新GRE数学：余数真题练习
<p> 1)<span word="ST">ST</span>+<span word="S">S</span>+<span word="T">T</span>是偶数 问<span word="S">S</span>和<span word="T">T</span>除以二的余数比大小 都是偶数所以相等;<span word="key">key</span>：<span word="C">C</span>相等 因为<span word="S">S</span>和<span word="T">T</span>都是偶数。</p><p> 2) <span word="n">n</span>平方+<span word="n">n</span>除2的余数和0去比 答案：一样。</p><p> 3) 10^11+10^10+10^9+10^8，被11除，求余数，余数与0比大小，相等。</p><p> 答案：<span word="C">C</span>：0。10^11+10^10+10^9+10^8=1111 <span word="X">X</span>108，被11整除。</p><p> 111100000000除以11=10100000000 余0</p><p> <span word="A">A</span>. <span word="X">X</span>+7被3除后余2，比较<span word="X">X</span>被2除后余数与0的大小 答案 <span word="D">D</span></p><p> <span word="B">B</span>. <span word="x">x</span> 除以2的余数 与 0 比较大小 <span word="x">x</span> ，<span word="y">y</span> 是奇数</p><p> 奇数偶数=偶数 除以2 余数为0 答案选<span word="C">C</span></p><p> <span word="C">C</span>. <span word="x">x</span>，<span word="y">y</span> <span word="are">are</span> <span word="odds">odds</span>. 比较<span word="x">x</span>/2的余数和1的大小 <span word="ans">ans</span>：1大</p><p> 2<span word="n">n</span> 和 -1分别除以2的余数和0比大小相等</p><p> 兩變數<span word="x">x</span>與<span word="y">y</span>皆大於零 <span word="xy">xy</span>+<span word="x">x</span>+<span word="y">y</span>是偶数比較 <span word="x">x</span>除2的余数與 <span word="y">y</span>除2的余数</p><p> <span word="A">A</span>： <span word="C">C</span>推理一下可知兩個都是偶数所以除2都餘0</p><p> 首先奇数奇数=奇数，偶数偶数=偶数，奇数偶数=偶数</p><p> 如果<span word="xy">xy</span>+<span word="x">x</span>+<span word="y">y</span>是偶数，必须三个都是偶数<span word="or">or</span>一个偶数+两个奇数。</p><p> 随便定义<span word="x">x</span>是奇数，若<span word="y">y</span>是奇数，则有三个奇数，<span word="xy">xy</span>+<span word="x">x</span>+<span word="y">y</span>是奇数。</p><p> 若<span word="y">y</span>是偶数，只有一个奇数，<span word="xy">xy</span>+<span word="x">x</span>+<span word="y">y</span>是奇数。</p><p> 所以都不成立，只有可能<span word="x">x</span>和<span word="y">y</span>都是偶数。</p>
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