2014美国数学竞赛AMC10A、10B试题及答案

2014 AMC 10B Problems Problem 1 Leah has 13 coins^ all of which are pennies and nickels. If 5h

已 had one more nickel than she has now, then she would h^ve the same number of pennies and nickels, lr )匚ents, how much are Leah's coins worth?

(A) 33 (B) 35 (C) 37 (D) 39 (E) 41

Problem 2

23 4 2s 2-彳 + 2-^ Problem 3

Randy drove the first third of his trip on a gravel road^ the next 20 miles on pavement, and ths remaining □ne -fifth on a dirt road . In miles how long was Randy's tripi?

(A) 30 (B)等 (C)粤(D) 40 (E)竽

Problem 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?

m 吨 了

(A) | (B)彩 (C) f (D) 2 (E)-

Problem 5

Doug constructs a square window using 8 equal-size panes of glass, as shown ・ The ratio of the height to width ft3『 each pane is 5 : 2f and the borders around and between the panes are 2 inches wide, in inches, what 谄 the sid& length of th© square wind 口w?

(A) 26 (B) 28 (C) 30 (D) 32 (E) 34

Problem 6

Orvin went to the store with just enough rrnoney to buy 30 balloons. When h@ arrived^ he discovered that the store had a special sale on b a I loons ：: buy 1 balloon at the regular p 『i 匚已 and get a second at g off the regular price. What is the greatest number of balloons Orvin could buy?

(A) 33 (B) 34 (C) 36 (D) 38 (E) 39

what im

(A) 16 (B) 24 (C) 32 (D) 48 (E) 64

Problem 7

Suppose A> U > 0 and A is 近% greater than B. what is £?

⑷100(#) (B) 1 叫字)(C) 100(字)(D) 1 叫乎)(E) 100(和

Solution

Problem 8

A truck tr^ve>l5 f feet every t seconds. There ars 3 feet in a yard i How many yards dDss the truck travel

6

in 3 rninute-s?

b frn 血m10i 1 口

⑷廖(X (①〒⑴)石㈣〒

Solution

problem 9

For real numbers w and z,

丄+丄

予二于=2014,

ut w

w + z

What is ----------- ?

w ― z

、一1 J 1

(A) - 2014 (B)艄(C) —(D) 1 (E) 2014

Problem 10

In the addition shown below A. [3. C.and D are distinct digits. How many different values are po^ible For

D?

ABBCB

+ BCADA

DI3DDD

(A) 2 (E) 4 (C) 7 (D) 8 (E) 9

Problem 11

11. For the consume^ a single discount of n%is more adv^ntagsous than any of the following discounts:

(1)two ^ucces^ive 15% discounts

(2)three successive 10% discounts

(3) a 25f/J discount Fellow sd by s 5xu discount

What is the- smallest possibls positive intsgsr valus uf n?

(A) 27 (B) 2S (C) 29 (D) 31 (E) 33

Problem 12

12. The largest divisor of 2, 014h 000* 000 is rtsslf. What is its fifth largest divisor?

(A) 125t875.000 (B) 20L400. 000 (C) 251, 750.000 (D) 402： 800.000 (E) 503.500.000