### All GMAT Math Resources

## Example Questions

### Example Question #31 : Solving Equations

Solve for . Give all real solutions:

**Possible Answers:**

The equation has no real solution.

**Correct answer:**

One way is to substitute , and, subsequently,

Set each binomial to 0 and solve separately:

or

Since no real number has as its principal square root, this yields no solution.

The only solution is .

### Example Question #31 : Solving Equations

Solve for , giving *all *solutions, real and imaginary:

**Possible Answers:**

**Correct answer:**

Factor the expression:

Rewrite:

or

### Example Question #32 : Solving Equations

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

, so the equation can be rewritten as follows:

Set the exponents equal to each other:

### Example Question #31 : Solving Equations

Daniel has candy bars. Andy has three more candy bars than the double of Daniel's candy bars.

How many candy bars does Andy have?

**Possible Answers:**

**Correct answer:**

Let A be the number of Andy's candy bars and D be the number of Daniel's candy bars.

We start by setting up the equation:

and

So

### Example Question #33 : Solving Equations

What is the value of ?

**Possible Answers:**

**Correct answer:**

To find the value of x we need to isolate x on one side of the equation and the rest of the numbers on the other side.

First, we multiply what is in the denominator on the left had side by the numerators on both sides.

Then we distribute the 5 to both terms in the binomial. Doing this we get a zero in the exponent.

Anything raised to the zero just becomes one.

From here we subtract 0.5 from each side to solve for x.

### Example Question #34 : Solving Equations

Define . Which of the following would be a valid alternative way of expressing the definition of ?

**Possible Answers:**

**Correct answer:**

By definition:

If , then ,and subsequently,

If , then ,and subsequently,

### Example Question #341 : Algebra

Which of the following expressions is equal to ?

**Possible Answers:**

**Correct answer:**

, so , and .

### Example Question #36 : Solving Equations

A factory makes barrels of the same shape but different sizes; the amount of water they hold varies directly as the *cube* of their height. The four-foot-high barrel holds 20 gallons of water; how much water would the six-foot-high barrel hold?

**Possible Answers:**

**Correct answer:**

Let be the height of a barrel and be its volume. Since varies directly as the cube of , the variation equation is

for some constant of variation .

We find by substituting from the smaller barrels:

Then the variation equation is:

Now we can substitute to find the volume of the larger barrel:

The larger barrel holds gallons.

### Example Question #31 : Solving Equations

Solve for .

**Possible Answers:**

**Correct answer:**

### Example Question #31 : Equations

To convert Celsius temperature to the equivalent in Fahrenheit temperature , use the formula

To the nearest tenth of a degree, convert to degrees Fahrenheit.

**Possible Answers:**

**Correct answer:**

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