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The figure represents a 5-foot-wide circular walkway that is bounded by two concentric circles. The outer boundary of the walkway is approximately how many feet longer than the inner boundary of the walkway?

A 10

B 15

C 20

D 30

E 40

• A

• B

• C

• D

• E

Answer explanation

The radius of concentric circles differs by 5 , and the circumference differs by 5*2 π =10 π, which is closest to 30. Choose D.

In quadrilateral QRST, the length of RS is less than the length of QT, and RS is parallel to QT.

Quantity A

The length of QR

Quantity B

The length of ST

• A

• B

• C

• D

Answer explanation

It can be seen from the figure that ∠Q is a right angle, and given RS∥QT, it can be deduced that ∠R is also a right angle. It is known that RS < QT, so ST > RQ, choose B.

Quantity A

y

Quantity B

115

• A

• B

• C

• D

Answer explanation

The sum of the internal angles of the hexagon (6-2)*180=720°, subtract 5 x, get y=720-115*5=145°>115°.

In the figure above, if square ABCD has a perimeter of 24, then x=?

• 12

• 10

• 8

• 11

Answer explanation

The perimeter of a square is 24, and the side length is 6

In the right-angled triangle, hypotenuse=10, vertical right-angled side=6, then use Pythagorean number 3:4:5 to get, horizontal right-angled side=8, so x=(6-4)+8= 10.

The two circles in the figure above both have center O. The square is inscribed in the larger circle and circumscribed about the smaller circle. If x is the radius of the larger circle, what is the radius of the smaller circle, in terms of x?

A √2x/6

B √2x/4

C √2x/2

D √2x

E 2√2x

• A

• B

• C

• D

• E

Answer explanation

The diameter of a great circle is 2x, that is, the diagonal of a square is 2x, and the side length of a square is √2x, the radius of the small circle is half the side length of the square, that is √2/2x

A pendulum 36 inches long swings through an angle of x degrees, and its pointed end travels through a distance of 41 inches before swinging back again, as shown in the figure. Which of the following is closest to the value of x?

A 60

B 65

C 70

D 75

E 80

• A

• B

• C

• D

• E

Answer explanation

Substituting into the arc length formula, (x/360)*2π*36=41 , the solution is x≈65.3 , which is closest to 65° .

As shown in the figure, the centers of the two circles are respectively on the circumference of each other, and the radius is 3. What is the perimeter of this figure?

A 4π

B 6π

C 8π

D 10π

E 12π

• A

• B

• C

• D

• E

Answer explanation

Draw the auxiliary line PRS, the two circles pass through the center of each other, PR, PS, RS are all radii, the triangle PRS is an equilateral triangle, and the triangle QRS is also an equilateral triangle, then ∠PRQ and ∠PSQ are both 120 °So PQ superior arc length=2π·3·(360-120)/360=4π,so the overall peripheral arc length=4π·2=8π.

In the figure above the circle has center O, and AB and AD are tangent to the circle. If the degree measures of angles ABC and ADC are 20 and 40, respectively, what is the value of x+y?

A 140

B 160

C 190

D 210

E 240

• A

• B

• C

• D

• E

Answer explanation

∠CB0=90-20=70°, ∠CDO=90-40=50°, so x+y=360-70-50=240°

A box contains 12 candies of four different flavors. The table above shows the numbers of candies of each flavor. If 2 candies are to be selected at random from the box, without replacement, what is the probability that of the 2 candies selected one will be a caramel candy and the other will be a cherry candy?

A 5/12

B 5/22

C 5/24

D 5/33

E 5/66

• A

• B

• C

• D

• E

Answer explanation

(1/12)*(5/11)+ (5/12)*(1/11)=10/132=5/66.

In polygon PRSTW, side RS is parallel to side PW.

Quantity A

x+y+z

Quantity B

360

• A

• B

• C

• D

Answer explanation