DSQ: Simplifying algebraic expressions

Practice Questions

GMAT Quantitative Reasoning › DSQ: Simplifying algebraic expressions

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1

Evaluate the expression $(x-2y)^{2}+8xy$ .

Statement 1:

Statement 2:

2

True or false?

$\frac{(x + y)^{2} - (x - y)^{2} }{y} \geq \frac{(x + y)^{2} + (x - y)^{2} }{x^{2}+y^{2}}$

Statement 1:

Statement 2:

3

The figure below shows a trinomial with its exponents replaced by shapes:

$x^{\bigcirc } + x^{\square} + x^{\bigtriangleup }$

Each shape replaces a whole number.

Is this a simplified expression?

Statement 1: The sum of the three exponents is 10.

Statement 2: The circle and the triangle are replacing different numbers.

4

Carleton's teacher challenged him to fill in the circle and the square below to form a polynomial with degree .

$x^{\bigcirc } + x^{\square }$

Did Carleton succeed?

Statement 1: The sum of the numbers Carleton filled in the two shapes was .

Statement 2: Carleton wrote a in the circle.

5

Michelle was challenged by her teacher to create a monomial of degree by filling in the square and the circle in the figure below.

$x^{\square }y^{\bigcirc}$

Did Michelle succeed?

Statement 1: Michelle wrote the same positive integer in both the circle and the square.

Statement 2: Michelle wrote a in the circle.

6

Evaluate the expression $(x + y)^{2} - (x-y)^{2}$

Statement 1:

Statement 2:

7

Stephanie was challenged by her teacher to create a monomial of degree 5 by filling in the square and the circle in the figure below.

$\square x^{\bigcirc }$

Did Stephanie succeed?

Statement 1: Stephanie wrote a 5 in the square.

Statement 2: Stephanie wrote a 7 in the circle.

8

Evaluate the expression for positive :

$\frac{4x^{2}}{y^{-4}} \cdot \frac{3x^{2}y^{2}}{8} \cdot \frac{5}{(2x^{2}y^{2})^{2}}$

Statement 1:

Statement 2:

9

True or false?

$\frac{(x + 4y)^{2} - (x - 4y)^{2} }{y} < \frac{(x + 3y)^{2} - (x - 3y)^{2} }{x}$

Statement 1:

Statement 2:

10

The figure below shows a binomial with its coefficients and exponents replaced by shapes:

$\square x^{\bigcirc } + \lozenge x ^{ \bigtriangleup }$

Each shape replaces a whole number.

Is this a simplified expression?

Statement 1: The square and the circle are replacing the same integer.

Statement 2: The diamond and the triangle are replacing different integers.

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