GMAT Math : Algebra

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #21 : Algebra

Solve the following system of equations:

Possible Answers:

Correct answer:

Explanation:

To solve, I used the elimination method by adding the tqo equations together. That eliminates y and leaves you with:

Therefore,

 

Example Question #1101 : Problem Solving Questions

Which of the following equations is parallel to the line given by the equation:

Possible Answers:

Correct answer:

Explanation:

For lines to be parallel, their equations must have equal slopes. Therefore, we are looking for another line with a slope of -4/3. If we convert the equation:

into slope - intercept form, we get:

It has the same slope, and therefore is parallel to the original line.

Example Question #1102 : Problem Solving Questions

The equations  and  intersect at the point . What is y?

Possible Answers:

Correct answer:

Explanation:

The easiest way to solve the problem is to solve for y in one of the equations and then plug it into the other equation:

We can then plug that x-value into one of the original equations:

Example Question #1 : Exponents

\frac{6^{3}}{36} + \frac{3^{68}}{3^{67}}=

Possible Answers:

cannot be determined

\dpi{100} \small 6

\dpi{100} \small 18

\dpi{100} \small 36

\dpi{100} \small 9

Correct answer:

\dpi{100} \small 9

Explanation:

\frac{6^{3}}{36} = \frac{6^{3}}{6^{2}} = 6

\frac{3^{68}}{3^{67}} = 3^{68-67} = 3

Putting these together,

\frac{6^{3}}{36} + \frac{3^{68}}{3^{67}}= 6 + 3 = 9

Example Question #1 : Understanding Exponents

\dpi{100} \small 3x^{4}\times x^{2}+x^{2}-x =

Possible Answers:

3x^{9}

x(3x^{5}-x+1)

3x^{5}+x-1

3x^{7}

x(3x^{5}+x-1)

Correct answer:

x(3x^{5}+x-1)

Explanation:

\dpi{100} \small 3x^{4}\times x^{2} =3x^{6}

Then,  \dpi{100} \small 3x^{4}\times x^{2}+x^{2}-x = 3x^{6}+x^{2}-x = x(3x^{5}+x-1)

Example Question #1 : Understanding Exponents

4^{\frac{3}{2}} + 27^{\frac{2}{3}} =

Possible Answers:

\dpi{100} \small 27

\dpi{100} \small 16

\dpi{100} \small 17

\dpi{100} \small 9

\dpi{100} \small 8

Correct answer:

\dpi{100} \small 17

Explanation:

4^{\frac{3}{2}}=(4^{\frac{1}{2}})^{3} = 2^{3} = 8

27^{\frac{2}{3}}=(27^{\frac{1}{3}})^{2} = 3^{2} = 9

Then putting them together, 4^{\frac{3}{2}} + 27^{\frac{2}{3}} = 8 + 9 = 17

Example Question #1 : Exponents

Which of the following expressions is equivalent to this expression?

 

You may assume that .

Possible Answers:

Correct answer:

Explanation:

 

 

Example Question #1 : Exponents

Simplify the following expression without a calculator:

 

Possible Answers:

Correct answer:

Explanation:

The easiest way to simplify is to work from the inside out. We should first get rid of the negatives in the exponents. Remember that variables with negative exponents are equal to the inverse of the expression with the opposite sign. For example,   So using this, we simplify:  

Now when we multiply variables with exponents, to combine them, we add the exponents together. For example,  

Doing this to our expression we get it simplified to .

The next step is taking the inside expression and exponentiating it. When taking an exponent of a variable with an exponent, we actually multiply the exponents. For example, . The other rule we must know that is an exponent of one half is the same as taking the square root. So for the  So using these rules, 

Example Question #6 : Exponents

Rewrite as a single logarithmic expression:

Possible Answers:

Correct answer:

Explanation:

First, write each expression as a base 3 logarithm:

 since 

Rewrite the expression accordingly, and apply the logarithm sum and difference rules:

 

Example Question #1 : Exponents

If , what is  in terms of ?

Possible Answers:

Correct answer:

Explanation:

We have .

So , and .

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