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.

5.1.png The table shown above represents the relationship of the working hours and the number of 20 employees who participate in the project. What is the median working hour of the 20 employees? A. 9.5 B. 10.0 C. 10.5 D. 11.0 E. 11.5 ==> The median working hour of 20 employees is the average of 10th and 11th working hours. In other words, median working hour=(10+11)/2=10.5. The answer is C. Answer: C

5.2.png If two circles have the same center and the larger circle’s area is 16π , what is the smaller circle’s area? A. π B. 4π C. 9π D. 12π E. 16π ==> The area of the larger circle= 16π=πr^2 , so r=4. Since width=1, you get 4-1=3, and the area of the smaller circle= 3^{2π}=9π . The answer is C. Answer: C

If x+y=3 and x^2+y^2=7 , then xy=? A. -2 B. -1 C. 0 D. 1 E. 2 ==> You get (x+y)^2=x^2+y^2+2xy , and if you substitute this, from 3^2=7+2xy , you get 2xy=2, and xy=1. Therefore, the answer is D. Answer: D

(\frac{1}{7})+(\frac{1}{8})+(\frac{1}{9}) is in between? A. (\frac{1}{6}) and (\frac{1}{5}) B. (\frac{1}{5}) and (\frac{1}{4}) C. (\frac{1}{4}) and (\frac{1}{3}) D. (\frac{1}{3}) and (\frac{1}{2}) E. (\frac{1}{2}) and 1 ==>The sum of consecutive reciprocal numbers is decided by the first and the last number. In other words, you get (1/9)+(1/9)+(1/9)< (1/7)+(1/8)+(1/9)< (1/7)+(1/7)+(1/7), and if you reorganize this, from =1/3=3/9=(1/9)+(1/9)+(1/9)<(1/7)+(1/8)+(1/9)<(1/7)+(1/7)+(1/7)=3/7<3/6=1/2, you get between (1/3) and (1/2). The answer is D. Answer: D

In the xy-plane, a triangle T is formed by x-axis, y-axis, and the line with equation y=4x+k. If the area of the triangle T is smaller than 2, what is the range of k? A. k Since y=4x+k passes through (0,k) and (-k/4,0), from the area of the triangle=(1/2)k(k/4)<2, you get k2<16, k2-16<0, (k-4)(k+4)<0, -4<k<4. The answer is B. Answer: B

If a prime number m can be expressed as 2^n-1 , where n is a positive integer, which of the following can be the value of m? A. 11 B. 15 C. 31 D. 63 E. 97 ==> If n=5, you get 2^5-1=31 . The answer is C. Answer: C

A store currently charges the same price per pound of salad. If the current price per pound were to be increased by $0.2, 0.5 pound smaller salad could be bought for $9. What is the current price of salad per pound? A. $1.6 B. $1.7 C. $1.72 D. $1.8 E. $1.84 ==> If you set the price of the salad per pound as $p, for n pounds, you get np=(n-0.5)(p+0.2)=9. From np=np+0.2n-0.5p-0.1, if you substitute 0.2n=0.5p+0.1, and n=2.5p+0.5, you get p=1.8. The answer is D. Answer: D

If x^2=√3 , then x^8 =? A. 2 B. 2√3 C. 4 D. 3√3 E. 9 ==> From x^8=(x^2)^4=(√3)^4=9 , the answer is E. Answer: E

For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder? A. 0 B. 3 C. 5 D. 6 E. 9 ==>From 12n=15Q+r, 12 and 15 are the multiples of 3, so remainder=r must also be the multiple of 3. Therefore, 5 cannot be the remainder. The answer is C. Answer: C

G(x) is the greatest integer less than or equal to x and L(x) is the least integer greater than or equal to x. When x is not an integer, which of the following is the value of L(x)-G(x)? A. -2 B. -1 C. 0 D. 1 E. 2 ==> You get G(x)=round down and L(X)=round up. Then, x≠integer, so if you substitute x=1.2, you get L(1.2)-G(1.2)=2-1=1. The answer is D. Answer: D