GRE Quantitative Reasoning - How to find the part from the whole

A given colony of ants was made up of insects. % of these were workers and % were drones. If the remainder were warrirors, how many warriors were there?

Explanation

To begin with, you know that there are , or % that are warriors. This means that % of are warriors. Remember, translate of as multiplication and "are" / "is" as equals. This gives you:

$0.35\cdot7500=2625$ warriors.

If % of students in a school have brown eyes and the rest have green, how many green-eyed students are there in a school of students?

Explanation

Based on our data, we know that , or percent of the students have green eyes. Explicitly written, this is: percent of students are green-eyed.

Remember that we translate "of" as multiplication and "is" / "are" as equals. Therefore, this is:

$0.55\cdot 1480 =x$

Bob and Nancy, while working together at the same rate, can clean their entire house in 3 hours. What fraction of the house can Bob clean in 45 minutes?

$\frac{1}{8}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{16}$

$\frac{1}{10}$

Explanation

Since Bob and Nancy work at the same rate, each person can finish $\frac{1}{2}$ of the job in 3 hours. Because 45 minutes is $\frac{1}{4}$ of 3 hours, Bob working alone would get $\frac{1}{8}$ of the job done, $\frac{1}{4}\cdot \frac{1}{2}$ .

Quantity A:

, where is of

Quantity B:

, where is of

Which of the following is true?

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

A comparison cannot be detemined from the given information.

Explanation

This type of problem is very easy. You merely need to translate the text into the form of an equation. For this, remember that "of" is translated as multiplication and "is" as equality. This gives us the following.

Quantity A:

is of

Becomes...

$x = 0.65 \cdot 408 = 265.2$

Quantity B:

is of

Becomes...

$y = 0.4 \cdot 663 = 265.2$

Therefore, the two quantities are equal.

Quantity A:

, where is of

Quantity B:

, where is of

Which of the following is true?

Quantity B is larger.

Quantity A is larger.

The two quantities are equal.

A comparison cannot be detemined from the given information.

Explanation

Quantity A:

is of

Becomes...

$x = 0.27 \cdot 150=40.5$

Quantity B:

is of

Becomes...

$y = 0.94 \cdot 75 = 70.5$

Therefore, quantity B is larger.

A bag contains $\textup{500 coins}$ . are quarters, are dimes and the rest are nickels. How much money is in the bag in nickels?

Explanation

To solve this problem we must first find what percent of the money in the bag is in nickels. We know that combined, quarters and dimes make up 40% of the coins and that the rest are nickels. Therefore 60% of the money in the bag are nickels. We then multiply the total amount of coins in the bag with that percentage in order to find out how many nickels are in the bag. . There are 300 nickels in the bag and nickels are worth 5 cents each. Therefore $300*0.05=15 \textup{ dollars}$ worth of nickels in the bag.