Comprehension
Four students — Ashish, Dhanraj, Felix and Sameer sat for the Common Entrance Exam for Management (CEEM). Each of the students has one profession among the four: Doctor, Chartered Accountant, Engineer, and Economist. One student got admission offers from three NIMs (National Institutes of Management), another from two NIMs, the third from one NIM, while the fourth got none. Below are some of the facts about who got admission offers from how many NIMs and what is their educational background.
I. The one who is an engineer didn’t get as many admissions as Ashish.
II. The one who got the offer for admissions in two NIMs isn’t Dhanraj nor is he a chartered accountant.
III. Sameer is an economist.
IV. Dhanraj isn’t an engineer and received more admission offers than Ashish.
V. The doctor got the most number of admission offers.
Question: 1
Which one of the following statements is necessarily true?
Which one of the following statements is necessarily true?
Show Hint
Carefully track the details for each individual and verify the number of offers they received against their field of study.
Updated On: Jul 31, 2026
- Ashish is a chartered accountant and got offer for admission in three NIMs.
- Dhanraj is a doctor and got admission offer in one NIM.
- Sameer is an economist who got admission offers in two NIMs.
- Felix who is not an engineer did not get any offer for admission.
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
From the data provided, Sameer is an economist, and he received admission offers from two NIMs, making option (3) the true statement.
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Question: 2
Five boys went to a store to buy sweets. One boy had Rs. 40. Another boy had Rs. 30. Two other boys had Rs. 20 each. The remaining boy had Rs. 10. Below are some more facts about the initial and final cash positions.
I. Alam started with more than Jugraj.
II. Sandeep spent Rs. 1.50 more than Daljeet.
III. Ganesh started with more money than just only one other person.
IV. Daljeet started with 2/3 of what Sandeep started with.
V. Alam spent the most, but did not end with the least.
VI. Jugraj spent the least and ended with more than Alam or Daljeet.
VII. Ganesh spent Rs. 3.50.
VIII. Alam spent 10 times than what Ganesh did.
In the choices given below, all statements except one are false. Which one of the following statements can be true?
Five boys went to a store to buy sweets. One boy had Rs. 40. Another boy had Rs. 30. Two other boys had Rs. 20 each. The remaining boy had Rs. 10. Below are some more facts about the initial and final cash positions.
I. Alam started with more than Jugraj.
II. Sandeep spent Rs. 1.50 more than Daljeet.
III. Ganesh started with more money than just only one other person.
IV. Daljeet started with 2/3 of what Sandeep started with.
V. Alam spent the most, but did not end with the least.
VI. Jugraj spent the least and ended with more than Alam or Daljeet.
VII. Ganesh spent Rs. 3.50.
VIII. Alam spent 10 times than what Ganesh did.
In the choices given below, all statements except one are false. Which one of the following statements can be true?
I. Alam started with more than Jugraj.
II. Sandeep spent Rs. 1.50 more than Daljeet.
III. Ganesh started with more money than just only one other person.
IV. Daljeet started with 2/3 of what Sandeep started with.
V. Alam spent the most, but did not end with the least.
VI. Jugraj spent the least and ended with more than Alam or Daljeet.
VII. Ganesh spent Rs. 3.50.
VIII. Alam spent 10 times than what Ganesh did.
In the choices given below, all statements except one are false. Which one of the following statements can be true?
Show Hint
Fix who started with which amount using facts III, VII, VIII and IV, then check each statement against what that person could have spent.
Updated On: Nov 4, 2026
- Alam started with Rs. 40 and ended with Rs. 9.50
- Sandeep started with Rs. 30 and ended with Re. 1
- Jugraj started with Rs. 10 and ended with Rs. 7
- Ganesh started with Rs. 20 and ended with Rs. 4
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Find who started with how much:
The starting amounts are 40, 30, 20, 20 and 10. By fact III, Ganesh started with more money than exactly one other person. If he had 40 or 30 he would beat three or more people; if he had 10 he would beat nobody. With one of the two Rs. 20 holders he beats only the Rs. 10 boy (the other Rs. 20 boy has the same amount, not less). So Ganesh started with Rs. 20.
