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Numbers - Common Sense

For COMPETITION
Number of Total Problems: 9.
FOR PRINT ::: (Book)

Problem Num : 1

From : NCTM

Type: Understanding

Section:Numbers

Theme:None
Adjustment# :

Difficulty: 1

Category Common Sense

Analysis

Solution/Answer

Problem Num : 2

From : NCTM

Type: None

Section:Numbers

Theme:Case Devision
Adjustment# :

Difficulty: 1

Category Common Sense

Analysis

Solution/Answer

Problem Num : 3

From : NCTM

Type: None

Section:Numbers

Theme:None
Adjustment# :

Difficulty: 1

Category Common Sense

Analysis

Solution/Answer

Problem Num : 4

From : NCTM

Type: None

Section:Numbers

Theme:None
Adjustment# :

Difficulty: 1

Category Common Sense

Analysis

Solution/Answer

Problem Num : 5

From : NCTM

Type: Complex

Section:Numbers

Theme:Num of Equations
Adjustment# :

Difficulty: 2

Category Common Sense

Analysis

Solution/Answer

Problem Num : 6

From : NCTM

Type: Application

Section:Numbers

Theme:Case Devision
Adjustment# :

Difficulty: 1

Category Common Sense

Analysis

Solution/Answer

Problem Num : 7

From : AMC10

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

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

Category Common Sense

Analysis

Solution/Answer
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 $2366div 26=oxed{mathrm{(B)} 91}$ .

Answer:

Problem Num : 8

From : AMC10

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

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

Category Common Sense

Analysis

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

Answer:

Problem Num : 9

From : AMC10B

Type:

Section:Numbers

Theme:
Adjustment# : 0

Difficulty: 1

'
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?

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

Category Common Sense

Analysis

Solution/Answer
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 $oxed{C}$

Answer:

Array ( [0] => 3688 [1] => 3691 [2] => 3694 [3] => 3699 [4] => 3707 [5] => 3716 [6] => 7769 [7] => 7788 [8] => 8115 ) 9