AMC8 2003

AMC8 2003 · Q17

AMC8 2003 · Q17. It mainly tests Logic puzzles.

The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim’s siblings? [table: Child Eye Hair Benjamin Blue Black; Jim Brown Blond; Nadeen Brown Black; Austin Blue Blond; Tevyn Blue Black; Sue Blue Blond]

下面列出的六个孩子来自两个每家三个兄弟姐妹的家庭。每个孩子有蓝眼睛或棕色眼睛，以及黑头发或金头发。同一家庭的孩子至少有一个这些特征相同。Jim 的兄弟姐妹是哪两个孩子？[表格：Child Eye Hair Benjamin 蓝黑；Jim 棕金；Nadeen 棕黑；Austin 蓝金；Tevyn 蓝黑；Sue 蓝金]

(A) Nadeen and Austin Nadeen和Austin

(B) Benjamin and Sue Benjamin和Sue

(D) Nadeen and Tevyn Nadeen和Tevyn

(E) Austin and Sue Austin和Sue

Answer

Correct choice: (E)

正确答案：（E）

Solution

(E) Because Jim has brown eyes and blond hair, none of his siblings can have both blue eyes and black hair. Therefore, neither Benjamin nor Tevyn can be Jim’s sibling. Consequently, there are only three possible pairs for Jim’s siblings – Nadeen and Austin, Nadeen and Sue, or Austin and Sue. Since Nadeen has different hair color and eye color from both Austin and Sue, neither can be Nadeen’s sibling. So Austin and Sue are Jim’s siblings. Benjamin, Nadeen and Tevyn are siblings in the other family.

（E）因为 Jim 有棕色眼睛和金色头发，所以他的兄弟姐妹中没有人可能同时拥有蓝色眼睛和黑色头发。因此，Benjamin 和 Tevyn 都不可能是 Jim 的兄弟姐妹。于是，Jim 的兄弟姐妹只有三种可能的配对：Nadeen 和 Austin、Nadeen 和 Sue，或 Austin 和 Sue。由于 Nadeen 的头发颜色和眼睛颜色都与 Austin 和 Sue 不同，因此 Austin 和 Sue 都不可能是 Nadeen 的兄弟姐妹。所以，Austin 和 Sue 是 Jim 的兄弟姐妹。Benjamin、Nadeen 和 Tevyn 是另一个家庭中的兄弟姐妹。

Topics

LM.001 Logic puzzles