AMC10 2011 A

AMC10 2011 A · Q4

AMC10 2011 A · Q4. It mainly tests Arithmetic sequences basics.

Let $X$ and $Y$ be the following sums of arithmetic sequences: $X = 10 + 12 + 14 + \cdots + 100$, $Y = 12 + 14 + 16 + \cdots + 102$. What is the value of $Y - X$?

设$X$和$Y$为以下等差数列的和：$X = 10 + 12 + 14 + \cdots + 100$，$Y = 12 + 14 + 16 + \cdots + 102$。$Y - X$的值是多少？

(A) 92 92

(B) 98 98

(D) 102 102

(E) 112 112

Answer

Correct choice: (A)

正确答案：（A）

Solution

Every term in $X$ except 10 appears in $Y$. Every term in $Y$ except 102 appears in $X$. Therefore $Y - X = 102 - 10 = 92$.

$X$中除了10外的所有项都出现在$Y$中。$Y$中除了102外的所有项都出现在$X$中。因此$Y - X = 102 - 10 = 92$。

Topics

AR.012 Arithmetic sequences basics