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 (1+x)y=y, which of the following must be true? A. x=-1 or y=0 B. x=0 or y=0 C. x=1 or y=1 D. x=-1 or y=-1 E. x=0 or y=1 From y+xy=y, we get xy=0. Hence, the correct answer is B.

A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)? A. 2 B. 3/2 C. 5/3 D. 8/5 E. 13/8 Ans: If we substitute directly, the answer comes out to be D.

What is the units digit of 3^66? A. 1 B. 3 C. 5 D. 7 E. 9 ANS: From 3^1=3, 3^2=9, 3^3=27, 3^4=81, the unit digit repeats in 3-->9-->7-->1-->3. Then, from 3^66=3^(4(16)+2), the unit digt is same as that of ^2. Hence, the answer is 9 and the correct answer choice is E.

Which of the following is closest to (10^19-10^3)/(10^17+1)? A. 0.01 B. 0.1 C. 0.2 D. 1 E. 10 ANS: We get (10^17-10^3)/(10^17+1)≒(10^19)/(10^17)=1/100=0.01. Hence, the correct answer is A.

Which of the following is closest to (10!-9!)/(10!+9!)? A. 0.01 B. 0.1 C. 0.2 D. 1 E. 10 ANS: (10!-9!)/(10!+9!)=(10-1)9!/(10+1)9!≒9/11=1. Hence, the correct answer is D

What is the scope including 1/21+1/12+1/13+......+1/30? A 1/6~1/5 B. 1/5~1/4 C. 1/4~1/3 D. 1/3~1/2 E. 1/2~1 ANS: The sum of sequence is determined by the first and the last number. So, 1/3=10/30<1/21+1/12+1/13+......+1/30<10/21<10/20=1/2. The correct answer is D

8√4n=(4√2)^8, n=? A. 4^8 B. 4^10 C. 4^12 D. 4^16 E. 4^32 ANS: D

What is the prime factors’ number of 24? A. 2 B. 3 C. 4 D. 5 E. 6 ANS: From 24=3(2^3), we get 2,2,2 and 3. Hence, the number of prime factors is 4.

a is an integer greater than 19 but less than 31, b is an integer greater than 29 but less than 41, what is the range of a/b? A. 1/4 B. 1/2 C. 3/4 D. 1 E. 5/4 ANS: From 20≤a≤30 and 30≤b≤40, we get 1/2=20/40≤a/b≤30/30=1. Hence, range=Max-min=1-1/2=1/2 and the correct answer is B.

What number is 72 more than three-fourth of itself? A. 138 B. 225 C. 288 D. 324 E. 336 ANS: From n=72+(3n/4), n/4=72, n=72(4)=288 Hence, the correct answer is C