Indicate all such gross incomes.
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So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 19 of Section 4 of Practice Test 1. Those questions testing our knowledge of Fractions can be kind of tricky, but never fear, thedesigningfairy.com has got your back!
Survey the Question
Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on your paper.
We can see two fractions in this question, so it likely tests our knowledge of Fractions. Let’s keep what we’ve learned about this skill at the tip of our minds as we approach this question.
What Do We Know?
Let’s carefully read through the question and make a list of the things that we know.Kate spent between $1/4$ and $1/3$ of her gross income on her mortgage last yearKate spent $$13,470$ on her mortgage last yearWe want to know possible values for her gross income
Develop a Plan
Let’s start with a top-down approach, where we will begin with what we’re looking for and work down to the details of what we’re given in this question. We want to know Kate’s gross income. We see that we’re given her mortgage and what fraction that is of her gross income. We know that the general form of an equation when we have a fraction of something is:
$$Amount of Something= (Fraction of Total) · Total Amount$$
Now let’s write this specifically for our problem. We know that Kate’s mortgage is a certain fraction of her gross income:
$$Mortgage = Fraction of Gross Income · Gross Income$$
We’re looking for her gross income, so let’s solve this equation for it:
$$Gross Income = Mortgage/Fraction of Gross Income$$
We know her mortgage is $$13,470$ and we have values for the fraction of gross income, so let’s use these numbers to solve for the gross income.
Solve the Question
We have two extreme values for the fraction of gross income, since we know it’s somewhere between $1/4$ and $1/3$ of the gross income. It makes sense that we should get the extreme possible values for gross income if we use the extreme values for the fraction of gross income. Let’s solve for these two extreme values for the gross income, first starting with the fraction of gross income being $1/4$:
|$Gross Income $||$=$||$$53,880$|
We can see that whenever we divide by a fraction, we can just flip the top and bottom and multiply by that number. So dividing by $1/4$ is the same as multiplying by $4/1$. So at one extreme value, Kate’s gross income was $$53,880$. Let’s solve for the other extreme value of gross income, using the fraction $1/3$:
|$Gross Income $||$=$||$$40,410$|
So we now know that the gross income is somewhere between $40,410$ minutes and $$53,880$ minutes. We can see that answer choices B, C, D, and E are between these two values.
The correct answers are B, C, D, and E.
What Did We Learn
When we are given extreme values (the greatest and least possible values) for one variable, we can often use those extreme values to determine the extreme values for another variable. This can be very helpful for finding the greatest and least possible values for a certain variable.
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