A teacher took a container filled with 16 liters of water to a school

A teacher took a container filled with $16$ liters of water to a school picnic. After several students had taken water from the container, the container had $14$ liters of water left. What was the percent decrease in the amount of water in the container?

  1. $6.25%$
  2. $8.00%$
  3. $12.50%$
  4. $14.30%$
  5. $87.50%$

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 9 of Section 6 of Practice Test 1. Those questions testing our knowledge of Ratios and Proportions 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 your paper.

This question wants us to calculate a percent decrease, so it likely evaluates how well we understand the principles covered in the Decimals section of the GRE math review book. Let’s keep this in mind as we proceed.

What Do We Know?

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

 

  1. A teacher starts with $16$ liters of water
  2. Some students remove some of the water
  3. The teacher ends up with $14$ liters of water
  4. We want to calculate the percent decrease for the water

 

Develop a Plan

Since the problem asks us to calculate a percent change, let’s start by recalling its formula.

$$\Percent \Change = {\New \Value – \Original \Value}/{\Original \Value}*100%$$

We can use this formula for either percent increase or percent decrease. We’ll just get a positive value for percent increases and a negative value for percent decreases. We know that the original value of the amount of water was $16$, and the new value for the amount of water is $14$. So let’s use this formula to calculate the percent change.

Solve the Question

Plugging in the numbers ($\New \Value = 14$ and $\Original \Value = 16$) into our percent change equation gives us:

$\Percent \Change$ $=$ ${14- 16}/16·100%$
$ $ $ $
$\Percent \Change$ $=$ ${-2}/16*100%$
$ $ $ $
$\Percent \Change$ $=$ $-12.50%$

Our calculation for percent change is negative, so it is a percent decrease. The correct answer is C, $12.50%$.

What Did We Learn

Being able to recall from memory the equation for percent change was extremely helpful in solving this question.
While there won’t be a ton of equations that we need to memorize to do well on the GRE quantitative section, this is definitely one of them. So let’s memorize it!

$$\Percent \Change = {\New \Value – \Original \Value}/{\Original \Value}·100%$$

Let’s also be careful to put the original value in the denominator, not the new value. In fact, we can predict that a smart test writer will make one of the wrong answer choices the value we would get if we placed “New Value” in the denominator. So let’s always be careful with percent change questions and make sure that we never make that mistake.

 

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