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Which of the following are roots of an equation (x^-2)+(2x^-1)-15=0 A. 1/5 and -1/3 B. -1/5 and 1/3 C. 1/5 and 1/3 D. -1/5 and -1/3 E. -5/2 and -1/3

*ANS: If we multiply both sides by x^2, we get 1+2x-15x^2=0, (15x^2)-2x-1=0, (3x-1)(5x+1)=0. Hence, x=1/3 or -1/5, and the correct answer is B.
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There are 7 red balls and 5 blue balls in a jar. If 3 balls are selected from the jar, what is the probability that 3 balls selected are red balls? A. 19/44 B. 5/44 C. 3/41 D. 13/44 E. 7/44

*ANS: From 7C3/12C3=7/44, the correct answer is E.
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If a=-1, which of the following is(are) true? I. a^a=-|a| II. a^0=-a^-1 III. |a|=a A. I only B. II only C. III only D. I & II only E. I , II & III only

*ANS: From (-1)0=1, (-1)-1=-1, |-1|=1, the correct answer is D.
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Which of the following points is symmetric with y=x at (-1,-2)? A. (-2,-1) B. (-2,1) C. (2,1) D. (-1,-2) E. (-1,2)

ANS: If the point is symmetric to y=x, we can put y-value to x coordinates and put x-value into y coordinates. Then we get (-1, -2) --> (-2, -1). Hence, the correct answer is A.
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How many factors of 330 are odd numbers greater than 1? A. 3 B. 4 C. 5 D. 6 E. 7

ANS: If we calculate, we get 330=2*3*5*11. We are trying to find odd factors. So we have to find 3*5*11. From (1+1)(1+1)(1+1)=8, we only have to get rid of 1. The answer is 7. Hence, the correct answer is E.
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If ABCD is a square with its side length is 10ft and points P, Q, M are midpoints of AD, AB, and BC, respectively, what is the area of region shaded as above figure? A. 40 B. 45 C. 50 D. 75/2 E. 33

ANS: The area of a triangle CDM is 25 and the area of a triangle APO is 25/2. The sum of areas is 25+(25/2)=75/2. Hence, the correct answer is D.
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If a certain coin is flipped, each of the probabilities that the coin will land heads or tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land twice tails up on the 4 flips? A. 3/8 B. 1/16 C. 1/2 D. 5/8 E. 11/16 ==> Just like HHTT, out of 4 flips, the chances of getting 2 heads and 2 tails is 6 (4!/2!2!=6) in HHTT. If so, the chances of getting HHTT is (1/2)(1/2)(1/2)(1/2)=1/16, and 1/16*6=3/8. Therefore the answer is A. Answer: A
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The revenue from sales items in 1996 increases by x percent, compared in 1995 and the revenue in 1997 decreases by x percent, compared in 1996. If the revenue from sales items in 1997 decreases by 4 percent, compared in 1995, what is the value of x? A. 10 B. 15 C. 20 D. 30 E. 35

==> If the revenue in creased by x% between 1995 and 1996, it is R --> R(1+x%). Since this decreased by x% in 1997, it becomes R(1+x%)(1-x%)=R(1-x^2%^2). However, this means 4% has been decreased in 1997 when compared to 1995, it becomes R --> R(1-4%). For these two be the same, x^2%^2=4%, x^2%=4 should kick in, and if you substitute %=1/100, you get x^2=400 and x=20. Therefore, the answer is C. Answer: C
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[(5√3+3√5)/(√5+√3)]2=? A. √6 B. √15 C. 15 D. √24 E. 6 ==> [(5√3+3√5)/(√5+√3)]2=[√15(√5+√3)/(√5+√3)]2=(√15)2=15 Hence the answer is C. Answer: C
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How many multiples of 3 are there between -40 and 40? A. 13 B. 17 C. 23 D. 26 E. 27

==> The number of multiples of three between 1 and 40 is 13, and the number of multiples of 3 between -1 and -40 is also 13. However, since 0 is a multiple of all integers, 13+13+1=27. Hence the answer is E. Answer: E
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If John traveled a trip at a constant rate 20 miles per hour for 30 minutes and at a constant rate 30 miles per hour for the remaining 20 minutes, what is the his average speed, in miles per hour? A. 20miles B. 24miles C. 30miles D. 32miles E. 36miles ==> Average speed=the sum of distances/the sum of hours taken John travelled 10 miles because he travelled at 20 mph for 30 minutes, and also travelled another 10 miles since he travelled at 30mph for 20 minutes. This leads to Average Speed = (10miles+10miles)/(30min.+20min.)=24miles/1hour Therefore, the answer is B.

If x is 8/3 percent of y, y is what percent of x? A. 3/8 B. 37.5 C. 375 D. 3,750 E. 3.75

==> according to ivy approach, from x=(8/3)(1/100)y, y=(something)(1/100)x, we get y=(something)(1/100)(8/3)(1/100)y, if we substitute x into y. If we cancel y from both sides of the equation, we get something=3,750. Hence, the correct answer is D. Answer: D
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John is reading a 50-page book, starting from 1 page. He places a white stick per 3 pages and a black stick per 4 pages. How many pages have neither white sticks nor black sticks? A. 20pages B. 24pages C. 26pages D. 30pages E. 32pages

==> n(3)=the number of pages with white sticks and n(4)=the number of pages with black sticks. If so, n(3U4)=n(3)+n(4)-n(3∩4)=16+12-4=24. However, the question is about the number of pages without white sticks and black sticks, so 50-24=26. C is the answer Answer: C
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