Linear Inequalities

Linear Inequalities: Level 3 Challenges


If AA is not equal to BB, which of the following is greater?

 First: AAB Second: BAB\text{ First: } \frac{ A } {A-B} \quad \quad \text{ Second: } \frac{ B}{A-B}

Let a,b,c,d,a, b, c, d, and ee be real numbers such that





Which among a,b,c,d,ea,b,c,d,e is the largest and smallest?

Put your answer in the form (largest, smallest). For example, if you think the largest is cc and the smallest is ee, then your answer should be (c,e)(c, e).

Verna decided to sell her collection of books.

To Fred, she sold 2 books, and one fifth of what was left.

Later to Joan she sold 6 books, and one fifth of what then remained.

If she sold more books to Fred than to Joan, what was the least possible number of books in her original collection?

0.33<mn<13 0.33 < \dfrac {m}{n} < \dfrac {1}{3}

Find the smallest positive integer nn such that there exists an integer mm for which the inequality above is fulfilled.

Mary and three other students took a math test. Each of their scores was a non-negative integer. The teacher announced that the average score (of the 4 students) was 20. Mary immediately knew that all of the other three students scored below average.

What is the minimum score that Mary could have gotten to be certain of the above situation?


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