Questions and Answers
What is the least common multiple of 9 and 12?
36
What is the greatest common divisor of 30 and 75?
15
19 / 7 (solve for the quotient and remainder)
quotient 2, remainder 5
-32 / 3 (solve for the quotient and remainder)
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What is the prime factorization of 12?
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(10/7)*( -1/3) =
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(3/10) / (7/13) =
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Simplify the √24
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(√5)/(√15) =
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(3²)(3⁴) =
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(y³)(y⁻¹) =
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T³ / t⁸ =
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(2³)(3³) =
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(3/4)² =
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(2⁵)² =
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F(x) = 2x / (x-6) Find the domain of f (all permissible inputs of x)
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On a circle, points A and C have the angle 50°. The radius length is 5. What is the length of points A to C?
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On a circle, a piece is cut that has an angle of 50°, where the radius length is 5. What is the area of the pie slice?
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What is the probability of rolling a 3 twice on a six-sided die?
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From a box of 10 lightbulbs you remove 4. How many different sets of 4 lightbulbs could you remove?
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Study Notes
Least Common Multiple and Greatest Common Divisor
- Least common multiple (LCM) of 9 and 12 is 36.
- Greatest common divisor (GCD) of 30 and 75 is 15.
Division with Quotients and Remainders
- For the division of 19 by 7, the quotient is 2, and the remainder is 5.
- For the division of -32 by 3, the quotient is -11, and the remainder is 1.
Prime Factorization and Simplification
- Prime factorization of 12 is expressed as (2)(3)(3) or (2²)(3).
- The result of (10/7) * (-1/3) simplifies to -10/21.
- The division (3/10) / (7/13) gives the result of 39/70.
- Simplifying √24 leads to 2√6, since √4 is 2 and √6 remains.
- (√5)/(√15) simplifies to √(1/3).
Exponentiation
- (3²)(3⁴) equals 3⁶, which is 729.
- The multiplication (2³)(3³) results in 6³, equivalent to 216.
- (3/4)² simplifies to 9/16, represented as 3²/4².
- Squaring (2⁵) gives 2¹⁰, which equals 1,024.
Functions and Domains
- The function f(x) = 2x / (x-6) has a domain of all real numbers except 6, as division by zero is undefined.
Circle Geometry
- For points A and C on a circle with a radius of 5 and an angle of 50°, the length between points A and C is approximately 4.4.
- The area of a pie slice with the same radius and angle measurement of 50° is approximately 10.9.
Probability and Combinations
- The probability of rolling a 3 twice on a six-sided die is 1/36, calculated as (1/6) * (1/6).
- The number of different sets of 4 lightbulbs removed from a box of 10 is 210, determined using combinations: (10)(9)(8)(7) / (4)(3)(2)(1).
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Description
Test your skills with these GRE math practice questions. The quiz covers various topics including least common multiples, greatest common divisors, and divisions with quotients and remainders. Perfect for anyone preparing for the GRE math section.
