### All GRE Math Resources

## Example Questions

### Example Question #1 : Absolute Value

Quantitative Comparison:

Column A

|–3 + 4|

Column B

|–3| + |4|

**Possible Answers:**

Column A and B are equal

Cannot be determined

Column A is greater

Column B is greater

**Correct answer:**

Column B is greater

The operations in the absolute value are always done first. So in Column A, |–3 + 4| = |1| = 1. In Column B, |–3| + |4| = 3 + 4 = 7.

### Example Question #2 : Absolute Value

Quantitative Comparison

|*x* – 3| = 3

Quantity A: *x*

Quantity B: 2

**Possible Answers:**

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

**Correct answer:**

The relationship cannot be determined from the information given.

It's important to remember that absolute value functions yield two equations, not just one. Here we have *x* – 3 = 3 AND *x* – 3 = –3.

Therefore *x* = 6 or *x* = 0, so the answer cannot be determined.

If we had just used the quation *x* – 3 = 3 and forgotten about the second equation, we would have had *x* = 6 as the only solution, giving us the wrong answer.

### Example Question #3 : Absolute Value

Quantitative Comparison

Quantity A: |10| – |16|

Quantity B: |1 – 5| – |3 – 6|

**Possible Answers:**

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined from the information given.

Quantity A is greater.

**Correct answer:**

Quantity B is greater.

Quantity A: |10| = 10, |16| = 16, so |10| – |16| = 10 – 16 = –6.

Quantity B: |1 – 5| = 4, |3 – 6| = 3, so |1 – 5| - |3 – 6| = 4 – 3 = 1.

1 is bigger than –6, so Quantity B is greater.

### Example Question #1 : Absolute Value

Quantitative Comparison

Quantity A: (|–4 + 1| + |–10|)^{2}

Quantity B: |(–4 + 1 – 10)^{2}|

**Possible Answers:**

Quantity A is greater.

The relationship cannot be determined from the information given.

Quantity B is greater.

The two quantities are equal.

**Correct answer:**

The two quantities are equal.

Quantity A: |–4 + 1| = |–3| = 3 and |–10| = 10, so (|–4 + 1| + |–10|)^{2} = (3 + 10)^{2} = 13^{2 }= 169

Quantity B: |(–4 + 1 – 10)^{2}| = |(–13)^{2}| = 169

The two quantities are equal.

### Example Question #1 : How To Find Absolute Value

Quantity A:

Quantity B:

**Possible Answers:**

Quantity A is greater

The two quantities are equal

The relationship cannot be determined from the information given

Quantity B is greater

**Correct answer:**

Quantity B is greater

If , then either or must be negative, but not both. Making them both positive, as in quantity B, and then adding them, would produce a larger number than adding them first and making the result positive.

### Example Question #5 : Absolute Value

What is the absolute value of the following equation when ?

**Possible Answers:**

**Correct answer:**

(–3)^{3} = –27. Any time a negative number is cubed, it remains negative. –27 + 5 = –22. The absolute value of any number will ALWAYS be positive so the absolute value of –22 is 22. This is our answer.