Study HubHubPage 176/182Scan verified MCQs with the answer highlighted, then open explanations when you want the reasoning.
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Inequalities
If a > b and b > a, then?
The statements 'a > b' and 'b > a' cannot both be true simultaneously for any real numbers a and b. Therefore, none of the given options correctly describe the situation, making 'None of these' the correct choice.
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Arithmetic Mean
What is the arithmetic mean between x - 3 and x + 3?
The arithmetic mean of two numbers is their sum divided by 2. Here, (x-3 + x+3)/2 = (2x)/2 = x, so the mean is x.
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Percentage and Depreciation
The value of a computer depreciates by 10% annually. If the present value of the computer is Rs. 100,000, what will be its value after two years?
The computer depreciates by 10% annually, so after one year its value is 90% of 100,000 = 90,000. After the second year, it is 90% of 90,000 = 81,000. Therefore, the value after two years is Rs. 81,000.
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Ratios and Proportions
A ratio equivalent to 3:7 is:
A ratio equivalent to 3:7 must have terms in the same proportion. Multiplying both terms of 3:7 by 3 gives 9:21, which is option C. Options A and B do not maintain the same ratio.
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Sequences and Series
Sum of 4 arithmetic means between 18 and 3 is:
To find the sum of 4 arithmetic means between 18 and 3, we consider the arithmetic sequence formed by 6 terms: 18, four arithmetic means, and 3. The common difference d = (3 - 18) / 5 = -3. The four arithmetic means are 15, 12, 9, and 6. Their sum is 15 + 12 + 9 + 6 = 42. Therefore, the correct answer is option C (42).
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Sequences and Series
If the arithmetic progression (A.P) is -15, -22, -29, …, then what is the 11th term?
The given arithmetic progression (A.P) has first term a = -15 and common difference d = -7. The nth term formula is a_n = a + (n-1)d. For the 11th term: a_11 = -15 + (11-1)(-7) = -15 - 70 = -85.
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Inequalities
What is the solution interval of the inequality 6x - 2 ≥ 3x + 10?
To solve the inequality 6x - 2 ≥ 3x + 10, subtract 3x from both sides to get 3x - 2 ≥ 10. Then add 2 to both sides: 3x ≥ 12. Dividing both sides by 3 (a positive number) gives x ≥ 4. Therefore, the solution interval is [4, ∞), which corresponds to option C.
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Percentage and Ratio
The tank-full petrol in Haroon's motorcycle lasts for 10 days. If he starts using 25% more every day, how many days will the tank-full petrol last?
If Haroon uses 25% more petrol each day, the daily consumption increases by a factor of 1.25. The total petrol amount remains the same, so the new duration is 10 ÷ 1.25 = 8 days. However, this calculation is incorrect; let's re-examine: If the original daily usage is x, total petrol = 10x. New daily usage = 1.25x. Days = total petrol ÷ new daily usage = 10x ÷ 1.25x = 8 days. So the correct answer is 8 days, which corresponds to option C, not B. Correcting answer to C.
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Algebra - Age Problems
If Amna is x years old, then 5 times Amna's age three years ago is:
Amna's age three years ago is (x - 3). Five times this age is 5(x - 3), which corresponds to option B.
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Work and Time
Mr. A can do a particular work in 6 hours, and Mr. B can do the same work in 12 hours. How much time will it take if they do the work together?
Mr. A's work rate is 1/6 work per hour, and Mr. B's work rate is 1/12 work per hour. Together, their combined rate is 1/6 + 1/12 = 1/4 work per hour, so they will complete the work in 4 hours.