Step 2: Alam:
Ganesh spent Rs. 3.50 (VII), so Alam spent \(10 \times 3.50 = \) Rs. 35 (VIII). Alam must have started with at least Rs. 35, so he started with Rs. 40 and ended with \(40 - 35 = \) Rs. 5.
Step 3: Sandeep, Daljeet and Jugraj:
The amounts left are 30, 20 and 10. Daljeet started with 2/3 of Sandeep (IV): \(20 = \tfrac{2}{3} \times 30\). So Sandeep started with Rs. 30, Daljeet with Rs. 20, and Jugraj with Rs. 10 (this agrees with I: Alam 40 > Jugraj 10).
Step 4: Test the four statements:
Option (1): Alam ended with Rs. 5, not Rs. 9.50. False.
Option (2): If Sandeep ended with Re. 1, he spent Rs. 29, so Daljeet spent \(29 - 1.50 = 27.50\), which is more than the Rs. 20 Daljeet had. Impossible. False.
Option (4): Ganesh spent Rs. 3.50, so he ended with \(20 - 3.50 = 16.50\), not Rs. 4. False.
Option (3): Jugraj started with Rs. 10 (correct). Ending with Rs. 7 means he spent Rs. 3, which is less than Ganesh's Rs. 3.50, so he can be the one who spent the least, and Rs. 7 is more than Alam's Rs. 5. For Alam not to end with the least, Daljeet must end with less than Rs. 5. For example, Daljeet spends Rs. 15.50 and ends with Rs. 4.50; Sandeep then spends Rs. 17 and ends with Rs. 13. Every fact I to VIII holds, so the statement can be true.
Final Answer:
The correct option is (3): Jugraj started with Rs. 10 and ended with Rs. 7.
The starting amounts are 40, 30, 20, 20 and 10. By fact III, Ganesh started with more money than exactly one other person. If he had 40 or 30 he would beat three or more people; if he had 10 he would beat nobody. With one of the two Rs. 20 holders he beats only the Rs. 10 boy (the other Rs. 20 boy has the same amount, not less). So Ganesh started with Rs. 20.
Step 2: Alam:
Ganesh spent Rs. 3.50 (VII), so Alam spent \(10 \times 3.50 = \) Rs. 35 (VIII). Alam must have started with at least Rs. 35, so he started with Rs. 40 and ended with \(40 - 35 = \) Rs. 5.
Step 3: Sandeep, Daljeet and Jugraj:
The amounts left are 30, 20 and 10. Daljeet started with 2/3 of Sandeep (IV): \(20 = \tfrac{2}{3} \times 30\). So Sandeep started with Rs. 30, Daljeet with Rs. 20, and Jugraj with Rs. 10 (this agrees with I: Alam 40 > Jugraj 10).
Step 4: Test the four statements:
Option (1): Alam ended with Rs. 5, not Rs. 9.50. False.
Option (2): If Sandeep ended with Re. 1, he spent Rs. 29, so Daljeet spent \(29 - 1.50 = 27.50\), which is more than the Rs. 20 Daljeet had. Impossible. False.
Option (4): Ganesh spent Rs. 3.50, so he ended with \(20 - 3.50 = 16.50\), not Rs. 4. False.
Option (3): Jugraj started with Rs. 10 (correct). Ending with Rs. 7 means he spent Rs. 3, which is less than Ganesh's Rs. 3.50, so he can be the one who spent the least, and Rs. 7 is more than Alam's Rs. 5. For Alam not to end with the least, Daljeet must end with less than Rs. 5. For example, Daljeet spends Rs. 15.50 and ends with Rs. 4.50; Sandeep then spends Rs. 17 and ends with Rs. 13. Every fact I to VIII holds, so the statement can be true.
