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

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Example Questions

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

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

Find x.

Possible Answers:

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

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

None

$\dpi{100} \small 0.25$

$\dpi{100} \small 50$

Correct answer:

$\dpi{100} \small 50$

Explanation:

Cross multiply:

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

$\dpi{100} \small 100 = 2x$

$\dpi{100} \small x = 50$

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Example Question #2 : 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:

$\frac{1}{2}$

$\frac{1}{3}$

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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Example Question #1575 : Gre Quantitative Reasoning

If $\frac{(x-7)}{2x} = \frac{5}{9}$ , what is the value of ?

Possible Answers:

$-\frac{35}{13}$

$\frac{73}{9}$

Correct answer:

Explanation:

Start by cross multiplying to get the equation

$5\cdot2x=(x-7)\cdot 9$

10x = 9x-63 .

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

x = -63 .

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Example Question #1576 : Gre Quantitative Reasoning

If $\frac{x}{4} = 15$ , then what is $\frac{3x}{5} - 36$ equal to?

Possible Answers:

Correct answer:

Explanation:

We start by solving for x in $\frac{x}{4} = 15$ by multiplying 4 and 15, which gives us x=60 .

Then substituting 60 for x in,

$\frac{3x}{5} - 36$ gives us

$\frac{180}{5} - 36=36-36=0$ which equals 0.

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

If $\frac{x-p}{r} = \frac{q}{pr}$ , and x, p, q, r > 0 , what is the value of ?

Possible Answers:

x=q + r

$x=\frac{q}{p} + p$

$x=q + \frac{r}{p}$

$x=\frac{q}{p} - q$

$x=\frac{p}{q} + r$

Correct answer:

$x=\frac{q}{p} + p$

Explanation:

Start by cross multiplying which gives us qr = pr(x-p) .

Simplify by dividing both sides by which gives us q = p(x-p) .

Isolate by dividing both sides by and then adding to both sides, which gives us $x = \frac{q}{p} +p$ .

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

If $\frac{2}{3x} = \frac{4x}{5}$ , and x>0 what is the value of ?

Possible Answers:

$\frac{15}{8}$

$\frac{8}{15}$

$\sqrt{10}$

$-\sqrt{\frac{5}{6}}$

$\sqrt{\frac{5}{6}}$

Correct answer:

$\sqrt{\frac{5}{6}}$

Explanation:

Start by cross multiplying which gives us

4x(3x)=2(5)

$12x^{^{2}} = 10$ .

Divide both sides by 12 and simplify which gives us $x^{^{2}} = \frac{5}{6}$ .

Since x>0 , we only take the positive square root as the solution, ${}x = {\sqrt{\frac{5}{6}}}$ .

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Example Question #4 : How To Solve For A Variable As Part Of A Fraction

If $\frac{6}{x}=\frac{9}{19}$ , then what is the value of ?

Possible Answers:

3/38

38/3

9/114

7/12

none of these

Correct answer:

38/3

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

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

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

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

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

Example Question #1575 : Gre Quantitative Reasoning

Example Question #1576 : Gre Quantitative Reasoning

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

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

Example Question #4 : How To Solve For A Variable As Part Of A Fraction

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