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Kara's math average went down 20% from freshman year to sophomore year. During the same time, her history average went up 8%. If her combined average in the two classes went down 8%, what is the ratio of her history average during her freshman year to her math average during freshman year?
A certain bakery that sells donuts and bagels reported that the revenue from donut sales in 2016 was up 12 percent from 2015 and the revenue from bagel sales in 2016 was down 3 percent from 2015. If total revenues from donut and bagel sales in 2016 were up 2 percent from 2015, what is the ratio of revenues from donut sales to bagel sales in 2015?
A bookstore that sells print books and ebooks reported that revenue from print book sales in 2016 was up 8 percent from 2015 and revenue from ebook sales in 2016 was down 7 percent from 2015. If total revenues from print book sales and ebook sales in 2016 were up 2 percent from 2015, what is the ratio of revenues from print book sales to ebook sales in 2015?
If , which of the following must be true?
I.
II. is negative.
III.
I. is positive.
II.
III. is positive.
III. is positive
The function is defined for each positive three-digit integer by where and are the hundreds, tens, and units digits of respectively. If and are three-digit positive integers such that , then what is the value of ?
If is a positive integer and is divisible by 60, then the largest positive integer that must divide is
If is a positive integer and is divisible by 98, then the largest positive integer that must divide is
If is a positive integer and , which of the following could be a value of ?
If is a positive integer and , which of the following could NOT be a value of ?
If are positive integers such that is a divisor of , and is a multiple of , which of the following is NOT necessarily an integer?
If and are positive integers such that is a multiple of , and is a factor of , which of the following is NOT necessarily an integer?
If , , and are positive integers such that is a factor of , and is a multiple of , which of the following is NOT necessarily an integer?
If is the center of the circle above, what fraction of the circular region is shaded?