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190113
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Two solutions of $$x^{2}$$+nx+60=0 are $$r_1$$ and $$r_2$$. What is the value of n?
(1) $$r_1$$$$r_2$$=60
(2) (x-5)is a factor of $$x^{2}$$+nx+60
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190113
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Is axy > bxy?
(1)ax > ay
(2) bx > by
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190113
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Positive integer m is a multiple of 3. How many different prime factors of m?
(1) m/3 can be divided by 3.
(2) m/3 is an integer and has exactly two different prime factors.
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190113 还原机经选题: 文字题&几何
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According to the picture, a cylinder was placed at an angle on a horizontal plane. A is the center of the bottom circle, and AD is the radius of the circle. BC=10. AC is horizontal to the horizontal plane and perpendicular to BD. DC=?
(1)∠ADE=60°
(2)AC=2AD
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190603
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X is a positive integer and r is a non-negative integer. x can be divisible by 10r and cannot be divided by 10r+1. What is the value of r?
(1) X can be divided exactly by 25, but not by 26
(2) X can be divided exactly by 56, but not by 57
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190321
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There are five numbers in the sequence, and the average is 12. What is the smallest of these 5 numbers?
1: The average of the four largest numbers is 15.
2: The average of the four smallest terms is 10.
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190321
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x,ware integers.$$x \neq 0. Is $$x^w$$ an integer?
1：w>0
2：x>0
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190321
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Every number in the set S is different. The set S contains all the solutions to (n-3)(n-5)(n-8) = 0. If a number will be picked from the set, what is the probability that this number satisfies the equation (n-3)(n-5)(n-8) = 0?
1: The numbers in the set are continuous.
2: There are 20 numbers in the set.
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190321
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What is the length and width of a rectangle?
1: The perimeter of the rectangle is 124.
2: The diagonal length of the rectangle is 50.
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190321
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The set S is made up of continuous positive integers. Is the number of integers in S greater than 6?
1: There are two numbers in S that are multiples of 5.
2: There are two numbers in S that are multiples of 3.
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190321
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Is $$(x-y)(x+3)(x-3) \geq 0$$？
1:x>y
2:x>3
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190321
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Is n an even number?
1: The least common multiple of n and 300 is 900.
2: The greatest common divisor of n and 300 is 150.
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190321
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$$y = 10^n +5^(x+2n)$$. n and x are positive integers. What`s the reminder of y when divided by 6?
1: x=3
2: n=4
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190415
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Is the convex quadrilateral a square?
1: The lengths of two diagonals are the same.
2: Two diagonals are perpendicular to each other.
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190415 还原机经选题: 数论&代数
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s,r,t are integers. Is $$\frac{t}{s^{2}}$$ an integer?
1: $$\frac{t}{sr}$$ is an integer.
2: $$\frac{r}{s}$$ is an integer.
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190321
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A ball is placed in a cubic box. How many times the volume of the cube is that of the ball?
1: The ball is tangent to the six faces of the cube.
2: The radius of the ball is 10.
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190124
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N is an integer. Is $$\frac{N}{225}$$ a terminating decimal?
1: N can be divided by 3.
2: N can be divided by 5.
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190124
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Is $$\frac{5m}{3n}$$ an integer? m,n are integers.
1: m is a multiple of 3.
2: n is a multiple of 5.
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190124 还原机经选题: 文字题&几何
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In the xy coordinate system, two lines,$$l_1$$ and $$l_2$$, are neither parallel to the x-axis nor to the y-axis. Do $$l_1$$ and $$l_2$$ intersect?
1: The slope of one line is twice that of the other
2: One line passes through (0,0) and the other passes through (2,0).
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190124 还原机经选题: 文字题&几何
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The equation of line l isy=ax+b . Does l go through the fourth quadrant?
1：a > 0
2：b < 0
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