SAT Practice Math Questions (Open-Ended) with 100% correct answers 2024

There c cars in a car service use a total of g gallons of gasoline per week. If each of the cars uses the same amount of gasoline, then, at this rate, which of the following represents the number of gallons used by 5 of the cars in 2 weeks? a) 10cg b) 2g/5c c) 5g/2c d) g/10c e) 10g/c - correct answer E) 10g/c What is the result when 436,921 is rounded to the nearest thousand and then expressed in scientific notation? - correct answer 4.37 x 10^5 The positive integer, n, is not divisible by 7. The remainder when n^2 and the remainder when n is divided by 7 are each equal to k. What is k? a) 1 b) 2 c) 4 d) 6 e) cannot be determined - correct answer 1 Since the positive integer n leaves nonzero remainder k when divided by 7, it can be written as n = (7 times a) + k, where a is a nonnegative integer and k is equal to one of the values 1, 2, 3, 4, 5, or 6. Since n^2 leaves the same nonzero remainder k when divided by 7, it can be written as n = (7 times b) + k, where b is a nonnegative integer and k has the same value. It is also true that n^2 = ((7 times a) + k)^2 = (49 times a^2) + (14 times a times k) + k^2, which can be written as 7 times ((7 times a^2) + 2 times a times k) + k^2. Since n^2 = (7 times b) + k = 7 times ((7 times a^2) + 2 times a times k) + k^2, it follows that k and k^2 leave the same remainder when divided by 7.