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.

When 240n is the square of an integer, what is the least possible value of n? A. 10 B. 15 C. 20 D. 25 E. 30 ==> From 240n=4^2(3)(5)n=integer^2, the least possible value of n becomes (3)(5)=15. The answer is B. Answer: B

When |x|>1 and |x-3|>1, which of the following is contained in the scope of x? A. -0.5 B. 0 C. 0.5 D. 1.5 E. 2.5 ==> |x|>1 becomes x 1, you get x-3 x<2 or 4<x. Then, what satisfies both becomes 1<x<2 or 4<x. The answer is D. Answer: D

The length of a rectangular photograph is 2 longer than the width of the photograph. If the area of the photograph is 35, what is the width? A. 3 B. 4 C. 5 D. 6 E. 7 ==>If width=w, you get length=w+2, and from w(w+2)=35, w^2+2x-35=0, (w+7)(w-5)=0, w=-7,5, you get w=5. The answer is c. Answer: C

There is a sequence An, such that A 1 =1，A 2 =2, and A n+2 =A n+1 +A n +A n-1 +….+A 2 +A 1 . What is the ratio of A 14 to A 11 ? A. 32 B. 16 C. 8 D. 4 E. 2 ==> If A 11 =A 10 +A 9 +A 8 +….+A 2 +A 1 =p, you get A 12 =A 11 +A 10 +A 11 +….+A 2 +A 1 =2p, and from A 13 =4p, A 14 =8p, you get A 14 :A 11 =8p:p=8:1=8. The answer is C. Answer: C

There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together? A. 10min B. 12min C. 15min D. 18min E. 20min ==> For work rate questions, if there is a “together and alone”, you need to solve the question reciprocally. In other words, A: 1,800pg/90mins, B:1,800pg/45mins, C: 1,800pg/30mins, and if you assume A&B&C:1,800pg/t mins, you get (1/90)+(1/45)+(1/30)=(1/t), and from (1+2+3)/90=1/t, you get t=15. The answer is C. Answer: C

When x is divided by 7, the remainder is 3. When x3 is divided by 7, what is the remainder? A. 2 B. 3 C. 4 D. 5 E. 6 ==> For remainder questions, it is important to use direct substitutions. From X=7p+3=3,10,17,…., if you substitute x=3, from x^3=3^3=27=7(3)+6, you get a remainder of 6. Therefore, the answer is E. Answer: E

If n is the product of 3 same prime numbers and 1 different prime number, then how many different factors of n are there? A. 6 B. 8 C. 9 D. 12 E. 18 ==> You get n=(3)(3)(3)(5), which becomes n=3^3*5^1. Thus, the number of factors of n becomes (3+1)(1+1)=8. The answer is B. Answer: B

When n is divided by 4, the remainder is 3. If 3^n+2 is divided by 5, what is the remainder? A. 1 B. 2 C. 3 D. 4 E. 0 ==> You get n=4p+3, which becomes 3^n+2=3^{4p+3}+2=(3^4)^p(3^3)+2=(~1)^p(27)+2=(~1)(27)+2=(~7)+2=~9. Thus, the remainder when it is divided by 5 becomes 4. The answer is D. Answer: D

8.2.png There are 2 circles, 1 big circle and 1 small circle, and they meet at one point. The diameter of the small circle is equal to the radius of the big circle, and the area of the big circle is 14π. What is the area of the small circle? A. 3π B. 3.5π C. 4π D. 4.5π E. 7π ==> Ratio of length^2=Ratio of area, and since the ratio of the length is 2, the ratio of the area becomes 4, so you get 14π/4=3.5π. The answer is B. Answer: B

What is the sum of all digits of 2^{13}5^7? A. 3 B. 4 C. 6 D. 8 E. 10 ==> You get 2^{13}5^7=2^6(2^75^7)=64(10^7)=640,000,000. The sum of the 0's at the back always becomes 0, so you get 6+4=10. The answer is E. Answer: E