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6 times of a fraction is greater than 7 times of its reciprocal by 11. What is the fraction? 
  • a)
    5/3 
  • b)
    7/3 
  • c)
    5/4 
  • d)
    4/5 
Correct answer is option 'B'. Can you explain this answer?
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6 times of a fraction is greater than 7 times of its reciprocal by 11....
To solve this problem, we can start by setting up an equation based on the given information.

Let's assume the fraction is represented by 'x'.

According to the problem, 6 times the fraction is greater than 7 times its reciprocal by 11. We can express this as:

6x > 7(1/x) + 11

Now, let's simplify the equation step by step to solve for 'x'.

Simplifying the right side of the equation:
7(1/x) + 11 = 7/x + 11

Finding a common denominator:
7/x + 11 = (7 + 11x) / x

Substituting the simplified expression back into the equation:
6x > (7 + 11x) / x

Multiplying both sides of the equation by 'x' to eliminate the denominator:
6x^2 > 7 + 11x

Rearranging the equation to isolate the terms on one side:
6x^2 - 11x - 7 > 0

Now we have a quadratic inequality. To solve it, we can factor the expression or use the quadratic formula.

Factoring the quadratic expression:
(2x - 7)(3x + 1) > 0

Setting each factor greater than zero to find the intervals where the inequality is satisfied:
2x - 7 > 0 or 3x + 1 > 0

Solving each inequality separately:
2x > 7 or 3x > -1

x > 7/2 or x > -1/3

Since we are looking for a fraction, the value of 'x' cannot be negative. Therefore, we discard the interval x > -1/3.

So, the solution is x > 7/2, which means the fraction is greater than 7/2.

Among the given answer choices, the only fraction that satisfies this condition is 7/3 (option B).

Therefore, the correct answer is option B, 7/3.
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Read the following passage carefully and choose the best answer to each question out of the five given alternatives.To teach is to create a space in which obedience to truth is practiced. Space may sound like a vague, poetic metaphor until we realize that it describes experiences of everyday life. We know what it means to be in a green and open field; we know what it means to be on a crowded rush-hour bus. These experiences of physical space have parallels in our relations with others. On our jobs, we know what it is to be pressed and crowded, our working space diminished by the urgency of deadlines and competitiveness of colleagues.But then there are times when deadlines disappear and colleagues cooperate when everyone has space to move, invent and produce with energy and enthusiasm. With family and friends, we know how it feels to have unreasonable demands placed upon us, to be boxed in the expectations of those nearest to us. 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6 times of a fraction is greater than 7 times of its reciprocal by 11. What is the fraction?a)5/3b)7/3c)5/4d)4/5Correct answer is option 'B'. Can you explain this answer?
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