Explanation

A and B You can use your on-screen calculator, but it will probably be faster to ballpark on at least some of these—for example, think of \(\sqrt{82}\) as slightly more than 9, or \(\sqrt{34}\)as slightly less than 6. In order to figure out which fractions are greater than one, just figure out if the top part of the fraction is bigger than the bottom part:


A. \(\frac{4(3 + 0.07)}{11.092}\) : : top bigger than 12, bottom smaller, so choice (A) works;
B. \((\sqrt{82}-1.7^2) \div \sqrt{34}\): : top bigger than 6, bottom smaller, so choice (B) works;
C. \(\frac{9978.4 - 0.0083}{101^2}\): : top smaller than 10,000, bottom bigger, so eliminate choice (C);
D. \(\sqrt{143}\times 7^{1/3} \div 24.034\):: top smaller than 24—you might think of it as less than 12 times less than 2—bottom bigger, so eliminate choice (D).

Hence A and B are correct!