Topic : Numbers-Common Sense
from: category_eng
1.

2.
Case Devision
3.

4.

5.
Num of Equations
6.
Case Devision
7. '

Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366, how many members are in the League?

mathrm{(A) } 77qquad mathrm{(B) } 91qquad mathrm{(C) } 143qquad mathrm{(D) } 182qquad mathrm{(E) } 286

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8. '

You and five friends need to raise 1500 dollars in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise?

mathrm{(A) } 250qquad mathrm{(B) } 300 qquad mathrm{(C) } 1500 qquad mathrm{(D) } 7500 qquad mathrm{(E) } ...

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9. '

As shown below, convex pentagon ABCDE has sides AB=3, BC=4, CD=6, DE=3, and EA=7. The pentagon is originally positioned in the plane with vertex A at the origin and vertex B on the positive x-axis. The pentagon is then rolled clockwise to the right along the x-axis. Which side will touch the point x=2009 on the x-axis?

unitsize(3mm);defaultpen(linewidth(.8pt)+fontsize(8pt));dotfactor=4;pair A=(0,0), Ep=7*dir(105), B=3*dir(0);pair D=Ep+B;pair ...

ext{(A) } overline{AB}qquad ext{(B) } overline{BC}qquad ext{(C) } overline{CD}qquad ext{(D) } overline{DE}qquad...

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1.
Understanding

2. 9

3.

4. -12

5. 5
Complex

6. 9
Application

7.

Since T-shirts cost 5 dollars more than a pair of socks, T-shirts cost 5+4=9 dollars.

Since each member needs 2 pairs of socks and 2 T-shirts, the total cost for 1 member is 2(4+9)=26 dollars.

Since 2366 dollars was the cost for the club, and 26 was the cost per member, the number of members in the League is 2366div 26=oxed{mathrm{(B)} 91}.


8.

There are 6 people to split the 1500 dollars among, so each person must raise frac{1500}6=250 dollars. Rightarrowmathrm{(A)}
9.

The perimeter of the polygon is 3+4+6+3+7 = 23. Hence as we roll the polygon to the right, every 23 units the side overline{AB} will be the bottom side.

We have 2009 = 23 imes 87 + 8. Thus at some point in time we will get the situation when A=(2001,0) and overline{AB} is the bottom side. Obviously, at this moment B=(2004,0).

After that, the polygon rotates around B until point C hits the x axis at (2008,0).

And finally, the polygon rotates around C until point D hits the x axis at (2014,0).
At this point the side oxed{overline{CD}} touches the point (2009,0). So the answer is oxed{C}