### All GRE Math Resources

## Example Questions

### Example Question #515 : Algebra

Simplify: 3^{2} * (4^{23} - 4^{21})

**Possible Answers:**

4^4

3^3 * 4^21

3^3 * 4^21 * 5

3^21

None of the other answers

**Correct answer:**

3^3 * 4^21 * 5

Begin by noting that the group (4^{23} - 4^{21}) has a common factor, namely 4^{21}. You can treat this like any other constant or variable and factor it out. That would give you: 4^{21}(4^{2} - 1). Therefore, we know that:

3^{2} * (4^{23} - 4^{21}) = 3^{2} * 4^{21}(4^{2} - 1)

Now, 4^{2} - 1 = 16 - 1 = 15 = 5 * 3. Replace that in the original:

3^{2} * 4^{21}(4^{2} - 1) = 3^{2} * 4^{21}(3 * 5)

Combining multiples withe same base, you get:

3^{3} * 4^{21} * 5

### Example Question #1 : How To Subtract Exponents

Quantitative Comparison

Quantity A: 6^{4} – 3^{2}

Quantity B: 5^{2} – 4^{2}

**Possible Answers:**

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined from the information given.

**Correct answer:**

Quantity A is greater.

We can solve this without actually doing the math. Let's look at 6^{4} vs 5^{2}. 6^{4} is clearly bigger. Now let's look at 3^{2} vs 4^{2}. 3^{2} is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.

### Example Question #2 : How To Subtract Exponents

, and is odd.

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined from the information given.

**Correct answer:**

Quantity A is greater.

The first thing to note is the relationship between (–b) and (1 – b):

(–b) < (1 – b) because (–b) + 1 = (1 – b).

Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.

Raising a negative number to an odd power produces another negative number.

Thus (–b)^{a} < (1 – b)^{a} < 0.

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