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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.

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
_________________

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.

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.

If you are flipping the coin 4 times, what is the probability of landing on head two times?

A. 3/5 B. 4/5 C. 3/7 D. 4/7 E. 3/8

==> Probability=Want/Total. Total=since the number of ways when throwing the coins each becomes head or tail 2 times, you get 2*2*2*2=16. Want=if it lands on head 2 times, it lands on tail 2 times, so you get 4!/2!2!=6. Thus, the probability=6/16=3/8.

There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. If you take out 2 apples from the bag, what is the probability that 1 apple selected is rotten?

A. 1/3 B. 1/4 C.2/5 D. 3/5 E.1/7

==> From probability=want/total, want=selecting one rotten apple and one good apple, and total=selecting 2 of 4 apples, so you get probability=4C1*1C1/5C2=(4)(1)/(5*4/2!)=4/10=2/5.

When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?

A. 30hrs B. 33hrs C. 35hrs D. 37hrs E. 40hrs

==> For work rate questions, you solve “together and alone” reciprocally. It takes A 14hrs alone, and if you set the hours it took B to work alone as B hrs, from (1/14)+(1/B)=1/10 and 1/B=(1/10)-(1/14)=1/35, you get B=35.

In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2), and D(2,2). If the line which passes through an origin bisects the area of the rectangle ABCD, what is the slope of the line?

A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 1/6

Attachment:

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The line should pass through the center (3,1) of the square ABCE. Thus its slope is 1/3.

An alarm of a certain clock rings every 20 minutes. If the clock's alarm first rings at 15:20, when will the 12th alarm of the clock ring? A. 17:30 B. 18:00 C. 18:30 D. 19:00 E. 19:30

=>The third alarm rings at 16:00, the sixth alarm rings at 17:00. Thus every third alarm rings every hour on the hour. The 12th alarm rings at 19:00.