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全部 图表题专项练习 分难度套题练习 GRE数学6000题170逐考点专项练习 GRE数学170超高频“脏”题 GRE数学170超高频“坑”题 GRE数学170超高频“神”题
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题目内容
Which of the following numbers CANNOT be the value of $$\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}$$, where $$a$$, $$b$$, and $$c$$ are nonzero numbers?
The integers $$s$$, $$t$$, and $$u$$ are each greater than $$1$$.

Quantity A

The average (arithmetic mean) of $$s$$, $$t$$, $$u$$, $$\frac{1}{s}$$, $$\frac{1}{t}$$, and $$\frac{1}{u}$$

Quantity B

$$1$$
For all integers $$k \gt 1$$, $$P_{k}=\frac{k+1}{k}$$. For all integers $$k \gt 2$$, $$b_{k}=P_{k}-P_{k-1}$$. The integer $$n$$ is greater than $$2$$.

Quantity A

$$b_{n}$$

Quantity B

$$\frac{-1}{n^2-n}$$


The figure shows a large equilateral triangle partitioned into 4 regular hexagons, 3 trapezoids, and 3 smaller equilateral triangles. If all sides of the hexagons are congruent, what is the ratio of the sum of the areas of the 4 hexagons to the sum of the areas of the 3 trapezoids to the sum of the areas of the 3 smaller triangles?
A certain number of toys were packed into $$x$$ boxes so that each box contained the same number of toys, with no toys left unpacked. If $$3$$ fewer boxes had been used instead, then $$12$$ toys would have been packed in each box, with $$5$$ toys left unpacked. What is the value of $$x$$?
Two water faucets are used to fill a certain tank. Running individually at their respective constant rates, these faucets fill the empty tank in 12 minutes and 20 minutes, respectively. If no water leaves the tank, how many minutes will it take for both faucets running simultaneously at their respective rates to fill the empty tank?
If $$xy=2$$ and the average (arithmetic mean) of $$x$$ and $$y$$ is 3, what is the value of $$x^2 + y^2$$ ?
If $$x$$ and $$y$$ are positive integers and $$\frac{(8)(7)(6)(5)(4)(3)}{(2^{x})(3^{y})}$$is an integer, what is the greatest possible value of $$xy$$?
The standard deviation of $$n$$ numerical data $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$ with mean $$\overline{x}$$ is equal to $$\sqrt{\frac{s}{n}}$$, where $$S$$ is the sum of the squared differences $$(x_{i} - \overline{x})^{2}$$ for $$1 \leq i \leq n$$.

Data set $$R$$ consists of $$1,000$$ values, where each value is a positive integer less than $$100$$. The mean of the values in $$R$$ is $$50$$, and $$500$$ of the values are between $$40$$ and $$60$$.

Quantity A

The standard deviation of the values in $$R$$

Quantity B

$$\frac{100}{3}$$
$$N$$ is a prime integer greater than $$5$$.

Quantity A

The units digit of $$N^4$$

Quantity B

3


In the figure, $$AB = AE$$ and $$BC = ED = 4$$. If the area of the shaded region is $$44$$, what is the value of $$AB$$?
If $$s$$ and $$t$$ are different positive integers, which of the following guarantees that $$\frac{t}{s}$$ is an integer?
For all integers $$x$$ greater than $$1$$, the function $$p(x)$$ is defined as the number of different prime factors of $$x$$. What is the value of $$\frac{p(12)}{p(9)}$$?


The figure shows part of a circle with two inscribed regular polygons—one with $$6$$ sides and one with $$12$$ sides. The two polygons have $$6$$ vertices in common. The radius of the circle is $$r$$, and the area of the $$6$$-sided polygon is $$x$$.

Quantity A

$$\pi r^2-x$$

Quantity B

$$24$$ times the area of the shaded region $$S$$
$$n$$ is the number of $$8$$-digit positive integers consisting only of the digits $$1$$ and $$2$$, where the digit $$1$$ appears three times and the digit $$2$$ appears five times.

$$r$$ is the number of combinations of $$8$$ different letters taken $$3$$ at a time.

Quantity A

$$n$$

Quantity B

$$r$$

Quantity A

$$a$$

Quantity B

$$b+55$$

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