大师教我SAT数学阿～

题目

大师教我SAT数学阿～
When the positive integer k is divided by 7,the remainder is 6.What is the remainder when k+2 is divided by
A.0 B.1 C.2 D.3 E.4
When 1.783 is rounded to the nearest whole number,the result is how much greater than when 1.783 is rounded to the nearest tenth?
In the 30-day month of April,for every three days it rained,there were two days it did not rain.The number of days in April on which it rained was how much greater than the number of days on which it did not rain?
A four-digit integer,WXYZ,in which W,X,Y and Z each represent a different digit,is formed according to the following rules.
1.X = W+Y+Z
2.W = Y+1
3.Z = W-5
What is the four-digit integer?
Five different points A,B,C,D and E lie on a line in that order.The length of AD is 4.5 and the length of BE is 3.5.If the length of CD is 2,what is one possible value for the length of BC?
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答案

① 应是余数是 6,也就是说,k = 7n + 6,n 是整数,所以 k + 2 = 7n + 2 + 6 = 7n + 7 + 1 = 7(n + 1) + 1,答案：B.
② 1.783 取与它最近的整数,就是 2,取保留小数点后一位最近的数是,1.8,结果就是 2 － 1.8 ＝ 0.2
③ 下雨的天数（3） 加 不下雨的天数（2）＝ 5,30 / 5 = 6 ,即在四月份里共有六次这样情况,所以下雨的天数 ＝ 6 * 3 ＝ 18,不下雨的天数 ＝ 6 * 2 ＝ 12 ,下雨的天数比不下雨的天数多 18－12 ＝ 6 天.
④ 首先,WXYZ 是四位数,所以,必须
9 >= W >= 1,W = 0 就不是四位数
9 >= X >= 0,
9 >= Y >= 0,
9 >= Z >= 0,
Z ＝ W － 5 >= 0,所以 W >= 5,
W = Y + 1 >= 5,所以 Y >= 4,
X ＝ W + Y + Z >= 5 + 4 + Z = 9 + Z,X 不可能大于 9,所以 X ＝ 9,Z 也不能大于 1,否则 X 大于 9,所以 Z ＝ 0,
Z ＝ W － 5,0 ＝ W － 5,所以 W ＝ 5,
W ＝ Y + 1,5 ＝ Y + 1,所以 Y ＝ 4,
所以四位数是 5940.
⑤ AD ＝ AB + BC + CD,
BE ＝ BC + CD + DE,
AD ＝ 4.5,
BE ＝ 3.5,
CD ＝ 2,
所以 4.5 ＝ AB + BC + 2 ,所以 AB + BC ＝ 2.5
所以 3.5 ＝ BC + 2 + DE,所以 BC + DE ＝ 1.5
BC 最大为 1.5,即 D 和 E 重合时,最小可为 0.
BC 可能值是 0 ＝< BC =< 1.5