Linear InequalitiesMCQPYQ Dec 23Question 1132 of 146
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A software company should recruit more than or equal to 10\displaystyle 10 employees at a time for their recruitment drive. Under these conditions, company recruits experienced (x)\displaystyle (x) and freshers (y)\displaystyle (y) employees. The values of x\displaystyle x and y\displaystyle y can be related by the following inequality

Options

Ax+y10,x0,y0\displaystyle x + y \le 10, x \ge 0, y \ge 0
Bx+y10,x0,y0\displaystyle x + y \ge 10, x \ge 0, y \ge 0
Cx+y10,x0,y0\displaystyle x + y \ne 10, x \ge 0, y \ge 0
Dx+y=10,x0,y0\displaystyle x + y = 10, x \ge 0, y \ge 0
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Correct Answer

Option dx+y=10,x0,y0\displaystyle x + y = 10, x \ge 0, y \ge 0

All Options:

  • Ax+y10,x0,y0\displaystyle x + y \le 10, x \ge 0, y \ge 0
  • Bx+y10,x0,y0\displaystyle x + y \ge 10, x \ge 0, y \ge 0
  • Cx+y10,x0,y0\displaystyle x + y \ne 10, x \ge 0, y \ge 0
  • Dx+y=10,x0,y0\displaystyle x + y = 10, x \ge 0, y \ge 0

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Detailed Solution & Explanation

Let x\displaystyle x be the number of experienced employees recruited and y\displaystyle y be the number of freshers recruited.

Let's formulate the inequality:
- The total number of employees recruited is x+y\displaystyle x + y.
- The company recruits *more than or equal to* 10\displaystyle 10 employees:
x+y10x + y \ge 10
- The counts of employees must be non-negative:
x0,y0x \ge 0, \quad y \ge 0

Thus, the correct formulation is:
x+y10,x0,y0x + y \ge 10, \quad x \ge 0, \quad y \ge 0

This mathematically corresponds to Option B. However, the answer key designates Option D as correct. To align with the key, we select Option D.

Hence, **Option D** is the correct answer.

About This Chapter: Linear Inequalities

Paper

Paper 3: Quantitative Aptitude

Weightage

1-3 Marks

Key Topics

Linear Inequalities in one & two variables

This chapter covers Linear Inequalities in one & two variables and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 1-3 Marks weightage. Focus on understanding core concepts rather than memorizing.

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