DSAT Math Algebra 3 — Questions and Answers
Question 1: A store sells pens for $1.50 each and notebooks for $3.00 each. Maria spent $18.00 buying a total of 8 items. How many pens did she buy?
- 2
- 4 (Correct answer)
- 6
- 3
Correct answer: 4
Let p = pens and n = notebooks; p + n = 8 and 1.5p + 3n = 18, solving gives p = 4.
Question 2: Which expression is equivalent to (3x² + 5x - 2) - (x² - 3x + 4)?
- 2x² + 8x - 6 (Correct answer)
- 2x² + 2x + 2
- 4x² + 2x - 6
- 2x² + 8x + 2
Correct answer: 2x² + 8x - 6
Distributing the minus sign and combining like terms: (3-1)x² + (5+3)x + (-2-4) = 2x² + 8x - 6.
Question 3: If 2(a + b) = 14 and a - b = 1, what is the value of a?
- 4 (Correct answer)
- 3
- 5
- 6
Correct answer: 4
From the first equation a + b = 7; adding a - b = 1 gives 2a = 8, so a = 4.
Question 4: The function g(x) = -2x + 7 represents a line. What is the x-intercept?
- (7, 0)
- (3.5, 0) (Correct answer)
- (0, 7)
- (0, 3.5)
Correct answer: (3.5, 0)
Set g(x) = 0: -2x + 7 = 0 → x = 3.5, so the x-intercept is (3.5, 0).
Question 5: Which inequality is represented by a dashed line with slope -1 and y-intercept 4, shaded below the line?
- y ≤ -x + 4
- y < -x + 4 (Correct answer)
- y > -x + 4
- y ≥ -x + 4
Correct answer: y < -x + 4
A dashed line means strict inequality, and shading below means y is less than the line, giving y < -x + 4.
Question 6: If 4^(x+1) = 64, what is the value of x?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Since 64 = 4³, we have 4^(x+1) = 4³, so x + 1 = 3 and x = 2.
Question 7: A quantity decreases from 200 to 50. By what percentage did it decrease?
- 25%
- 50%
- 75% (Correct answer)
- 150%
Correct answer: 75%
Percent decrease = (200 - 50)/200 × 100 = 150/200 × 100 = 75%.
DSAT Math Algebra 3
A store sells pens for $1.50 each and notebooks for $3.00 each.
Maria spent $18.00 buying a total of 8 items.
How many pens did she buy?