\(Q21.\:\) Which of the following inequalities best describes the situation where an elevator can lift a maximum of 20 pounds?
\( a) \quad \) \(w \leq 20 \)
\( b) \quad \) \(w < 20 \)
\(c) \quad \) \(w=20\)
\( d) \quad \) \(w \geq 20 \)
\( \text{Answer/Explanation}\)
\(Q22.\:\) If \(xy<0\), which is True?
\( a) \quad \) \(x>0\) and \(y>0\)
\( b) \quad \) \(x<0\) and \(y<0\)
\(c) \quad \) \(x<0\) and \(y>0\)
\( d) \quad \) All are false
\( \text{Answer/Explanation}\)
\(Q23.\:\) If \(x<z\) and \(a<0\) then which statement is true.
\( a) \quad \) \(\frac{x}{a} < \frac{z}{a}\)
\( b) \quad \) \(\frac{x}{a} > \frac{z}{a}\)
\(c) \quad \) \(\frac{x}{a} \leq \frac{z}{a}\)
\( d) \quad \) \(\frac{x}{a} \geq \frac{z}{a}\)
\( \text{Answer/Explanation}\)
\(Q24.\:\) \(5x-7y \leq c\), and \(\left(0,0\right)\) satisfy the inequality then which of the following is true.
\( a) \quad \) \(c \leq 0\)
\( b) \quad \) \(c \geq 0 \)
\(c) \quad \) \(c <0 \)
\( d) \quad \) \(c >0\)
\( \text{Answer/Explanation}\)
\(Q25.\:\) If \(4x-9y \geq c \) and \(z<0\), \(\left(0,0\right)\) satisfy the inequality then which of the following is true.
\( a) \quad zc \leq 0 \)
\( b) \quad zc \geq 0\)
\(c) \quad zc <0\)
\( d) \quad zc >0\)
\( \text{Answer/Explanation}\)
\(Q26.\:\) If the length of a rectangle is \(9\) meters more than its width and the area is at most \(162 m^2\), which of the following inequalities best represents this relationship, where \(l\) is the length and \(w\) is the width?
\( a) \quad lw \leq 162\)
\( b) \quad lw \geq 162 \)
\(c) \quad lw < 162\)
\( d) \quad lw > 162\)
\( \text{Answer/Explanation}\)
\(Q27.\:\) The base of a triangle is \(7 m\) more than its height. If the area of the triangle is at most \(84 m^2\), which of the following inequalities represents this situation, where \(b\) is the base and \(h\) is the height?
\( a) \quad \) \(bh < 84\)
\( b) \quad \) \(h(h+7) \leq 168 \)
\(c) \quad \) \(\frac{1}{2}bh = 84\)
\( d) \quad \) \(h(h+7) \leq 84 \)
\( \text{Answer/Explanation}\)
\(Q28.\:\) An AI company charges a flat fee of \($20\)/month plus an additional \($0.10\) per token used. If the total monthly cost must not exceed \($100\), which of the following inequalities represents this situation, where \(t\) is the number of tokens used?
\( a) \quad \)\(20+0.10t\leq 100\)
\( b) \quad \) \(20+0.10t\geq 100\)
\(c) \quad \) \(0.10+20t\leq 100\)
\( d) \quad \) \(0.10+20t\geq 100\)
\( \text{Answer/Explanation}\)
\(Q29.\:\) Ethan wants to buy some pens and pencils. Each pen costs \($5\), and each pencil costs \($3\). If he does not want to spend more than \($70\), which of the following inequalities represents this situation, where \(p\) is the number of pens and \(c\) is the number of pencils he buys?
\( a) \quad \) \(5p+3c≤70\)
\( b) \quad \) \(5p+3c≥70\)
\(c) \quad \) \(5p−3c≤70\)
\( d) \quad \) \(3p+5c≤70\)
\( \text{Answer/Explanation}\)
\(Q30.\:\) Umar is creating a math worksheet for his students. Each question is worth 5 marks or 3 marks. If he wants the total score of the worksheet to be at least 50 marks, which of the following inequalities represents this situation, where \(x\) is the number of 5-mark questions and \(y\) is the number of 3-mark questions?
\( a) \quad \) \(5x+3y≥50\)
\( b) \quad \) \(5x+3y≤50\)
\(c) \quad \) \(5x−3y≥50\)
\( d) \quad \) \(3x+5y≥50\)
\( \text{Answer/Explanation}\)