# np < 0

\$\$np<0\$\$

 Quantity A \$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\$ Quantity B \$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\$ \$|p+n|\$ \$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\$ \$|p|\$+\$|n|\$
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 3 of the second Quantitative section of Practice Test 1. Those questions testing our knowledge of Real Numbers 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 see that both quantities have absolute value signs. Also, we have an inequality showing that the product of two variables is less than \$0\$. We know that comparing the product of two numbers to \$0\$ is a special case. Both of these tidbits of info are part of the Real Numbers GRE math skill. 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.

1. The product of \$n\$ and \$p\$ is negative
2. We want to compare two expressions involving \$n\$ and \$p\$ with absolute value signs

## Develop a Plan

We know that the product between \$n\$ and \$p\$ is negative. This tells us that one of the two variables must be positive and the other must be negative. Seems like an important bit of information. Might also be just what we need to solve this question.

## Solve the Question

Absolute value signs represent the distance a number is away from \$0\$. For example, the value \$2\$ is a distance of \$2\$ away from \$0\$, and the value \$-2\$ is also a distance of \$2\$ away from \$0\$. For Quantity B, we’re taking the absolute value of \$n\$ and \$p\$ separately, so we’re adding together their distances from \$0\$. For Quantity A, we’re taking the absolute value of \$(n+p)\$. Since \$n\$ and \$p\$ have opposite signs with one being positive and the other being negative, it’s analogous to starting at position \$0\$, traveling in one direction a distance \$n\$, and then reversing direction and traveling a distance \$p\$. We won’t be as far away from our starting position as if we had started at position \$0\$, traveled in one direction a distance \$n\$, and then kept traveling in the same direction a distance \$p\$. So since for Quantity A we’re traveling in one direction a distance \$n\$ and then doubling back and traveling a distance \$p\$, we won’t be as far away from our starting position as we would for Quantity B, where we’re traveling a distance \$n\$ and then staying in the same direction and traveling a distance \$p\$.
So the correct answer is B, Quantity B is greater.

## What Did We Learn

It was very helpful to think of absolute value signs as representing the distance a value is from \$0\$. Here, it was easier to see that if we have numbers with opposite signs, the total distance traveled would be less than how far away the starting and final positions were.

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