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.

If x and y are integers, what is the least positive number of 24x+15y? A. 1 B. 3 C. 6 D. 9 E. 12 Since 24(2)-15(3)=3, B is the correct answer.

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.

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.

Which of the following is closer to √0.5+√0.05? A. 0.5 B. 0.7 C. 0.9 D. 1.1 E. 1.2 ANS: √0.5+√0.05=approximately √0.49+√0.04=0.7+0.2=0.9. Hence, the correct answer is C.

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.

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.

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. ANS:

What is the sum of 60 consecutive integers from -29 inclusive, in a increasing order? A. -29 B. 29 C. -30 D. 30 E. 60 ANS: (-29)+(-28)+…….+(-1)+0+1+…….+28+29+30=30. Hence, the correct answer is D.