# GMAT Quantitative Reasoning – Fun with Percentages

A grad student possesses 5 liters of blood that is 0.16% alcohol by volume. If the grad student injects 2 liters of blood in a ritual to improve his research results, his new blood alcohol content will be approximately what?

This problem tests our ability to use percentages to determine how much of something we have, and then find what percentage our amount is of some other number. We begin by determining the amount of alcohol in the grad student’s bloodstream by finding 0.16% of 5 liters. Since 0.16% is 0.0016 in decimal form, we use the following equation:

$0.0016*5=0.008$

This tells us that there is 0.008 liters of alcohol in the grad student’s blood. After injecting 2 liters of pure blood, however, the amount of alcohol will not change, but the percentage of alcohol in the grad student will. The grad student now has 7 liters of blood inside of him, so we must determine that 0.008 liters of alcohol is some percentage of those 7 liters of blood using the following:

$\frac{0.008}{7}=\frac{x}{100}$

Cross multiply:

$7x=0.8$
$x=0.114$

This gives us our final answer of 0.114%.

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