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 n is the least common multiple of 18 and 60, which of the following can be the factor of n? I. 24 II. 36 III. 45 A. Ⅰonly B. Ⅱ only C. Ⅲ only D.Ⅰ& Ⅲ only E. Ⅱ&Ⅲ only ==> You get 18=2(3^2) 60=(2^2)(3)(5), and since the least common multiple is the maximum value of the index, and you get n=(22)(32)(5). Therefore, you get I. 24=(2^3)(3) (X) II. 36=(2^2)(3^2) (O) III. 45=(3^2)(5) (O) The answer is Ⅱ&Ⅲ, which is E. Answer: E

(11+1/11)^2-(11-1/11)^2=? A. 2 B. 3 C. 4 D. 5 E. 9 ==> You get (11+1/11)^2-(11-1/11)^2= = 2/11(22)=4. The answer is C. Answer: C

If p is the sum of all odd numbers greater than 0 but less than 50, and q is the sum of all even numbers greater than 0 but less than 50, what is the value of p-q? A. -24 B. 0 C. 1 D. 24 E. 25 ==> Since p=1+3+….+47+49, from q=2+4+…+46+48, the difference between 3+5+…+47+49 (part of p) and q=2+4+..+46+48 is 1 each, so there are 24. Since there is also +1 at the front of p, you get 24+1=25. The answer is E. Answer: E

If set A={a,b,c,d,e}, what is the number of subsets that must include only 3 elements? A. 8 B. 10 C. 12 D. 15 E. 18 ==> You get 5C3=5C2=(5)(4)/2!=10. The answer is b. Answer: B

When 2 dices are tossed, what is the probability that the 2 faced numbers have a difference of 3? A.1/9 B. 2/9 C. 1/3 D. 4/9 E. 1/6 ==> Numerator:(6,3), (5,2), (4,1), (3,6), (2,5), (1,4). Denominator:6*6. Thus, you get 6/6*6=1/6. The answer is E. Answer: E

If f(2x+3)=-6x, f(5)=? A. -6 B. -3 C. -2 D. 3 E. 6 ==> From2x+3=5, you get x=1, and then you get f(5)=-6(1)=-6. The answer is A. Answer: A

If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z? A. 15 B. 20 C. 25 D. 40 E. 47 ==> You get x=4z and y=2z, and the average=(x+y+3z)/3=(4z+2z+3z)/3=3z, so it always needs to be the multiple of 3. Therefore, the answer is A. Answer: A

If $10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars? A. 10,000(1+ )^10 B. 10,000(1+0.08)^5 C. 10,000(1+0.08) D. 10,000(1-0.08)^2 E. 10,000*1.08 ==> if it is invested at 8 percent annual interest and is compounded semiannually, From 10,000(1+8%(1/2))^2*5= 10,000(1+)^10 the answer is A Answer: A

3^11+3^12+3^13=? A. 13(3^11) B. 17(3^11) C. 19(3^11) D. 13(3^10) E. 3^36 ==> 3^11+3^12+3^13=(1+3+3^2)3^11=13(3^11) Answer: A

3 robots can finish the same task in 6hrs, 7hrs, and 8hrs.What is the greatest part of the task that can be finished by two of these robots together in 1 hour? A. 13/42 B. 11/42 C. 42/13 D. 42/11 E. 13/21 ==> Assuming that A, B, and C finishes their tasks in 6hrs, 7hrs, and 8 hrs each, the work rate of A and B are good, and each finished 1/6 and 1/7, so you get 1/6+1/7=13/42. The answer is A. Answer: A