D} and Profitable \(=\) B.
Step 2: Profitable's lowest revenue is in UP:
Case 1: Profitable \(=\) D, with UP 55 and Bihar, MP 65 each. Its lowest revenue is from UP. This is consistent.
Case 2: Profitable \(=\) B, whose lowest revenue is MP (63). This does not match.
So Case 1 holds and Truthful \(=\) A.
Step 3: Truthful's lowest:
A has UP 49, Bihar 69, MP 72, so the lowest is UP.
Final Answer:
The correct option is (4): Truthful Ltd.'s lowest revenues are from UP.
Totals: A \(=49+69+72=190\), B \(=82+72+63=217\), C \(=80+70+72=222\), D \(=55+65+65=185\).
Aggressive and Honest differ by 5: only the pairs {A, D} (190, 185) and {B, C} (217, 222) qualify.
Truthful has the highest MP share: A or C (both 72; B is 63, D is 65).
Case 1: Truthful \(=\) A, then {Honest, Aggressive} \(=\) {B, C} and Profitable \(=\) D.
Case 2: Truthful \(=\) C, then {Honest, Aggressive} \(=\) {A, D} and Profitable \(=\) B.
Step 2: Profitable's lowest revenue is in UP:
Case 1: Profitable \(=\) D, with UP 55 and Bihar, MP 65 each. Its lowest revenue is from UP. This is consistent.
Case 2: Profitable \(=\) B, whose lowest revenue is MP (63). This does not match.
So Case 1 holds and Truthful \(=\) A.
Step 3: Truthful's lowest:
A has UP 49, Bihar 69, MP 72, so the lowest is UP.
Final Answer:
The correct option is (4): Truthful Ltd.'s lowest revenues are from UP.
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