Final Answer:
The correct option is (3): Jugraj started with Rs. 10 and ended with Rs. 7.
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Question: 3
In a hospital there were 200 diabetes, 150 hyperglycaemia and 150 gastro-enteritis patients. Of these, 80 patients were treated for both diabetes and hyperglycaemia. Sixty patients were treated for gastro-enteritis and hyperglycaemia, while 70 were treated for diabetes and gastro-enteritis. Some of these patients have all the three diseases. Dr. Dennis treats patients with only gastro-enteritis. Dr. Paul is a generalist. Therefore, he can treat patients with multiple diseases. Patients always prefer a specialist for their disease. If Dr. Dennis had 80 patients, then the other three doctors can be arranged in terms of the number of patients treated as:
In a hospital there were 200 diabetes, 150 hyperglycaemia and 150 gastro-enteritis patients. Of these, 80 patients were treated for both diabetes and hyperglycaemia. Sixty patients were treated for gastro-enteritis and hyperglycaemia, while 70 were treated for diabetes and gastro-enteritis. Some of these patients have all the three diseases. Dr. Dennis treats patients with only gastro-enteritis. Dr. Paul is a generalist. Therefore, he can treat patients with multiple diseases. Patients always prefer a specialist for their disease. If Dr. Dennis had 80 patients, then the other three doctors can be arranged in terms of the number of patients treated as:
Show Hint
Find the number of patients with all three diseases from the 80 gastro-enteritis-only patients, then compare the totals for each doctor.
Updated On: Nov 4, 2026
- Cannot be determined
- Paul > Hormis > Gerard
- Gerard > Paul > Hormis
- Paul > Gerard > Hormis
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Set up the Venn diagram:
Let \(t\) be the number of patients with all three diseases. The pair counts include the triple group: \(D\cap H = 80,\ G\cap H = 60,\ D\cap G = 70\).
Step 2: Use Dr. Dennis's 80 patients:
Dennis treats only gastro-enteritis, so the number of patients with only G is 80:
\[150 - (70 + 60 - t) = 80 \Rightarrow 20 + t = 80 \Rightarrow t = 60.\]
Step 3: All regions:
Only D and H: \(80 - 60 = 20\). Only D and G: \(70 - 60 = 10\). Only G and H: \(60 - 60 = 0\). All three: 60. So the number of patients with two or more diseases is \(20 + 10 + 0 + 60 = 90\), and these go to the generalist Dr. Paul.
Only D: \(200 - (80 + 70 - 60) = 110\). Only H: \(150 - (80 + 60 - 60) = 70\).
Step 4: Compare the doctors:
Paul has 90 patients. Gerard and Hormis are the specialists for the other two diseases, so one of them has 110 patients (diabetes only) and the other has 70 (hyperglycaemia only). Paul is therefore always in the middle. The question never states which of Gerard and Hormis treats diabetes and which treats hyperglycaemia.
Options (4) and (2) put Paul first, which is false because 90 is less than 110. Option (3) holds only if Gerard is the diabetes specialist, and that is not given (if Hormis were, the order would be reversed). So the order of the three doctors cannot be fixed.
Final Answer:
The correct option is (1): Cannot be determined.
Let \(t\) be the number of patients with all three diseases. The pair counts include the triple group: \(D\cap H = 80,\ G\cap H = 60,\ D\cap G = 70\).
Step 2: Use Dr. Dennis's 80 patients:
Dennis treats only gastro-enteritis, so the number of patients with only G is 80:
\[150 - (70 + 60 - t) = 80 \Rightarrow 20 + t = 80 \Rightarrow t = 60.\]
Step 3: All regions:
Only D and H: \(80 - 60 = 20\). Only D and G: \(70 - 60 = 10\). Only G and H: \(60 - 60 = 0\). All three: 60. So the number of patients with two or more diseases is \(20 + 10 + 0 + 60 = 90\), and these go to the generalist Dr. Paul.
