So, you were trying to be a great test taker and exercise for the GRE with PowerPrep digital. Buuuut then you had some inquiries about the quant section—especially question 20 of Section 4 of Practice Test 1. Those inquiries experimentation our knowledge of **Ratios and Proportions** have the right to be type of tricky, however never are afraid, soimg.org has actually gained your back!

## Survey the Question

Let’s search the difficulty for ideas as to what it will be experimentation, as this will certainly assist change our minds to think about what form of math expertise we’ll usage to settle this question. Pay attention to any words that sound math-particular and also anything distinct about what the numbers look prefer, and mark them on your paper.

You are watching: The quantities s and t are positive and are related by the equation

We see the word “percent” pointed out a pair of times. So we need to intend to use our knowledge of **Fractions, Decimals, and Percents** below.

## What Do We Know?

Let’s very closely read via the question and make a list of the things that we know.

$S$ and $T$ are associated by the equation $S=k/T$$k$ is a constant that doesn’t changeWe will rise the worth of $S$ by $50$ percentWe want to understand by what percent $T$ decreases## Develop a Plan

We understand that we have actually two situations for $S$ and $T$: 1) Before enhancing $S$ by $50$ percent and 2) After enhancing $S$ by $50$ percent. Our equation with $S$ and $T$ in it has a continuous, $k$. We recognize that if we fix this equation for $k$, then the product between $S$ and also $T$ should be continuous because $k$ is continuous.

$$S·T = k$$

We recognize that the product in between the original worths of $S$ and also $T$ should be $k$:

$$S_original·T_original = k$$

We additionally recognize that the product in between the brand-new values of $S$ and $T$ need to additionally be $k$:

$$S_new·T_new = k$$

**Due to the fact that both equations are equal to $k$, we deserve to collection them equal to each other**.

$$S_new·T_new = S_original·T_original$$

We are told $S$ raised by $50$ percent. We remember that the equation for percent rise is:

$$New Value = (1 + Percent Change/100) * Old Value$$

Now let’s rewrite this equation for the $S$ value being raised by $50$ percent:

$$S_new = 1.50*S_original$$

We know if we deserve to plug this equation right into our equation with 4 variables, then we deserve to solve for the new worth of $T$.

## Solve the Question

Solving the mechanism of equations we get:

$S_new·T_new$ | $=$ | $S_original·T_original$ |

$1.5*S_original*T_new$ | $=$ | $S_original*T_original$ |

$T_new$ | $=$ | $T_original/1.5$ |

$T_new$ | $=$ | $0.6667*T_original$ |

We understand we want an answer as a **percent decrease**, so let’s go ahead and readjust this decimal worth into a percentage.

$$0.6667 = 66.67%$$

Great, so we’ve solved this equation and found out that the brand-new $T$ is $66.67$ percent of the original value of $T$. We understand that we deserve to subtract this number from $100$ percent to acquire the percent decrease in $T$:

$$100 – 66.67% = 33.33%$$

So our last ** correct answer will be B, $33 1/3%$**.

Math equations rock! While it might have been tempting to try to figure out this answer without creating out these equations with the original and brand-new values of $S$ and $T$, the trouble was certainly exceptionally controllable when we decided to rely on these math equations. Translating words into math equations is a beneficial skill that we should continue to boost.

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