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190113 还原机经选题
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5A3 and 8B6 are all three-digit integers. The sum of these two numbers can be divided by 9. What is the possible maximum value of A + B?
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190113 还原机经选题
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1, 11, 111, 1111, 11111, -
What are the tens of the sum of the first 40 items in this series?
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190215 还原机经选题
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There are two four digit abcd,dcba. 1 ≤ a, b, c, d ≤ 9. a,b,c,d are natural numbers and may be equal. What is the maximum value of abcd - dcba?
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190215 还原机经选题: 数论&代数
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Is n the square of an integer? n is an integer.
1:4n is the square of an integer
2:$$n^{3}$$ is the square of an integer
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190302 还原机经选题
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n=1234567891011121314-. n is an integer composed of positive integers arranged in order. From left to right, what is the 72nd digit of n?
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191222 还原机经选题
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A two-digit number can be formed by the integers in set {1, 5, 7, x, y}. The five integers could form 20 two-digit numbers without any digit repeated. We find that the sum of all the 20 numbers is 1056=44*24, then what is the value of x+y?
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200301 还原机经选题: 数论&代数
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If n, m, and k are positive integers, and $$\frac { 9 } { 10 } < \frac { 1 } { n } + \frac { 1 } { m } + \frac { 1 } { k } < 1$$, is n+m+k >11?
(1)n=2 and m=3
(2)k=7
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200301 还原机经选题
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From 1 to 10, choose any two numbers to multiply, and the numbers can be selected repeatedly. What is the sum of all the products?
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190113 还原机经选题
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X=$$\frac{1}{2\sqrt{3}+\sqrt{7}}$$.X+$$\frac{1}{X}$$=?
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190113 还原机经选题
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(($$\frac{1}{3})^{2}+\frac{1}{3}*\frac{1}{4}$$)*(($$\frac{1}{3})^{2}-\frac{1}{3}*\frac{1}{4}$$)=?
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190215 还原机经选题
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$$\frac{0.00048*10^{n}}{4^{2}}$$ < 2*10^{18}.n is an integer. What is the maximum value of n?
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190415 还原机经选题: 数论&代数
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12! can be divided by $$(4!)^{n}$$ but cannot be divided by $$(4!)^{n+1}$$ .n=?
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190302 还原机经选题: 数论&代数
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What is the unit digit number of $$5^{5}$$+$$6^{5}$$+$$7^{5}$$+$$8^{5}$$?
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190302 还原机经选题: 数论&代数
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$$d_1$$=$$\sqrt{6^{2}+8^{2}}$$ ,$$d_2$$=$$\sqrt{8^{2}+(6+4\frac{3}{4})^{2}}$$.Which range does $$d_2$$ - $$d_1$$ fall in?
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190415 还原机经选题
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a,b,c,d are integers. 1 ≤ a,b,c,d ≤ 9.(a+d)(b+c)=?
1:abcd+dcba=7557.
2:abcd+ dba =1957
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190302 还原机经选题
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A,B are two-digit integers. The tens of A is three. The unit digit of B is 5. A(B+1)=2016. 5A+2B=?
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190302 还原机经选题
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X(Y+1)=2016. 5X+2Y=?
1:Y(2+3X)=2020
2:X=Y
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190113 还原机经选题
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Two students, Tom and Mary, solved the equation at the same time. Tom thought that the solutions of the equation were 1 and – 9, but he misread the corresponding number of c in the calculation. Mary thought that the solutions of the equation were 1 and 7, but Mary mistook the corresponding number of b in the calculation. What are correct solutions of this equation?
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191031 还原机经选题: 数论&代数
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A straight line y=mx+b, a parabola$$ y=x^2+c$$. are the number of intersections of these two images no less than 1?
(1)b≥c
(2)m^2≥4(c-b)
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190207 还原机经选题
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a,b,c,d are positive one-digit integers. ac+bc+ad+bd=65. |a+b-c-d|=?
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