List of top Questions asked in GRE

The arithmetic mean of \( a, b, \) and \( c \) is 13.
Quantity A: The arithmetic mean of \( 2a + b, b + 3c, 39 - c \)
Quantity B: 39

A boy with a lemonade stand sells cups of lemonade for a quarter each. He has bought $ 20 worth of supplies and is able to make 500 cups of lemonade with the supplies. If he has to pay a business tax of 4% for each cup he sells, how many cups will he have to sell in order to break even?

The average of five consecutive integers is 6. What is the largest of these integers?

Simplify: \[ \frac{1}{2} + \frac{x}{4} \]

How many real solutions are there for the following equation? \[ x^4 + 5x^2 - 14 = 0 \]

Simplify the following expression: \[ 3\sqrt{27} + 5\sqrt{18} - 3\sqrt{147} \]

Simplify the following expression: \[ 0.327 + \left( \frac{3}{8} \times (0.048 + 2.176) \right) \]

Which of the following is true? \[ \text{Quantity A: } \frac{12}{11} \div \frac{7}{6}, \quad \text{Quantity B: } \frac{17}{8} \div \frac{7}{6} \]

If the product of two distinct integers is 143, which of the following could not represent the sum of those two integers?

Compare Quantity A and Quantity B:
\[ \text{Quantity A: } (x + y)^3, \quad \text{Quantity B: } x^3 + y^3 \] Given that \( x<0 \) and \( y>0 \), compare the two quantities.

Compare Quantity A and Quantity B: \[ \text{Quantity A: } (x + y)^3, \quad \text{Quantity B: } x^3 + y^3 \] Given that \( x<0 \) and \( y>0 \), compare the two quantities.

Find the algebraic expression to represent the following statement:
\textit{The square of \( x \) multiplied by 3, the result has 18 subtracted from it and the final result divided by 15.}

Compare Quantity A and Quantity B and determine which is larger.
\[ \text{Quantity A: } x^3 - 6, \quad \text{Quantity B: } x + 1 \] For when \( x<2 \), compare the two quantities.

Reduce the following fraction: \[ \frac{a^2b^2 + c^2}{5ab^2} \div \frac{5ab + c}{5c} \]

If \( x = 55 \), \( x + y = 23 \), and \( y - x = 2 \), find the value of \( 2x + y \).

Which of the following are answers to the equation below? \[ x^2 - 4 = 0, \quad x^2 + 5x + 6 = 0 \] I. \( x = 2 \)
II. \( x = -2 \)
III. \( x = -3 \)

Find the relationship between Quantity A and Quantity B: \[ (a + b)^2 = 34, \quad \frac{ab}{2} = 6 \] Quantity A: \( a^2 + b^2 \)
Quantity B: 11

The arithmetic mean of \( a, b, c, d \) is 14.
Quantity A: 32
Quantity B: The arithmetic mean of \( a + b \), \( c + d \), and \( a - b + c - d = 48 \)

A line is parallel to the y-axis and passes through the point \( (2,3) \). What is its gradient (m) and x-intercept?

What is the equation of the new parabola created by shifting \( y = x^2 \), three units in the positive y-axis direction?

A sphere with diameter 1 unit is enclosed in a cube of side 1 unit each. Find the unoccupied volume remaining inside the cube.

The function \( y = -3x^2 \) is shifted 2 units towards the positive x-axis (right) and 3 units towards the positive y-axis (up). Find the resulting function.

Find the shaded area when two squares with side \( a \) intersect as shown in the figure below.

If the largest side of a triangle is \( A \), and the other two sides are \( B \) and \( C \), what relation exists between them?

What is the area of triangle ALC in the figure given below?