Last year Kate spent in between $1/4$ and $1/3$ of her gross earnings on she mortgage payments. If Kate spent $13,470$ on her mortgage payments last year, which of the following might have been her gross earnings last year?

Indicate every such gross incomes.

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So, you to be trying to it is in a great test taker and also practice for the GRE with PowerPrep online. Buuuut then you had actually some questions about the quant section—specifically inquiry 19 of ar 4 of exercise Test 1. Those questions trial and error our expertise of Fractions have the right to be sort of tricky, however never fear, has got your back!

Survey the Question

Let’s search the trouble for clues regarding what it will be testing, together this will certainly help shift our minds to think about what type of math expertise we’ll usage to settle this question. Pay fist to any kind of words that sound math-specific and anything special about what the number look like, and also mark lock on your paper.

We deserve to see 2 fractions in this question, so it most likely tests our knowledge of Fractions. Let’s keep what we’ve learned about this skill at the tip of ours minds together we technique this question.

What do We Know?

Let’s carefully read through the question and make a perform of the things that us know.

Kate spent in between $1/4$ and $1/3$ of she gross revenue on her mortgage last yearKate spent $$13,470$ on she mortgage last yearWe desire to know feasible values for her gross income

Develop a Plan

Let’s start with a top-down approach, where we will begin with what we’re looking for and also work down to the details that what we’re provided in this question. We want to understand Kate’s pistol income. We see that we’re given her mortgage and also what fraction that is of she gross income. We recognize that the general type of one equation when we have a portion of other is:

$$Amount of Something= (Fraction of Total) · Total Amount$$

Now let’s compose this especially for our problem. We know that Kate’s mortgage is a certain portion of she gross income:

$$Mortgage = Fraction of Gross Income · Gross Income$$

We’re in search of her pistol income, for this reason let’s resolve this equation because that it:

$$Gross Income = Mortgage/Fraction of Gross Income$$

We recognize her mortgage is $$13,470$ and also we have actually values for the fraction of gross income, therefore let’s usage these number to resolve for the gun income.

Solve the Question

We have two excessive values because that the fraction of gross income, due to the fact that we understand it’s somewhere between $1/4$ and also $1/3$ of the gun income. It renders sense that we should gain the extreme possible values because that gross earnings if we usage the extreme values for the fraction of gross income. Let’s resolve for these two excessive values because that the gross income, very first starting v the fraction of gross earnings being $1/4$:

$Gross Income$$=$$$13,470/1/4$
$Gross Income$$=$$$13,470·4$
$Gross Income $$=$$$53,880$

We deserve to see the whenever we division by a fraction, we can just upper and lower reversal the top and also bottom and multiply by the number. So splitting by $1/4$ is the very same as multiply by $4/1$. So in ~ one excessive value, Kate’s gross revenue was $$53,880$. Let’s fix for the other extreme value of gun income, utilizing the portion $1/3$:

$Gross Income$$=$$$13,470/1/3$
$Gross Income$$=$$$13,470·3$
$Gross Income $$=$$$40,410$

So us now recognize that the gross earnings is somewhere between $40,410$ minutes and also $$53,880$ minutes. We can see that answer choices B, C, D, and also E are in between these 2 values.

The correct answers space B, C, D, and also E.

What Did we Learn

When us are offered extreme values (the greatest and also least feasible values) because that one variable, we can often use those too much values to identify the extreme values for another variable. This can be an extremely helpful because that finding the greatest and least feasible values because that a particular variable.

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