Only D: \(200 - (80 + 70 - 60) = 110\). Only H: \(150 - (80 + 60 - 60) = 70\).
Step 4: Compare the doctors:
Paul has 90 patients. Gerard and Hormis are the specialists for the other two diseases, so one of them has 110 patients (diabetes only) and the other has 70 (hyperglycaemia only). Paul is therefore always in the middle. The question never states which of Gerard and Hormis treats diabetes and which treats hyperglycaemia.
Options (4) and (2) put Paul first, which is false because 90 is less than 110. Option (3) holds only if Gerard is the diabetes specialist, and that is not given (if Hormis were, the order would be reversed). So the order of the three doctors cannot be fixed.
Final Answer:
The correct option is (1): Cannot be determined.
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Question: 4
Three children won the prizes in the Bournvita Quiz contest. They are from the schools: Loyola, Convent, and Little Flowers, which are located at different cities. Below are some of the facts about the schools, the children, and the city they are from.
One of the children is Bipin.
Loyola School’s contestant did not come first.
Little Flower’s contestant was named Riaz.
Convent School is not in Hyderabad.
The contestant from Pune is not from Loyola School.
The contestant from Bangalore did not come first.
Convent School’s contestant’s name is not Balbir.
Which of the following statements is true?
Three children won the prizes in the Bournvita Quiz contest. They are from the schools: Loyola, Convent, and Little Flowers, which are located at different cities. Below are some of the facts about the schools, the children, and the city they are from.
One of the children is Bipin.
Loyola School’s contestant did not come first.
Little Flower’s contestant was named Riaz.
Convent School is not in Hyderabad.
The contestant from Pune is not from Loyola School.
The contestant from Bangalore did not come first.
Convent School’s contestant’s name is not Balbir.
Which of the following statements is true?
One of the children is Bipin.
Loyola School’s contestant did not come first.
Little Flower’s contestant was named Riaz.
Convent School is not in Hyderabad.
The contestant from Pune is not from Loyola School.
The contestant from Bangalore did not come first.
Convent School’s contestant’s name is not Balbir.
Which of the following statements is true?
Show Hint
Clue-based logic and process of elimination are essential for solving such ranking problems.
Updated On: Jul 31, 2026
- 1st prize: Riaz (Little Flowers), 2nd prize: Bipin (Convent), 3rd prize: Balbir (Loyola)
- 1st prize: Bipin (Convent), 2nd prize: Riaz (Little Flowers), 3rd prize: Balbir (Loyola)
- 1st prize: Riaz (Little Flowers), 2nd prize: Balbir (Loyola), 3rd prize: Bipin (Convent)
- 1st prize: Bipin (Convent), 2nd prize: Balbir (Loyola), 3rd prize: Riaz (Little Flowers)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
From the given clues:
- Loyola's contestant did not come first, so Balbir can't be first.
- The contestant from Pune isn't from Loyola, so Bipin must be from Convent.
- Riaz is from Little Flowers and didn’t come first.
- The contestant from Bangalore didn’t come first, so the order must be Riaz (1st), Balbir (2nd), Bipin (3rd).
Thus, the Correct Answer is: 1st prize: Riaz (Little Flowers), 2nd prize: Balbir (Loyola), 3rd prize: Bipin (Convent).
\[
\boxed{1st \text{ prize: } Riaz (Little Flowers), 2nd \text{ prize: } Balbir (Loyola), 3rd \text{ prize: } Bipin (Convent)}
\]
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Question: 5
Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of mother of the younger boy. The mother of the younger boy is younger to his father by 3 years. Then, what is the age of the younger boy?
Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of mother of the younger boy. The mother of the younger boy is younger to his father by 3 years. Then, what is the age of the younger boy?
Show Hint
Translate "cube root of the product" into a relation between the two ages, then test the few single-digit pairs that remain.
