2015 AMC 12B 第 6 题

Question

早在

1930

年，Tillie 必须背熟从

0 \times 0

到

12 \times 12

的乘法表。她得到的乘法表中，行和列标有因数，表格主体是乘积。四舍五入到小数点后两位，表格主体中奇数所占的比例是多少？

Back in

1930,

Tillie had to memorize her multiplication facts from

0 \times 0

through

12 \times 12.

The multiplication table she was given had rows and columns labeled with the factors, and the products formed the body of the table. To the nearest hundredth, what fraction of the numbers in the body of the table are odd?

0.21

0.25

0.46

0.50

0.75

答案：A

知识点：奇偶性基本计数

难度评级：1290

小提示：

只有两个因数都是奇数时，乘积才是奇数

A product is odd only when both factors are odd

大提示：

统计从

0

到

12

的奇数个数，再与

13 \times 13

个表项比较

Count the odd numbers from

0

to

12,

then compare with the

13 \times 13

entries

解答：

表格主体有

13 \times 13 = 169

个表项。乘积为奇数，当且仅当两个因数都是奇数。

在

0, 1, \ldots, 12

中有

6

个奇数，因此有

6 \times 6 = 36

个奇数表项。所求比例是

\dfrac{36}{169} = 0.213\ldots \approx 0.21

。

因此，正确选项是 A。

The body has

13 \times 13 = 169

entries. A product is odd exactly when both factors are odd.

There are

6

odd numbers among

0, 1, \ldots, 12,

giving

6 \times 6 = 36

odd entries. The fraction is

\dfrac{36}{169} = 0.213\ldots \approx 0.21.

Thus, the correct answer is A.

2015 AMC 12B 第 6 题

答案：A

难度评级：1290

小提示：

大提示：

解答：

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