A 4 min read Question: Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the...

A 3 min read Question: If m = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? A. c, m, w B. c, w, m C. m, w, c D. w, c, m E. w, m, c Solution Section: Translate the...

A 4 min read Question: From the consecutive integers (-10) to (10) inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers? Options: A....

A 4 min read Question: What values of x have a corresponding value of y that satisfies both xy > 0 and xy = x + y ? Options: A. x <= 1 B. -1 < x <= 0 C. 0 < x <= 1 D. x > 1 E. All real numbers Solution Section...

A 4 min read Question: The product of 3305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of...

A 5 min read Question: From a committee of 25 legislators, n members formed a task force. Each member of the task force sent a report to each committee member who was not on the task force. If a letter was sent in response to...

A 4 min read Question: By how much does the larger root of the equation 2x² + 5x = 12 exceed the smaller root? Options: (A) 5/2 (B) 10/3 (C) 7/3 (D) 14/3 (E) 11/2 Solution section: Solution: Translate the problem requirements:...

A 4 min read Question: For each positive integer n, p(n) is defined to be the product of the digits of n. For example, p(724) = 56 since 7 × 2 × 4 = 56. Which of the following statements must be true? I. p(10n) = p(n) II. p(n+1)...

A 4 min read If n = 9! – 6^4, which of the following is the greatest integer k such that 3^k is a factor of n? A. 1B. 3C. 4D. 6E. 8 Solution: Translate the problem requirements: We need to find the greatest integer k such...

A 4 min read Question: The number sqrt(63-36sqrt(3)) can be expressed as x + y sqrt(3) for some integers x and y. What is the value of xy ? Options: A. – 18B. -6C. 6D. 18E. 27 Solution We found that (\sqrt{63-36\sqrt{3}} =...