Try the following GMAT Problem Solving question that tests your understanding of algebraic inequalities with three variables.

Question 58:

Which of the following must be true ?

1. If $xy < xz$, then $y < z$.
2. If $x^2y < x^2 z$, then $y < z$.
3. If $x-y < x-z$, then $z < y$.

1. $\quad \textrm{None}$
2. $\quad \textrm{I and II only}$
3. $\quad \textrm{II and III only}$
4. $\quad \textrm{I and III only}$
5. $\quad \textrm{I, II, and III}$

 
Try the following GMAT data sufficiency question on dealing with quadratic equation forms in the context of data sufficiency.

Question 57:

What is the value of $x^4 + 2x^2 + 12$ ?

1. (1) $x=2$ or $x=-2$
2. (2) $x^4+2x^2 – 12 = 12$

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

 
Try the following GMAT Problem Solving question on how to turn a decimal product to a whole number.

Question 56:

What is the least integer value of $n$ for which the product $(0.004)(0.015)(0.0025)(10^n)$ is an integer ?

1. $\quad -10$

2. $\quad -8$

3. $\quad 0$

4. $\quad 8$

5. $\quad 10$

 
Try the following GMAT data sufficiency question on finding roots of algebraic equations.

Question 55:

What is the value of $x$ ?

1. (1) $(|x|-2)(x+2)=0$
2. (2) $(|x|+2)(x-2)=0$

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.