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    不定方程的三種常用解法-2019年浙江公務員考試行測技巧
    http://www.hrbjintong.com       2019-05-15      來源:浙江公務員考試網
    【字體: 】              

      在行測運算題當中,設方程是常用的技巧,含有未知數的等式叫做方程。不定方程中未知數的個數多于獨立方程的個數。比如:x+y=5。在行測里也經常列出不定方程,但是很多人都不會解。其實只要掌握好三種常用的方法,問題自然迎刃而解。浙江公務員考試網(www.hrbjintong.com)進行講解。


      1、整除法:利用不定方程中各數能被同一個數整除的關系來求解。


      例1:小張的孩子出生的月份乘以29,出生的日期乘以24,所得的兩個乘積加起來剛好等于900。問孩子出生在哪一個季度?


      A.第一季度 B.第二季度 C.第三季度 D.第四季度


      【答案】D


      【解析】關鍵詞:等于,所以找到等量關系。設出生月份為x,出生的日期為y。29x+24y=900,24與900的最大公約數為12,意味著24y能被12整除,900能被12整除,29為質數,所以x能被12整除,由于12表示的是月份,所以是第四季度。


      2、奇偶性:未知數的系數奇偶性不同


      例2:辦公室工作人員使用紅、藍兩種顏色的文件袋裝29份相同的文件。每個紅色文件袋可以裝7份文件,每個藍色文件袋可以裝4份文件。要使每個文件袋都恰好裝滿,需要紅色、藍色文件袋的數量分別為()個。


      A.1、6 B.2、4 C.4、1 D.3、2


      【答案】D


      【解析】由題可知袋子的個數肯定是為整數,設紅色袋子數量為x,藍色袋子數量為y,由題意可得7x+4y=29,此時未知數的系數為7和4,奇偶性不同。4y為偶數,29為奇數,則 7x為奇數,得出x為奇數,排除B、C。接下來代入A選項,x=1,y不是整數,排除A,選擇D。驗證:x=3,y=2滿足題意。


      3、尾數法:未知數的系數是5的倍數


      超市將99個蘋果裝進兩種包裝盒,大包裝盒每個裝12個蘋果,小包裝盒每個裝5個蘋果,共用了十多個盒子剛好裝完。問兩種包裝盒相差多少個?


      A.3 B.4 C.7 D.13


      【答案】D


      【解析】由題可知,大包裝盒的個數和小包裝盒的個數為整數,設大包裝盒的個數為x,小包裝盒為y,可得到12x+5y=99,x+y>10。5y尾數只能是0、5,對應的12x的尾數只能是9、4,又因為12x為偶數,所以尾數只能是4。當x=2時,y=15,x+y=17,滿足題意。15-2=13;當x=7,y=3,x+y=10,不滿足題意,選擇D。


      小編提醒大家,整除法、奇偶性、尾數法在不定方程中運用是很多的,記住各個方法的適用環境,就能夠更快的解出題目了。



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