Quantitative Reasoning Study Guide (Latest 2024/ 2025 Update) Questions and Verified Answers| 100% Correct| Grade A

Quantitative Reasoning Study Guide (Latest 2024/ 2025 Update) Questions and Verified Answers| 100% Correct| Grade A Q: greatest common factor of a pair of integers Answer: largest factor the pair of integers share. what is the greatest common factor of 36 and 48? 36=(2)(2)(3)(3) 48=(2)(2)(2)(2)(3) they have a common two 2s and one 3 So the GCF is (2)(2)(3)= 12 Q: prime number Answer: integer greater than one that has only 2 factors, itself and one. the number 1 is not considered a prime number because it is divisible only by itself The number 2 is the only even prime number and the smallest Q: prime numbers from beginning Answer: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 Q: prime factors (prime factorization) Answer: expression of the number as the product of its prime factors. work your way up through the prime numbers, starting with 2. Q: what is the prime factorization of 210? Answer: 210=(2)(105) 210=(2)(3)(35) 210=(2)(3)(5)(7) Q: least common multiple Answer: is the smallest number that is multiple of each of the integers. 1). Determine the prime factorization of each integer. 2). Write out each prime number the maximum number of times that it appears in any one of the prime factorizations 3). Multiply those prime numbers together to get the least common multiple of the original integer Q: what is the least common multiple of 6 and 8 Answer: - start by finding the prime factors of 6 and 8 6=(2)(3) 8=(2)(2)(2) - the factor 2 appears three times in prime factorization of 8, while 3 appears as only a single factor of 6. (2)(2)(2)(3)= 24 Q: remainder Answer: what is left over in a division problem Q: the slats of fence are painted three colors, which appear in fixed order, such as red, yellow, blue, red, yellow, blue... If the first slat is red, what color is the 301st slot? Answer: since 3 goes into 300 evenly, whole pattern finished the 300th slat. pattern will start over on the 301st slat. RED Q: every positive number has 2 square roots, one positive one negative Answer: radical symbol (square root symbol) stands for the positive square root only! therefore (radical symbol) square root of 9 = 3 only Q: only like radicals can be added and subtracted from each other Answer: Q: multiply or divide the numbers outside the radical signs, then the numbers inside the radical signs Answer: Q: simplifying radicals Answer: if the number inside the radical is a multiple of a perfect square, the expression can be simplified. square root(72) squareroot(36)squareroot(2) 6 squareroot(2) Q: reciprocals Answer: turn the fraction upside down so numerator becomes denominator. What is the reciprocal of (1/25) ? 25. Q: dividing fractions Answer: multiply by the reciprocal of the number of the fraction that follows the division sign