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Maya W.
Grad Student at UT Austin
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SAT II Mathematics Level 2
TutorMe
Question:

Which is larger? a) x = 1/3 b) x = 0.333333 c) neither, both are equivalent.

Maya W.
Answer:

a) is larger; it's infinitely repeating threes all the way down, instead of the truncated threes given in b).

Latin
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Question:

How do you say "give me the book" in Latin? What mood is the word "give"? Identify the cases of the two nouns.

Maya W.
Answer:

Da mihi librum. Da is the imperative mood—it's a command! Liber, libri is singular, accusative, and masculine. It's the direct object in this scenario, so it's accusative; it's second declension, so -um is the proper ending to use. Mihi is dative, because you're giving a book *TO* someone, and that's the most common usage of the dative.

GRE
TutorMe
Question:

There is a circle inscribed within a square of side length s=4. What is the perimeter of a square that has the same area as the circle?

Maya W.
Answer:

The area of the circle is (0.5)*pi*r^2, where r is the radius. r = 2, as the diameter of the circle spans the whole length of the square. Thus, the area of the circle is 2*pi. A square that has an area of 2*pi has a sidelength of s_new = sqrt(2*pi). Thus, the perimeter of the square is 4 * s_new = 4 * sqrt(2*pi), which is approximately equal to 10.03.

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