Quiz about AMC10B 2014 (1-22)

Question 1

Leah has 13 coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah's coins worth?

Accepted Answer

37

Answer

33

Answer

35

Answer

39

Answer

41

Question 2

What is $$\frac{2^3+2^3}{2^{-3}+2^{-3}}$$ ?

Accepted Answer

64

Answer

16

Answer

24

Answer

32

Answer

48

Question 3

Peter drove the first third of his trip on a gravel road, the next 20 miles on pavement, and the remaining one-fifth on a dirt road. In miles how long was Peter's trip?

Accepted Answer

$$\frac{300}{7}$$

Answer

30

Answer

$$\frac{400}{11}$$

Answer

$$\frac{75}{2}$$

Answer

40

Question 4

Susie pays for 4 muffins and 3 bananas. Calvin spends twice as much paying for 2 muffins and 16 bananas. A muffin is how many times as expensive as a banana?

Accepted Answer

$$\frac{5}{3}$$

Answer

$$\frac{3}{2}$$

Answer

$$\frac{7}{4}$$

Answer

2

Answer

$$\frac{13}{4}$$

Question 5

Camden constructs a square window using 8 equal-size panes of glass, as shown. The ratio of the height to width for each pane is 5 : 2, and the borders around and between the panes are 2 inches wide. In inches, what is the side length of the square window?

Accepted Answer

26

Answer

28

Answer

30

Answer

32

Answer

34

Question 6

Orvin went to the store with just enough money to buy 30 balloons. When he arrived, he discovered that the store had a special sale on balloons: buy 1 balloon at the regular price and get a second at $$\frac{1}{3}$$ off the regular price. What is the greatest number of balloons Orvin could buy?

Accepted Answer

36

Answer

33

Answer

34

Answer

38

Answer

39

Question 7

Suppose A > B > 0 and A is x% greater than B . What is x?

Accepted Answer

$$100\ \frac{\left(A-B\right)}{B}$$

Answer

$$100\left(\frac{A+B}{B}\right)$$

Answer

$$100\left(\frac{A+B}{A}\right)$$

Answer

$$100\left(\frac{A-B}{A}\right)$$

Answer

$$100\left(\frac{A}{B}\right)$$

Question 8

A truck travels $$\frac{b}{6}$$ feet every t seconds. There are 3 feet in a yard. How many yards does the truck travel in 3 minutes?

Accepted Answer

$$\frac{10b}{t}$$

Answer

$$\frac{b}{1080t}$$

Answer

$$\frac{30t}{b}$$

Answer

$$\frac{30b}{t}$$

Answer

$$\frac{10t}{b}$$

Question 9

For real numbers w and z, $$\frac{\frac{1}{w\ }+\frac{1}{z}}{\frac{1}{w}-\frac{1}{z}}=2014$$ What is $$\frac{w+z}{w-z}$$ ?

Accepted Answer

-2014

Answer

$$\frac{-1}{2014}$$

Answer

$$\frac{1}{2014}$$

Answer

1

Answer

2014

Question 10

In the addition shown below A, B, C, and D are distinct digits. How many different values are possible for D?

Accepted Answer

7

Answer

2

Answer

4

Answer

8

Answer

9

Question 11

For the consumer, a single discount of n% is more advantageous than any of the following discounts:

(1) two successive 15% discounts

(2) three successive 10% discounts

(3) a 25% discount followed by a 5% discount

What is the smallest possible positive integer value of n?

Accepted Answer

29

Answer

27

Answer

28

Answer

31

Answer

33

Question 12

The largest divisor of 2,014,000,000 is itself. What is its fifth largest divisor?

Accepted Answer

251,750,000

Answer

125,875,000

Answer

201,400,000

Answer

402,800,000

Answer

503,500,000

Question 13

Six regular hexagons surround a regular hexagon of side length 1 as shown. What is the area of $$\Delta ABC$$ ?

Accepted Answer

$$3\sqrt[]{3}$$

Answer

$$2\sqrt[]{3}$$

Answer

$$1+3\sqrt[]{2}$$

Answer

$$2+2\sqrt[]{3}$$

Answer

$$3+2\sqrt[]{3}$$

Question 14

Danica drove her new car on a trip for a whole number of hours, averaging 55 miles per hour. At the beginning of the trip, abc miles was displayed on the odometer, where is abc is a 3-digit number with $$a\ge1$$ and $$a+b+c\le7$$ . At the end of the trip, the odometer showed cba miles. What is $$a^2+b^2+c^2$$ ?

Accepted Answer

37

Answer

26

Answer

27

Answer

36

Answer

41

Question 15

In rectangle ABCD, DC = 2CB and points E and F lie on $$\overline{AB}$$ so that $$\overline{ED}$$ and $$\overline{FD}$$ trisect $$\angle ADC$$ as shown. What is the ratio of the area of $$\Delta DEF$$ to the area of rectangle ABCD?

Accepted Answer

$$\frac{\sqrt[]{3}}{6}$$

Answer

$$\frac{\sqrt{6}}{8}$$

Answer

$$\frac{3\sqrt{3}}{16}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{\sqrt[]{2\ }}{4}$$

Question 16

Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?

Accepted Answer

$$\frac{7}{72}$$

Answer

$$\frac{1}{36}$$

Answer

$$\frac{1}{9}$$

Answer

$$\frac{5}{36}$$

Answer

$$\frac{1}{6}$$

Question 17

What is the greatest power of 2 that is a factor of $$10^{1002}-4^{501}$$ ?

Accepted Answer

$$2^{1005}$$

Answer

$$2^{1002}$$

Answer

$$2^{1003}$$

Answer

$$2^{1004}$$

Answer

$$2^{1006}$$

Question 18

A list of positive integers has a mean of 10, a median of 9, and a unique mode of 8. What is the largest possible value of an integer in the list?

Accepted Answer

35

Answer

24

Answer

30

Answer

31

Answer

33

Question 19

Two concentric circles have radii and . Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?

Accepted Answer

$$\frac{1}{3}$$

Answer

1/6

Answer

1/4

Answer

$$\frac{2-\sqrt[]{2}}{2}$$

Answer

$$\frac{1}{2}$$

Question 20

For how many integers x is the number $$x^4-51x^2+50$$ negative?

Accepted Answer

12

Answer

8

Answer

10

Answer

14

Answer

16

Question 21

Trapezoid ABCD has parallel sides $$\overline{AB}$$ of length 33 and $$\overline{CD}$$ of length 21. The other two sides are of lengths 10 and 14. The angles at A and B are acute. What is the length of the shorter diagonal of ABCD?

Accepted Answer

25

Answer

$$10\sqrt[]{6}$$

Answer

$$8\sqrt[]{10}$$

Answer

$$18\sqrt[]{2}$$

Answer

26

Question 22

Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles?

Accepted Answer

$$\frac{\sqrt{5\ }-1}{2}$$

Answer

$$\frac{1+\sqrt[]{2}\ }{4}$$

Answer

$$\frac{\sqrt[]{3}+1}{4}$$

Answer

$$\frac{2\sqrt[]{3}}{5}$$

Answer

$$\frac{\sqrt[]{5}}{3}$$

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