Updated On: Nov 4, 2026
- 3
- 2
- 4
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Translate the first condition:
Let the younger boy be \(x\) years and the elder \(y\) years, with \(x < y < 10\). Then \(x = \sqrt[3]{xy}\), so \(x^3 = xy\) and \(y = x^2\).
Step 2: List the possibilities:
Since \(x < y < 10\), \(x\) can only be 2 or 3 (x = 1 gives y = 1, so the boys would be the same age, not "younger" and "elder"). The pairs are \((x, y) = (2, 4)\) and \((3, 9)\).
Step 3: Use the father and mother conditions:
Father's age \(= 10x + y\), mother's age \(= \dfrac{10y + x}{2}\).
For (2, 4): father \(= 24\), mother \(= \dfrac{42}{2} = 21\). The difference is 3. This fits.
For (3, 9): father \(= 39\), mother \(= \dfrac{93}{2} = 46.5\), which is not a whole number and is more than the father's age. This does not fit.
Step 4: Conclusion:
The younger boy is 2 years old.
Final Answer:
The correct option is (2): 2.
Let the younger boy be \(x\) years and the elder \(y\) years, with \(x < y < 10\). Then \(x = \sqrt[3]{xy}\), so \(x^3 = xy\) and \(y = x^2\).
Step 2: List the possibilities:
Since \(x < y < 10\), \(x\) can only be 2 or 3 (x = 1 gives y = 1, so the boys would be the same age, not "younger" and "elder"). The pairs are \((x, y) = (2, 4)\) and \((3, 9)\).
Step 3: Use the father and mother conditions:
Father's age \(= 10x + y\), mother's age \(= \dfrac{10y + x}{2}\).
For (2, 4): father \(= 24\), mother \(= \dfrac{42}{2} = 21\). The difference is 3. This fits.
For (3, 9): father \(= 39\), mother \(= \dfrac{93}{2} = 46.5\), which is not a whole number and is more than the father's age. This does not fit.
Step 4: Conclusion:
The younger boy is 2 years old.
Final Answer:
The correct option is (2): 2.
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Question: 6
Flights A and B are scheduled from an airport within the next one hour. All the booked passengers of the two flights are waiting in the boarding hall after check-in. The hall has a seating capacity of 200, out of which 10% remained vacant. 40% of the waiting passengers are ladies. When the boarding announcement came, passengers of flight A left the hall and boarded the flight. Seating capacity of each flight is two-thirds of the passengers who waited in the waiting hall for both flights put together. Half the passengers who boarded flight A are women. After boarding for flight A, 60% of the waiting hall seats became empty. For every twenty of those who are still waiting in the hall for flight B, there is one air hostess in flight A. What is the ratio of empty seats in flight B to the number of air hostesses in flight A?
Flights A and B are scheduled from an airport within the next one hour. All the booked passengers of the two flights are waiting in the boarding hall after check-in. The hall has a seating capacity of 200, out of which 10% remained vacant. 40% of the waiting passengers are ladies. When the boarding announcement came, passengers of flight A left the hall and boarded the flight. Seating capacity of each flight is two-thirds of the passengers who waited in the waiting hall for both flights put together. Half the passengers who boarded flight A are women. After boarding for flight A, 60% of the waiting hall seats became empty. For every twenty of those who are still waiting in the hall for flight B, there is one air hostess in flight A. What is the ratio of empty seats in flight B to the number of air hostesses in flight A?
Show Hint
These seating and ratio problems require logical thinking and careful breakdown of the given numbers and ratios.
Updated On: Jul 2, 2026
- 10:1
- 5:1
- 20:1
- 1:1
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The seating capacity of each flight is two-thirds of the total number of passengers, so after flight A's passengers board, 60% of the seats are empty. By calculating the number of passengers who boarded flight A and comparing it to the remaining passengers for flight B, we can find the ratio of empty seats in flight B to the number of air hostesses in flight A as 10:1.
\[
\boxed{10:1}
\]
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