AMC8 1995

AMC8 1995 · Q12

AMC8 1995 · Q12. It mainly tests Divisibility & factors, Primes & prime factorization.

A lucky year is one in which at least one date, when written in the form month/day/year, has the following property: The product of the month times the day equals the last two digits of the year. For example, 1956 is a lucky year because it has the date 7/8/56 and $7 \times 8 = 56$. Which of the following is NOT a lucky year?

幸运年是指至少有一个日期，以月/日/年形式书写时，具有如下性质：月份乘以日期等于年份的最后两位数字。例如，1956是幸运年，因为有日期7/8/56且$7 \times 8 = 56$。以下哪个不是幸运年？

(A) 1990 1990

(B) 1991 1991

(D) 1993 1993

(E) 1994 1994

Answer

Correct choice: (E)

正确答案：（E）

Solution

The last two digits of 1994 can only be factored as 94 = 2 × 47. All the other choices have at least one date that makes them lucky: (A) 9/10/90 (B) 7/13/91 (C) 4/23/92 (D) 3/31/93.

1994的最后两位数字94只能分解为2×47。其他选项都有至少一个使其成为幸运年的日期：(A) 9/10/90 (B) 7/13/91 (C) 4/23/92 (D) 3/31/93。

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