Quantitative Reasoning: Algebra Flashcards

If 2x + 5 = 17, what is the value of x?

Answer: 6

2x + 5 = 17 → 2x = 12 → x = 6.

What is the value of (a + b)² if a = 3 and b = 4?

Answer: 49

(a + b)² = (3 + 4)² = 7² = 49.

Solve for y: 3y - 9 = 2y + 4

Answer: 13

3y - 9 = 2y + 4 → 3y - 2y = 4 + 9 → y = 13.

If x² - 9 = 0, what are the possible values of x?

Answer: ±3

x² - 9 = 0 → x² = 9 → x = ±3.

What is the sum of the first 10 natural numbers?

Answer: 55

Sum = n(n+1)/2 = 10(11)/2 = 55.

Simplify: 5(2x - 3) + 4x

Answer: 14x - 15

5(2x - 3) + 4x = 10x - 15 + 4x = 14x - 15.

Find the value of x: x/4 + 3 = 7

Answer: 16

x/4 + 3 = 7 → x/4 = 4 → x = 16.

If a = 2, b = -3, what is the value of a² + b² - 2ab?

Answer: 25

a² + b² - 2ab = (a-b)² = (2-(-3))² = 5² = 25.

What is the product of (x + 3)(x - 3)?

Answer: x² - 9

Using the identity (a+b)(a-b) = a² - b²: (x+3)(x-3) = x² - 9.

Solve the simultaneous equations: x + y = 10 and x - y = 4

Answer: x=7, y=3

Adding both equations: 2x = 14, so x = 7. Substituting: 7 + y = 10, so y = 3.

If 4^x = 64, what is the value of x?

Answer: 3

64 = 4³, so 4^x = 4³, therefore x = 3.

What is the LCM of 12 and 18?

Answer: 36

LCM of 12 and 18: 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 36.