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In the coordinate plane a slope of the line K is 4 times the y-intercept of the line K. What is the x-intercept of the line K? A. -4 B. 4 C. -1/4 D. 1/4 E. 2

ANS: As Y=4mx+m, from 0=4mx+m we get x=-1/4. Hence, the correct answer choice is C.
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When x, y are positive integers, x@y=xy/(x+y). If a, b, and c are positive numbers, what is the value of 1/a@(1/b@1/c)? A. a+b+c B. 1/abc C. 1/(a+b+c) D. 1/(ab+bc+ca) E. 3/abc

ANS: Since (1/b@1/c)=1/(b+c), we get 1/a@(1/b@1/c)=1/(a+b+c). Hence, the correct answer is C.
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8 red card number 1-8 put in one box， 8 blue card number 1-8，put in another box, take one card from each of the box，what is the probability that the number match each other? A. 1/2 B. 1/4 C. 1/8 D. 1/16 E. 1/64

ANS: From (1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(8,8), the probability of the number match each other is 8. Hence, 8C1/(8C1)(8C1)=1/8. So, the correct answer is C.
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In the x- y plane, there are 4 points (0,0), (0,4), (6,4), and (6,0). If these 4 points makes a rectangle, what is the probability that x+y<4? A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 2/5

ANS: As you can see from the diagram below, the correct answer is 1/3. Hence, B is our answer choice.

A has x mailing lists and Company B has y mailing lists. If the total mailing lists’ number combined Company A and Company B is equal to 3 times the mailing lists’ number of Company A, what is the number of mailing lists that both Company A and Company B have, in terms of x and y? A. 2x-y B. y-2x C. 3x+y D. y+2x E. y-3x

ANS: (x-b)+b+(y-b)=3x, x+y-b=3x , therefore b=y-2x. Hence, the correct answer is B.

A larger cube has 27 cubic inch as a volume and in the cube there are 27 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 27 smaller cubes and the surface area of the larger cube, in square inch? A. 54 B. 64 C. 81 D. 108 E. 120

ANS: If we calculate 6*27-6*9=108, D becomes our answer.
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There are two circle-shaped pizzas. The diameter of the smaller pizza is 10 and the larger pizza’s area is 2 times of the smaller pizza’s area, what is the diameter of the larger pizza, in whole number? A. 12 B. 15 C. 18 D. 20 E. 25

ANS: Since √(proportion of area) = proportion of length. If the proportion of area is 2, then we have √2. Hence, the proportion of length becomes approximately 1.5. So, from 10*1.5=15. Thus, the correct answer is B.
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What is the greatest prime factor of 1+2+3+。。。+40? A. 17 B. 29 C. 31 D. 37 E. 41

We can calculate 1+2+3+…..+n=n(n+1)/2. Then, 1+2+3+。。。+40=40(40+1)/2=20(41)=(2^2)(5)(41). Hence, the biggest prime factor is 41 and the correct answer is E.

A ball dropped from a certain height. The height that it reached after rebounding from the floor was 60 percent of the initial height. The height was 292cm when it touched the floor for the third time. What was the initial height? A. 80cm B. 90cm C. 100cm D. 120cm E. 130cm

ANS: If we consider the initial height as x, then from x+2(60%)x+2(60%)^2(x)=292, we get x=100. Hence, the correct answer is C.
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3 years before, dog A’s age was 4 times the age of dog B’s and after 4 years, dog A’s age will be 3 times the age of dog B. What is the difference of dog A’s age and dog B’s now? A. 36 B. 42 C. 54 D. 60 E. 64

ANS: A-3=4(B-3) and A+4=3(B+4), B=17 and A=59. Hence, the correct answer is B.
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The side of a square has the length of 8. What is the area of the region shaded? A. 48-8π B. 48-6 π C. 24+6π D. 16+8π E. 64-8π

ANS: The area of a square whose side is 8 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded The correct answer is A.

If n is the product of the 5 different prime numbers, how many factors n have except 1 and n? A. 20 B. 22 C. 24 D. 30 E. 32 ANS: (1+1)(1+1)(1+1)(1+1)(1+1)=32. Hence, from 32-2=30, we can see that D is the correct answer.
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The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of them is 18, what is the value of a? A. 3 B. 6 C. 9 D. 12 E. 15

ANS: a=2k, b=3k, c=4k, a+b+c=2k+3k+4k=(18)(3), 9k=18(3), k=6. Therefore, a=2k=2(6)=12, and the correct answer is D.
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