AMC10 2001 A

AMC10 2001 A · Q22

AMC10 2001 A · Q22. It mainly tests Logic puzzles.

In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by $v, w, x, y, z$. Find $y + z$.

在所示的幻方中，每行、每列和对角线上的数字之和相同。其中五个数字用 $v, w, x, y, z$ 表示。求 $y + z$。

(A) 43 43

(B) 44 44

(D) 46 46

(E) 47 47

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) Since $v$ appears in the first row, first column, and on diagonal, the sum of the remaining two numbers in each of these lines must be the same. Thus, $25 + 18 = 24 + w = 21 + x,$ so $w = 19$ and $x = 22$. now 25,22, and 19 form a diagonal with a sum of 66, so we can find $v = 23$, $y = 26$, and $z = 20$. Hence $y + z = 46$.

（D）由于 $v$ 出现在第一行、第一列以及对角线上，因此这些线中其余两个数的和必须相同。因此， $25 + 18 = 24 + w = 21 + x,$ 所以 $w = 19$ 且 $x = 22$。现在 25、22 和 19 构成一条对角线，和为 66，因此可得 $v = 23$、$y = 26$、$z = 20$。因此 $y + z = 46$。

Topics

LM.001 Logic puzzles