一支人數(shù)是5的倍數(shù)且不少于1000人的游行隊伍,若按每橫排4人編隊,最后差3人;若按每橫排3人編隊,最后差2人;若按每橫排2人編隊,最后差1人.則這只游行隊伍的最少人數(shù)是( )
試題分析:設(shè)所求數(shù)為
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,由已知
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末尾為0或5,
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是4的倍數(shù)+1,
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是3的倍數(shù)+1.
若“每橫排4人編隊,最后差3人 ”成立,
“每橫排2人編隊,最后差1人”肯定成立 不必考慮,
則
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是3與4的公倍數(shù)+1,那么就是12的倍數(shù)+1
可見
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末位為奇數(shù),即為5,則
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的末位為4.
可使數(shù)x滿足
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,
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;
要使
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末尾為4,
必須使
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末位為2 、7 (
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末位都為
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),
滿足條件的最小
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為87,所求數(shù)為1045,故選C.
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