MBAOver30 GMAT Quant Practice #3

Here’s GMAT Quant/Math Batch #3 from our friends at Target Test Prep . Throw these problems into your GMAT prep mix to increase your chance of breaking into scores of 680-750 and above. And don’t just go through the problem, really seek to understand the underlying rules and relationships that lead to a solution.

Here you goes:

PRACTICE PROBLEM 3A

If 5^x – 5^x-1 = 500 , what is the value of (x – 1)²?

(A) 1      (B) 4       (C) 9      (D) 25       (E) 36

Solution:

We should recognize that we have subtraction of bases with exponents. This means before we can combine the equation’s terms, we need to factor out. However, to help see what we can factor out, we can rewrite the equation.

 5^x – 5^x-1 = 500

 5^x – (5)^x(5)^-1 = 500

Now we can easily see to factor out the common term of 5^x. We now have:

 5^x – (5)^x(5)^-1 = 500

 5^x (1-5^-1) = 500

 5^x (1-1/5) = 500

 5^x × 4/5 = 500

Our next step is to break down all the values into prime factors. This will make canceling out much easier.

Finally, we have to solve for (x – 1)², so (4 – 1)² = 3² = 9

Answer: C

 

PRACTICE PROBLEM 3B

If x is an integer and -2x + 1> 7, what is the value of x?

1)  x² + 9x + 20 = 0

2)  x ≥ -4

Solution:

Question Stem Analysis:

Begin by simplifying the information given in the stem.

-2x + 1 > 7

-2x > 6

x < -3

We’ll use this information in conjunction with the statements that follow.

Statement One Alone:

x² + 9x + 20 = 0

Solve the above equation:

x² + 9x + 20 = 0

(x+4)(x+5) = 0

x = -4, x = -5

From the information given in the stem, x < -3. Since both -4 and -5 are less than -3, statement one alone is not sufficient to give us one value for x.

Eliminate answer choices A and D.

Statement Two Alone:

x ≥ -4

Since the only integer value of x that is less than -3, as required by the stem, and greater than or equal to -4 is -4, we have a single value for x.  Statement two alone is sufficient.

Answer: B

For more GMAT Help, go here.