AMC10 2020 B
AMC10 2020 B · Q6
AMC10 2020 B · Q6. It mainly tests Digit properties (sum of digits, divisibility tests), Number theory misc.
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?
梅根在高速公路上行驶时，注意到她的里程表显示15951（英里）。这个数字是一个回文数——正读反读都相同。然后2小时后，里程表显示了下一个更大的回文数。这2小时期间她的平均速度是多少英里每小时？
(A)
50
50
(B)
55
55
(C)
60
60
(D)
65
65
(E)
70
70
Answer
Correct choice: (B)
正确答案：（B）
Solution
A five-digit palindrome is determined by its leftmost three digits, so the next palindrome after 15951 is 16061. This occurs in $16061 - 15951 = 110$ miles. Therefore her average speed over those 2 hours was $110 \div 2 = 55$ miles per hour.
五位回文数由其最左边的三位数字决定，因此15951之后的下一个回文数是16061。这相差$16061 - 15951 = 110$英里。因此这2小时的平均速度是$110 \div 2 = 55$英里每小时。
Topics
Related Questions
Practice full AMC exams on amcdrill.
Try full-length practice and diagnostics at www.amcdrill.com.