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# Cracking the GRE Premium 2017

## Educators

### Problem 1

Line $A B$ is tangent to the circle $C$ at point $A$. The radius of the circle with center $C$ is 5 and $B C=$ $\frac{10 \sqrt{3}}{3}$.
Quantity A
The length of line segment $A B$
Quantity B
The length of line segment $A C$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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### Problem 2

$x \neq 0$
Quantity $\mathbf{A}$
$\frac{x}{10}$
Quantity $\mathbf{B}$
$\frac{\frac{x}{5}}{2}$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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### Problem 3

The test scores for a class have a normal distribution, a mean of $50,$ and a standard deviation of 4.
Quantity $\mathbf{A}$
Percentage of scores at or above 58
Quantity $\mathbf{B}$
Percentage of scores at or below 42
a. Quantity A is greater.
b. Quantity $\mathrm{B}$ is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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### Problem 4

The line $y=-\frac{5}{6} x+1$ is graphed on the rectangular coordinate axes.
Quantity A
$O Q$
Quantity B
$O P$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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### Problem 5

At a dog show, there are 20 judges and 10 dogs in the final round.
Quantity $\mathbf{A}$
The number of distinct pairs of judges
Quantity $\mathbf{B}$
The number of possible rankings of dogs from first to third place
a. Quantity A is greater
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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### Problem 6

$k>0$
$l>1$
Quantity A
$\frac{1}{\frac{1}{k}+\frac{1}{l}}$
Quantity B
$\frac{k l}{\frac{1}{k}+\frac{1}{l}}$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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### Problem 7

Quantity $\mathbf{A}$
The greatest odd factor of 78
Quantity $\mathbf{B}$
The greatest prime factor of 78
a. Quantity A is greater.
b. Quantity B is greater
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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a. 180
b. 192
c. 384
d. 524
e. 768

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