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How can I solve the equation?

This topic has 5 expert replies and 0 member replies

How can I solve the equation?

Post Fri Nov 10, 2017 6:31 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    $$If\ y\ne0\ and\ \frac{x}{y}=3,\ then\ \frac{\left(x-y\right)}{x}=\ ?$$

    A. -2
    B. -1
    C. -2/3
    D. 2/3
    E. 1

    The OA is D .

    How can I use the hypothesis to solve the equation? It is not the same fraction.

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    Post Fri Nov 10, 2017 6:52 am
    Vincen wrote:
    $$If\ y\ne0\ and\ \frac{x}{y}=3,\ then\ \frac{\left(x-y\right)}{x}=\ ?$$

    A. -2
    B. -1
    C. -2/3
    D. 2/3
    E. 1

    The OA is D .

    How can I use the hypothesis to solve the equation? It is not the same fraction.
    Pick easy numbers. If x = 3 and y = 1, then (x-y)/x = (3-1)/3 = 2/3. The answer is D

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    Post Fri Nov 10, 2017 7:00 am
    You have a few options here:

    #1: Substitution
    If x/y = 3, then x = 3y
    So, given
    $$\ \frac{\left(x-y\right)}{x}=\ ?$$
    Rewrite as
    $$\frac{3y-y}{3y}$$
    $$\frac{2y}{3y}$$
    $$\frac{2}{3}$$

    The answer is D.

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    Post Fri Nov 10, 2017 7:04 am
    Option #2: Split the fraction
    If we have a single term in our denominator & we're adding or subtracting in the numerator, we're allowed to split it into 2 fractions:
    $$\frac{x-y}{x}=\frac{x}{x}-\frac{y}{x}$$
    $$1-\frac{y}{x}$$

    If $$\frac{x}{y}=3$$
    then $$\frac{y}{x}=\frac{1}{3}$$

    So, $$1-\frac{1}{3}=\frac{2}{3}$$

    The answer is D.

    _________________


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    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


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    Post Fri Nov 10, 2017 1:12 pm
    Quote:
    $$If\ y\ne0\ and\ \frac{x}{y}=3,\ then\ \frac{\left(x-y\right)}{x}=\ ?$$

    A. -2
    B. -1
    C. -2/3
    D. 2/3
    E. 1

    The OA is D .

    How can I use the hypothesis to solve the equation? It is not the same fraction.
    Hi Vincen,
    Let's take a look at your question.

    We will use the substitution method to solve it.
    The first equation is :
    $$\frac{x}{y}=3$$
    Which implies:
    $$x=3y\ $$

    Plugin x = 3y in second equation.
    $$\frac{\left(x-y\right)}{x}=?$$
    $$=\frac{\left(3y-y\right)}{3y}$$
    $$=\frac{2y}{3y}=\frac{2}{3}$$

    Therefore, Option D is correct.

    Hope it helps.
    I am available if you'd like any follow up.

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    GMAT/MBA Expert

    Post Fri Nov 10, 2017 1:24 pm
    Since x/y = 3, we know x = 3y.

    Replacing x with with 3y in our other fraction gives

    (x - y)/x =>

    (3y - y)/3y =>

    2y/3y =>

    2/3

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