A certain recipe requires 3/2 cups of sugar and makes 2 dozen

A certain recipe requires $3/2$ cups of sugar and makes $2$ dozen cookies. ($1 \dozen=12$)

Quantity A $\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ Quantity B
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$
The amount of sugar required for the same recipe to make $30$ cookies $\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ $2$ cups
  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given

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 2 of Section 4 of Practice Test 1. Those Fractions questions can be kind of tricky, but never fear, PrepScholar 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 our paper.

We can see a fraction ($3/2$) in this question, so let’s keep in mind what we’ve learned about Fractions
from arithmetic.

What Do We Know?

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

 

  1. We are given a conversion between cups of sugar and cookies
  2. We want to compare the amount of sugar needed to make $30$ cookies to $2$ cups of sugar

 

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 compare the amount of sugar needed to make $30$ cookies to $2$ cups of sugar. It’s hard to compare two quantities written in different units, so let’s convert Quantity A so that it only has “cups of sugar” as its units.

What do we know about Quantity A? Well, it definitely has $30$ cookies, so let’s start there. We can see that we have a conversion between dozens of cookies and the number of cookies:

$$1 \Dozen \Cookies = 12 \Cookies$$

We also have a conversion between cups of sugar and dozens of cookies:

$$3/2 \Cups \of \Sugar = 2 \Dozen \Cookies$$

So let’s plan to convert Quantity A from cookies to dozens of cookies to cups of sugar in two steps:

$$30 \Cookies →?\; \Dozens \of \Cookies → ?\; \Cups \of \Sugar$$

Solve the Question

For converting units we always start with what we are given. Then we multiply it by a conversion factor which is a fraction with the units we’re converting to on top and the units that we had before on the bottom.Let’s start by converting $30$ cookies into dozens of cookies.

$$30 \Cookies · ({1 \Dozen \Cookies}/{12 \Cookies}) = 30/12\; \Dozens \of \Cookies$$

The “Cookies” unit cancels since it is on both the top and bottom. Also, no need to simplify the numbers yet, we’ll just save them all and do the arithmetic at the end. Now, let’s convert the Dozens of Cookies into cups of sugar, using the conversion equation that has both of these units:

$$30/12\; {\Dozens \of \Cookies} ·({3/2 \Cups \of \Sugar}/{2 \Dozens \of \Cookies})= {30·3}/{12·2·2} \Cups \of \Sugar$$

Any numbers that started on top of a fraction stay on top of the fraction, and numbers on the bottom stay on the bottom. Excellent! Now we just need to finish out this arithmetic and compare this value for Quantity A to the value in Quantity B, $2$ cups of sugar. Let’s just go ahead and plug these numbers into our calculator, since it won’t take much time:

$${30·3}/{12·2·2}={90}/{48} = 1.875$$

So Quantity A is $1.875$ cups of sugar, which is less than Quantity B.

The correct answer is B, Quantity B is greater.

What Did We Learn

For questions where we must convert units, we will always begin by writing down what we definitely know we have on our paper. In this case, for Quantity A we definitely have $30$ cookies, so that’s what we start with. Then, we multiply by conversion fractions, being sure to put the units that we want to cancel on the bottom part of the fraction.

 

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