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If ☉ denotes a mathematical operation, does
x☉y=y☉x for all x and y?

(1) For all x and y, x☉y = 2(x² + y²).
(2) For all y, 0☉y = 2 y²

Highlight to see answer: A

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The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?

(A) 10,100
(B) 10,200
(C) 15,050
(D) 20,050
(E) 20,100

Highlight to see answer: E

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If p,q,r, and s are nonzero numbers, is (p – 1)(q – 2)²(r – 3)³(s – 4)4 ≧ 0?

(1) q > 2 and s > 4
(2) p > 1 and r > 3

Highlight to see answers: B

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Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle?

(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3

Highlight to see answer: D

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Your study guide outlines a really great study plan. After scoring a 650 on my first attempt, I followed all of your tips and techniques and managed to score a 750 only one month later!
- David Chu

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