AMC12 2004 A

AMC12 2004 A · Q4

AMC12 2004 A · Q4. It mainly tests Logic puzzles.

Bertha has 6 daughters and no sons. Some of her daughters have 6 daughters, and the rest have none. Bertha has a total of 30 daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no daughters?

Bertha 有 6 个女儿，没有儿子。她的一些女儿有 6 个女儿，其余的没有。Bertha 总共有 30 个女儿和孙女，没有曾孙女。Bertha 的女儿和孙女中有多少个没有女儿？

(A) 22 22

(B) 23 23

(D) 25 25

(E) 26 26

Answer

Correct choice: (E)

正确答案：（E）

Solution

Since Bertha has $6$ daughters, she has $30-6=24$ granddaughters, of which none have daughters. Of Bertha's daughters, $\frac{24}6=4$ have daughters, so $6-4=2$ do not have daughters. Therefore, of Bertha's daughters and granddaughters, $24+2=26$ do not have daughters. $\boxed{\mathrm{(E)}\ 26}$

由于 Bertha 有 $6$ 个女儿，所以她有 $30-6=24$ 个孙女，而这些孙女都没有女儿。Bertha 的女儿中，有 $\frac{24}6=4$ 个有女儿，因此有 $6-4=2$ 个没有女儿。因此在 Bertha 的女儿和孙女中，没有女儿的共有 $24+2=26$ 个。$\boxed{\mathrm{(E)}\ 26}$

Topics

LM.001 Logic puzzles