SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1151 : Algebra

If \dpi{100} \small z>0, what is 40 percent of \dpi{100} \small 30z?

Possible Answers:

\dpi{100} \small 12z

\dpi{100} \small 20z

\dpi{100} \small 5z

\dpi{100} \small 30z

\dpi{100} \small 120z

Correct answer:

\dpi{100} \small 12z

Explanation:

To find 40 percent of \dpi{100} \small 30z multiply \dpi{100} \small 30z\times 0.4

The result is \dpi{100} \small 12z 

Example Question #1152 : Algebra

Solve for .

\frac{1}{3}(3x-6)+\frac{1}{2}(2x+4)=\frac{1}{5}(15x -5)

Possible Answers:

-2

-3

2

0

Correct answer:

Explanation:

First distribute the fractions:

Combine like terms:

Example Question #1153 : Algebra

Solve for x.

(2x+3)-3(x+5)=-(3x-4)

Possible Answers:

-8

0

-4

4

Correct answer:

Explanation:

First distribute to eliminate the parentheses:

2x+3-3x-15=-3x+4

Then combine like terms:

2x=16 

x=8

Example Question #1154 : Algebra

x = 1/2

What does 1/x + 1/(x + 4) equal?

Possible Answers:

20

4

20/9

9/2

4/9

Correct answer:

20/9

Explanation:

1/x + 1/(x+4) =

1/(1/2) + 1/ (1/2 + 4) =

1/ (1/2) + 1 / (9/2)  =

2 + 2/9

20/9

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Solve for .

Possible Answers:

Correct answer:

Explanation:

Cross multiply.

Dsitribute.

Solve for .

Example Question #1155 : Algebra

If , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.

45 / -9 = -5

 

Example Question #1156 : Algebra

Solve:

 

Possible Answers:

Correct answer:

Explanation:

We want to isolate the x. First, we take away 3 from both sides. Then we have: 

 

To get x by itself, we multiply by the reciprocal on both sides. 

Then, we have: 

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

If  , then what is the value of ?

Possible Answers:

none of these

38/3

3/38

7/12

9/114

Correct answer:

38/3

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

Example Question #2 : How To Solve For A Variable As Part Of A Fraction

\dpi{100} \small \frac{4 }{x} = \frac{2}{25}

Find x.

Possible Answers:

None

\dpi{100} \small 0.25

\dpi{100} \small \frac{8}{25}

\dpi{100} \small \frac{25}{8}

\dpi{100} \small 50

Correct answer:

\dpi{100} \small 50

Explanation:

Cross multiply:

\dpi{100} \small 4 \times 25 = 2x

\dpi{100} \small 100 = 2x

\dpi{100} \small x = 50

Example Question #3 : How To Solve For A Variable As Part Of A Fraction

The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.

Possible Answers:

Correct answer:

Explanation:

Let numerator = N and denominator = D.

According to the first statement, 

N = (D x 5) + 4.

According to the second statement, N / 2 = 3 * D. 

Let's multiply the second equation by –2 and add itthe first equation:

–N = –6D

+[N = (D x 5) + 4]

=

–6D + (D x 5) + 4 = 0

–1D + 4 = 0

D = 4

Thus, N = 24.

Therefore, N/D = 24/4 = 6.

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