2020 AMC 10B 第 6 题

Question

Megan 在高速公路上开车时，注意到里程表显示

15951

英里。这个数是回文数，也就是正读倒读相同。

2

小时后，里程表显示下一个更大的回文数。在这

2

小时内，她的平均速度是多少英里每小时？

Driving along a highway, Megan noticed that her odometer showed

15951

(miles). This number is a palindrome—it reads the same forward and backward. Then

2

hours later, the odometer displayed the next higher palindrome. What was her average speed, in miles per hour, during this

2

-hour period?

50

55

60

65

70

先找出

15951

之后的下一个回文数，再计算速度。

Find the next palindrome after

15951

before computing the speed

增加中间数字会产生进位，从而得到下一个回文数。

Increasing the middle digit forces a carry to the next palindrome

五位回文数由它的前三位数字唯一确定。

15951

的前半部分是

159

；把它增加到

160

，再把前两位数字对称地反射到后两位，就得到下一个回文数

16061

。

Megan 行驶了

16061-15951=110

英里，用时

2

小时，所以平均速度为每小时

\frac{110}{2}=55

英里。所以正确答案是 B。

A five-digit palindrome is determined by its first three digits. The first half of

15951

is

159

; increasing this to

160

and reflecting the first two digits gives the next palindrome,

16061.

Megan traveled

16061-15951=110

miles in

2

hours, so her average speed was

\frac{110}{2}=55

miles per hour. Thus, B is the correct answer.

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