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Beijing, Shenzhen and other cities have increased down payment requirements for purchases of homes by varying amounts, up to 35% for first homes and 70% for second homes.
讲解：
北京、深圳还有一些其它的城市在不同程度上提高了买第一套房和第二套房首付的价格
increase 提高 increase sth by … 提高了…（多大的额度、程度、比例…）
varying amounts 不同的额度/比例
down payment 首付
requirement 要求
purchase n./v. 购买
up to … 最高可达…
Hefei in Anhui province has stated that property prices may not change for six months after registration.
讲解：
合肥规定购房后半年内该套房价格不可改变
state 规定
property price 房价
registration 登记、注册
Some other cities have also put in place measures to cool the property market, such as higher down payments and reducing the number of homes residents can purchase.
讲解：
put in place sth=put sth in place 落实、实施…
measure 措施
cool the property market 给房地产市场降温
resident 居民
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