GRE Math : How to solve for a variable as part of a fraction

Study concepts, example questions & explanations for GRE Math

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Example Questions

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

find x

6/x = 9/19

Possible Answers:

7/12

3/38

9/114

none of these

not possible

Correct answer:

none of these

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

Example Question #3251 : Sat Mathematics

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

Find x.

Possible Answers:

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

None

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

\dpi{100} \small 0.25

\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 #71 : Algebraic Fractions

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.

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

If  , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Start by cross multiplying to get the equation

.

Then simplify by subtracting  from each side to get the solution,

 .

Example Question #481 : Algebra

If , then what is  equal to?

Possible Answers:

Correct answer:

Explanation:

We start by solving for x in  by multiplying 4 and 15, which gives us .

Then substituting 60 for x in,

 gives us

  which equals 0.

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

If  , and , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Start by cross multiplying which gives us .

Simplify by dividing both sides by  which gives us .

Isolate  by dividing both sides by  and then adding  to both sides, which gives us .

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

If , and  what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Start by cross multiplying which gives us 

.

Divide both sides by 12 and simplify which gives us .

Since , we only take the positive square root as the solution, .

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