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Question 1 of 5
1. Question
Question is given followed by two Statements I and II. Consider the Question and the Statements.
Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.
Question: What is the difference of their ages?
Statement-I: The age of P is greater than the age of Q.
Statement-II: The sum of their ages is 44/27 times their difference.Which one of the following is correct in respect of the above Question and the Statements?
Correct
Answer: A
Solution:
Given that,
Age of P and Q is less than 100 years but more than 10 years.
Digits of P when interchanged the number represents Q.Statement I: The age of P is greater than the age of Q.
Statement II: The sum of their ages is 44/27 times their difference.Now,
Let P = 10x + y and Q = 10y + x.
Statement I: 10x + y > 10y + x ⇒ x > y, but the difference cannot be determined.
Hence statement I is insufficient.Statement II: 11x + 11y = (44/27)(9x − 9y)
11(x + y) = (44/3)(x − y)
Multiply by 3: 33x + 33y = 44x − 44y ⇒ 11x = 77y ⇒ x = 7y.With 1 ≤ y ≤ 9 and x ≤ 9, the only possibility is y = 1, x = 7.
So P = 71 and Q = 17. Difference = 71 − 17 = 54.Hence statement II is sufficient to answer the question.
Therefore option (a) is correct.
Incorrect
Answer: A
Solution:
Given that,
Age of P and Q is less than 100 years but more than 10 years.
Digits of P when interchanged the number represents Q.Statement I: The age of P is greater than the age of Q.
Statement II: The sum of their ages is 44/27 times their difference.Now,
Let P = 10x + y and Q = 10y + x.
Statement I: 10x + y > 10y + x ⇒ x > y, but the difference cannot be determined.
Hence statement I is insufficient.Statement II: 11x + 11y = (44/27)(9x − 9y)
11(x + y) = (44/3)(x − y)
Multiply by 3: 33x + 33y = 44x − 44y ⇒ 11x = 77y ⇒ x = 7y.With 1 ≤ y ≤ 9 and x ≤ 9, the only possibility is y = 1, x = 7.
So P = 71 and Q = 17. Difference = 71 − 17 = 54.Hence statement II is sufficient to answer the question.
Therefore option (a) is correct.
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Question 2 of 5
2. Question
If in a particular year 12th January is a Sunday, then which one of the following is correct?
Correct
Answer: C
Solution:
Given that,
12th January is a Sunday
There are two possibilities if the year is a leap year or not a leap year
Possibility 1: Leap year
Total number of days up to 15th August = (19 + 29 + 31 + 30 + 31 + 30 + 31 + 15) = 216 = 30 weeks and 6 odd days
So, 15th August is Sunday + 6 odd days = SaturdayPossibility 2: Not a Leap year
Total number of days up to 15th August = (19 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 215 = 30 weeks and 5 odd days
So, 15th August is Sunday + 5 odd days = FridayHence option (c) is correct
Incorrect
Answer: C
Solution:
Given that,
12th January is a Sunday
There are two possibilities if the year is a leap year or not a leap year
Possibility 1: Leap year
Total number of days up to 15th August = (19 + 29 + 31 + 30 + 31 + 30 + 31 + 15) = 216 = 30 weeks and 6 odd days
So, 15th August is Sunday + 6 odd days = SaturdayPossibility 2: Not a Leap year
Total number of days up to 15th August = (19 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 215 = 30 weeks and 5 odd days
So, 15th August is Sunday + 5 odd days = FridayHence option (c) is correct
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Question 3 of 5
3. Question
A and B decide to travel from place X to place Y by bus. A has Rs. 8 with him and he finds that it is 40% of the bus fare for two persons. B finds that he has Rs. 7 with him and hands it over to A. In this context, which one of the following statements is correct?
Correct
Answer: B
Solution:
Given that,
A has Rs. 8 which is 40% of the fare for two persons.
B has Rs. 7 and gives it to A.Now,
Let total fare for two persons be Rs. F.
40% of F = 8 ⇒ F = (8 × 100) / 40 = Rs. 20.
Total money with A after B’s contribution = 8 + 7 = Rs. 15.
Shortfall = 20 − 15 = Rs. 5.Hence option (b) is correct.
Incorrect
Answer: B
Solution:
Given that,
A has Rs. 8 which is 40% of the fare for two persons.
B has Rs. 7 and gives it to A.Now,
Let total fare for two persons be Rs. F.
40% of F = 8 ⇒ F = (8 × 100) / 40 = Rs. 20.
Total money with A after B’s contribution = 8 + 7 = Rs. 15.
Shortfall = 20 − 15 = Rs. 5.Hence option (b) is correct.
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Question 4 of 5
4. Question
Education has always been a critical driver of social mobility and economic growth. In modern societies, universal access to quality education is viewed as a fundamental right, not merely a privilege. It equips individuals with skills, broadens their opportunities, and strengthens democratic participation. Yet, the challenge lies not only in expanding enrolment but also in ensuring the quality and equity of education. Without adequate investment, well-trained teachers, and inclusive curricula, education risks reproducing existing inequalities rather than reducing them. Thus, the success of a nation’s educational system must be measured not only by literacy rates but also by its ability to empower all sections of society equally.
Which one of the following statements best reflects the critical message conveyed by the author of the passage?
Correct
Answer: (b)
Explanation:
Option (a) is incorrect: The passage stresses that enrolment without quality and equity can reproduce inequalities. Hence, access alone is not enough.
Option (b) is correct: The author clearly emphasizes that apart from accessibility, education must also be equitable and of high quality to truly empower society.
Option (c) is incorrect: While employment is one outcome, the passage also mentions democratic participation and equality, showing a broader purpose.
Option (d) is incorrect: The author explicitly argues that success should not be judged only by literacy rates but by empowerment of all sections.Incorrect
Answer: (b)
Explanation:
Option (a) is incorrect: The passage stresses that enrolment without quality and equity can reproduce inequalities. Hence, access alone is not enough.
Option (b) is correct: The author clearly emphasizes that apart from accessibility, education must also be equitable and of high quality to truly empower society.
Option (c) is incorrect: While employment is one outcome, the passage also mentions democratic participation and equality, showing a broader purpose.
Option (d) is incorrect: The author explicitly argues that success should not be judged only by literacy rates but by empowerment of all sections. -
Question 5 of 5
5. Question
With reference to the above passage, the following assumptions have been made:
I. Education without quality and equity cannot reduce social inequalities.
II. Investment in infrastructure and teacher training is essential for improving educational outcomes.Which of the above assumptions is/are valid?
Correct
Answer: (c)
Explanation:
Assumption I is valid: The passage states that without quality and equity, education risks reproducing existing inequalities. This directly supports assumption I.
Assumption II is valid: The passage highlights the importance of adequate investment and well-trained teachers as prerequisites for effective education, making assumption II valid.
Thus, both assumptions follow logically, making option (c) the correct answer.Incorrect
Answer: (c)
Explanation:
Assumption I is valid: The passage states that without quality and equity, education risks reproducing existing inequalities. This directly supports assumption I.
Assumption II is valid: The passage highlights the importance of adequate investment and well-trained teachers as prerequisites for effective education, making assumption II valid.
Thus, both assumptions follow logically, making option (c) the correct answer.
