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.

The probability which event E occurs is 0.7 and the probability which event F occurs is 0.3. When event E and event F are independent, what is the range including the probability that neither E occurs nor F occurs? A. 0.01~0.1 B. 0.1~0.2 C. 0.2~0.4 D. 0.4~0.6 E. 0.6~0.8 ==> It is about the probability that event E and F don’t occur. Then, (1-0.7)(1-0.3)=(0.3)(0.7)=0.21 is derived, which includes C. Answer: C

Which of the following options is the smallest？ A. -33% B. -3/10 C. -1/3 D. -0.3333 E. -0.333 A. -33%=-0.33 B. -3/10=-0.3 C. -1/3=-0.3333… D. -0.3333 E. -0.333 Hence, amongst them, C is the smallest. Answer: C

There are a bunch of buildings and their building numbers are all even numbers. If the numbers are 312 between 590 inclusive, what is the number of buildings? A. 139 B. 140 C. 141 D. 142 E. 143 ==> The number of consecutive even numbers of odd numbers=(the last term+the first term) )/2 +1. That is, (590-312)/2 +1=139+1=140. That is, (590-312)/2 +1=139+1=140 and the answer is B. Answer: B

4^-^4/16^-^3=? A. 4 B. 1/4 C. 8 D. 1/8 E. 16 ==> 4^-^4=(2^2)^-^4=2^-^8 and 16^-^3=(2^4)^-^3=2^-^1^2 is derived. Then, 4^-^4/16^-^3=2^-^8/2^-^1^2=2^-^8^-^(^-^1^2^)=2^4=16. Hence, the answer is E. Answer: E

There is a sequence an for a positive integer such that a 3 =a 1 +a 2 , a 4 =a 3 +a 2 +a 1 , a n =a n-1 +a n-2 +a n-3 +….+a 2 +a1. If a n =p, a n+2 =? A. 2p B. 4p C. 8p D. 16p E. 24p ==> Since a n =a n-1 +a n-2 +a n-3 +….+a 2 +a 1 =p, a n+1 =a n + a n-1 +a n-2 +a n-3 +….+a 2 +a 1 =p+p=2p a n+2 =a n+1 +a n +a n-1 +a n-2 +a n-3 +….+a 2 +a 1 =2p+p+p=4p. Hence, the answer is B. Answer: B

(1/7!)-(1/8!)=? A. 1/6! B. 1/7! C. 7/8! D. 8/7! E. 7/6! ==> As 8!=8(7!), (1/7!)-(1/8!)=(1/7!)-(1/8!)=8/8(7!)-1/7!=(8/8!)-(1/8!)=(8-1)/8!=7/8! is derived. Hence, the answer is C. Answer: C

If x=-1 and n is the sum of the first 100 prime numbers, what is the value of x^n+x^n^+^1+x^n^+^2 ? A. -2 B. -1 C. 0 D. 1 E. 2 ==> From n=2+3+5+…….+p, prime is all odd numbers apart from 2. Then, n=2+99 odd numbers=2+odd=odd is derived. And x^n+x^n^+^1+x^n^+^2=(-1)^o^d^d+(-1)^e^v^e^n+(-1)^o^d^d=-1+1-1=-1 . Hence, the answer is B. Answer: B

(√3+√2)/(√3-√2) is approximately between which two numbers? A. 3 and 4 B. 4 and 5 C. 5 and 8 D. 9 and 11 E. 11 and 13 ==>From √3+√2/√3-√2=(√3+√2)^2/(√3-√2)( √3+√2)=3+2+2√6/3-2=5+2√6=5+2(2.xxx)=9.xxx , the answer is D. Answer: D

If sphere A’s volume is 64 times of sphere B’s volume, sphere A’s surface area is how many times of sphere B’s surface area? A. 4 B. 8 C. 12 D. 16 E. 32 ==> Since sphere A’s volume is 64 times of sphere B’s volume, sphere A’s length is Sphere A’s 3√64 times of sphere B’s length, in other words, 3√4^3=4 . However, since the ratio of the surface area is equal to the square of ratio of the length, you get 4^2=16, hence 16 times. Therefore, the answer is D. Answer: D

If rs>0, which of the following cannot be true? A. r>0 B. s>0 C. r+s>0 D. r+s With 0 in the middle, r and s has to be at the same place, E. r<0<s is impossible. Therefore, the answer is E. Answer: E