1. if the ratio of x to y in the rectangle above is 2:3, which of the following represents twice the area of the rectangle?
(A) x^2/3 cm^2 (B) 3x^2 cm^2 (C) 6x^2 cm^2 (D) 6xy cm^2 (E) 9x^2 cm^2
2. in how many different ways can three men and women be arranged in a line so that the men and the women alternate?
3. if all of the books on a shelf with fewer than 45 books were put into piles of five books each, no books would remain. if the same books were put into piles of seven books each, two books would remain. what is the greatest number of books that could be on the shelf?
4. if a and b are positive integers, w hat is the smallest value of a+b for which 2a+3b is divisible by 24?
(A) x^2/3 cm^2 (B) 3x^2 cm^2 (C) 6x^2 cm^2 (D) 6xy cm^2 (E) 9x^2 cm^2
2. in how many different ways can three men and women be arranged in a line so that the men and the women alternate?
3. if all of the books on a shelf with fewer than 45 books were put into piles of five books each, no books would remain. if the same books were put into piles of seven books each, two books would remain. what is the greatest number of books that could be on the shelf?
4. if a and b are positive integers, w hat is the smallest value of a+b for which 2a+3b is divisible by 24?