Question: If x>0, y>0, and |x| > |y|, which of the following must be true?
Options:
(A) x > y
(B) y^2 > x^2
(C) x^3 > y^2
(D) x < y
(E) x < y
Ans: (A)
CoT: Correct Answer: (E)
Let's go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn't have to be true consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us x > y. Remember that x < 0, so x = |x|, and y is positive, so |y| = y. Thus x > y is the same statement as |x| > |y|, and (A) must be true.
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Question: What is the probability of rolling a nine with two, fair, six-sided dice?
Options:
(A) 1/6
(B) 1/9
(C) 2/13
(D) 1/12
(E) 5/36
Ans: (B)
CoT: There are 4 ways to roll a nine: 3 and 6, 6 and 3, 4 and 5, 5 and 4 with two six-sided dice. There are 6 times 6 = 36 ways to roll two dice. The probability of rolling a 9 is thus 4/36 = 1/9.
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Question: Amanda sees a sale for 30% off all items, she sees a dress on sale that originally cost $50. How much will it cost Amanda to buy the dress after the sale amount of 30% has been take off?
Options:
(A) $40
(B) $35
(C) $50
(D) $65
(E) $15
Ans: (B)
CoT: Final number = original number - 30%(original number) = 50 - 30%(50) = 50 - 15 = $35.
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