DSAT MAth Practice questions – all topics
- Algebra Weightage: 35% Questions: 13-15
- Linear equations in one variable
- Linear equations in two variables
- Linear functions
- Systems of two linear equations in two variables
- Linear inequalities in one or two variables
DSAT MAth and English – full syllabus practice tests
Question Hard
A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?
A\(0 < x \leq 10\)
B\(0 < x \leq 11\frac{2}{3}\)
C\(0 < x \leq 17\frac{1}{2}\)
D\(0 < x \leq 20\)
▶️Answer/Explanation
Ans A
Height of the box: \( h = 60 \)
Length of the box: \( l = 2.5x \) (since length is 2.5 times the width)
The perimeter of the base of a rectangular prism is:
\(
2(l + x) = 2(2.5x + x) = 2(3.5x) = 7x
\)
The total shipping restriction states:
\(
\text{Perimeter of base} + \text{Height} \leq 130
\)
Set up the inequality:
\(
7x + 60 \leq 130
\)
\(7x \leq 70\)
\(x \leq 10\)
Since width (\( x \)) must be positive, we include the lower bound:**
\(
0 < x \leq 10
\)
Question Hard
A business owner plans to purchase the same model of chair for each of the \(\textbf{81} employees\). The total budget to spend on these chairs is \(\textbf{\$14,000}\), which includes a \(\textbf{7\%}\) sales tax. Which of the following is closest to the maximum possible price per chair, before sales tax, the business owner could pay based on this budget?
A\(\textbf{\$148.15}\)
B\(\textbf{\$161.53}\)
C\(\textbf{\$172.84}\)
D\(\textbf{\$184.94}\)
▶️Answer/Explanation
Ans: B
Let \( x \) be the price per chair before tax.
Since the total cost includes a 7% sales tax, the equation is:
\(
1.07 \times 81x = 14000
\)
Solve for \( x \):
\(
x = \frac{14000}{1.07 \times 81}
\)
\(
x = \frac{14000}{86.67}
\)
\(
x \approx 161.53
\)
Question Hard
Ken is working this summer as part of a crew on a farm. He earned \($8\) per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to \($10\) per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least \($270\) for the week?
A.38
B. 33
C 22
D 16
▶️Answer/Explanation with Desmos
Ans C
Calculate earnings from the first 10 hours:
\( 10 \times 8 = 80 \)
Let \( x \) be the additional hours worked at $10 per hour.
Earnings from these hours:
\( 10x \)
Total earnings equation:
\( 80 + 10x \)
Ken saves 90% of his earnings, so the equation for savings:
\( 0.9(80 + 10x) \geq 270 \)
Question Hard
\(y>2x-1\)
\(2x>5\)
Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above?
A y>6
B.y>4
C \(y>\frac{5}{2}\)
D \(y>\frac{3}{2}\)
▶️Desmos
Ans B
From the graph, it is observed that \(y>4\) satisfy the given system of inequalities.