GMAT Quantitative Reasoning - Solving by Factoring

1

If and are positive, what is the value of ?

(1) $(x )^{2}-(y )^{2}=15$

(2)

2

Willy's teacher challenged him to write two whole numbers in the square and circle in the diagram below in order to make a polynomial that could be factored.

$\square x ^{2} - \bigcirc$

Did Willy succeed?

Statement 1: The number Willy wrote in the square is a multple of 4.

Statement 2: The number Willy wrote in the circle is a multiple of 9.

3

Chad's teacher challenged him to write two whole numbers in the square and circle in the diagram below in order to make a polynomial that could be factored.

$\square x ^{3} - \bigcirc y^{3}$

Did Chad succeed?

Statement 1: The cube root of the number Chad wrote in the square is a whole number.

Statement 2: The cube root of the number Chad wrote in the circle is an irrational number.

4

Julia's teacher challenged her to write two whole numbers in the square and circle in the diagram below in order to make a polynomial that could be factored.

$\square x ^{3}+ \bigcirc y^{3}$

Did Julia succeed?

Statement 1: The cube root of the number Julia wrote in the circle is a whole number.

Statement 2: The number Julia wrote in the square is ten times the number Julia wrote in the circle.

5

Theresa's teacher challenged her to write whole numbers in the circle and the square in the diagram below in order to make a polynomial that could be factored.

$x^{2} - \bigcirc y ^{\square}$

Assuming Theresa wrote two whole numbers, did she succeed?

Statement 1: Theresa wrote a 64 in the circle.

Statement 2: Theresa wrote a multiple of 6 in the square.

6

Karen's teacher challenged her to write two whole numbers in the square and circle in the diagram below in order to make a polynomial that could be factored.

$\square x ^{3}+ \bigcirc y^{3}$

Assuming both numbers are whole numbers, did Karen succeed?

Statement 1: The cube root of the number Julia wrote in the circle is a whole number.

Statement 2: The number Julia wrote in the square is twenty-seven times the number Julia wrote in the circle.

7

Simplify: $\frac{-3x + 3}{x^2 - 1}$

8

Don's teacher challenged him to write two whole numbers in the square and circle in the diagram below in order to make a polynomial that could be factored.

$x^{2}+ \square x+ \bigcirc$