NTS Quantitative Reasoning: Algebra 2 — Questions and Answers
Question 1: If 2x + 5 = 17, what is the value of x?
- 4
- 5
- 6 (Correct answer)
- 7
Correct answer: 6
2x + 5 = 17 → 2x = 12 → x = 6.
Solving step by step: 2x + 5 = 17. Subtract 5 from both sides: 2x = 12. Divide both sides by 2: x = 6. Verification: 2(6) + 5 = 12 + 5 = 17. Linear equations in one variable are fundamental to NTS quantitative reasoning.
Question 2: What is the value of (a + b)² if a = 3 and b = 4?
- 25
- 36
- 49 (Correct answer)
- 64
Correct answer: 49
(a + b)² = (3 + 4)² = 7² = 49.
(a + b)² = (3 + 4)² = 7² = 49. Alternatively, using the algebraic identity: (a+b)² = a² + 2ab + b² = 9 + 24 + 16 = 49. Both methods give the same answer. Algebraic identities and their applications are regularly tested in NTS.
Question 3: Solve for y: 3y - 9 = 2y + 4
- 11
- 12
- 13 (Correct answer)
- 14
Correct answer: 13
3y - 9 = 2y + 4 → 3y - 2y = 4 + 9 → y = 13.
Solving: 3y - 9 = 2y + 4. Subtract 2y from both sides: y - 9 = 4. Add 9 to both sides: y = 13. Verification: 3(13) - 9 = 39 - 9 = 30; 2(13) + 4 = 26 + 4 = 30. Both sides equal 30. Equations with variables on both sides are common in NTS algebra.
Question 4: If x² - 9 = 0, what are the possible values of x?
- ±2
- ±3 (Correct answer)
- ±4
- ±9
Correct answer: ±3
x² - 9 = 0 → x² = 9 → x = ±3.
x² - 9 = 0 can be solved by: Method 1: x² = 9, so x = ±√9 = ±3. Method 2: Factor as difference of squares: (x+3)(x-3) = 0, giving x = -3 or x = 3. The difference of squares factoring pattern (a² - b² = (a+b)(a-b)) is frequently tested in NTS algebra.
Question 5: What is the sum of the first 10 natural numbers?
- 45
- 50
- 55 (Correct answer)
- 60
Correct answer: 55
Sum = n(n+1)/2 = 10(11)/2 = 55.
The sum of the first n natural numbers is given by the formula S = n(n+1)/2. For n = 10: S = 10 × 11 / 2 = 110/2 = 55. This can also be verified by adding: 1+2+3+4+5+6+7+8+9+10 = 55. This formula, attributed to Gauss, is a standard NTS mathematics topic.
Question 6: Simplify: 5(2x - 3) + 4x
- 14x - 15 (Correct answer)
- 14x - 3
- 10x - 15
- 14x + 15
Correct answer: 14x - 15
5(2x - 3) + 4x = 10x - 15 + 4x = 14x - 15.
Step 1: Distribute 5 across (2x - 3): 5 × 2x = 10x, 5 × (-3) = -15. So 5(2x-3) = 10x - 15. Step 2: Add 4x: 10x - 15 + 4x = 14x - 15. Combining like terms (10x + 4x = 14x) gives the final answer: 14x - 15. Simplification using distribution is a core NTS algebra skill.
NTS Quantitative Reasoning: Algebra 2
If 2x + 5 = 17, what is the value of x?