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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.

\((\frac{1}{7})+(\frac{1}{8})+(\frac{1}{9})\) 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).

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<-4, 4<k B. -4<k<4 C. k<-3, 5<k D. -3<k<5 E. k<-2, 8<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.

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.

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.

If two integers x and y such x>y are selected at random between -8 and 11, inclusive, how many cases are possible?

A. 150 B. 180 C. 190 D. 210 E. 240

==> Since two integers from -8 to 11 are being randomly selected and x>y, you use combination. Thus, the number of integers from -8 to 11 becomes 11-(-8)+1=20, so 20, then 20C2=(20)(19)/2!=190.

Which of the following points reflect to y=-x at (-3,2)?

A. (-2, 3) B. (2,-3) C. (3,2) D. (3,-2) E. (2,3)

==> In order to become symmetrical to y=-x, you need to substitute –y value on x coordinate, and –x value on y coordinate. Thus, you get (-3,2)-->(-2,3).

5 people including A and B line up in a row. How many possible cases are there such that at least one person stands between A and B?

A. 24 B. 36 C. 48 D. 60 E. 72

==> Since it is the number of cases such that at least one person stands between A and B when 5 people are lined up in a row, you need to subtract the number of cases where A and B stands next to each other from the total number of cases. Then, you get ABCDE-(AB)CDE, which becomes 5!-4!(2)=72. You get 4!(2) because there are cases where A and B switch the order in the line.

Therefore, the answer is E. Answer: E
_________________

==> From 13^1=~3, 13^2=~9, 13^3=~7, 13^4=~1, the units digit has a period of 3-->9--->7--->1--->3… Thus, from 1386=13^4(21)+2, the numerical index has a period of 4, and so the units digit of 13^2 becomes the same, which is ~9. Therefore, the answer is E.