Operations - GRE Quantitative Reasoning

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Question

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

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Answer

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

$\frac{15}{x}\frac{y}{y}+\frac{12}{y}\frac{x}{x}$

This is the same as:

$\frac{15y}{xy}+\frac{12x}{xy}$ , or $\frac{15y+12x}{xy}$

This is the same as Quantity B. They are equal!

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Question

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

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Answer

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

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Question

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

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Answer

Simplify expressions inside parentheses first: $\dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}$ and $\dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}$

Now we have: $\frac{1}{4} + \frac{1}{2} - \frac{2}{3}$

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

$\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}$

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Question

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

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Answer

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

$\frac{15}{x}\frac{y}{y}+\frac{12}{y}\frac{x}{x}$

This is the same as:

$\frac{15y}{xy}+\frac{12x}{xy}$ , or $\frac{15y+12x}{xy}$

This is the same as Quantity B. They are equal!

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Question

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Tap to reveal answer

Answer

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

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Question

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

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Answer

Simplify expressions inside parentheses first: $\dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}$ and $\dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}$

Now we have: $\frac{1}{4} + \frac{1}{2} - \frac{2}{3}$

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

$\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}$

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Question

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

Tap to reveal answer

Answer

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

$\frac{15}{x}\frac{y}{y}+\frac{12}{y}\frac{x}{x}$

This is the same as:

$\frac{15y}{xy}+\frac{12x}{xy}$ , or $\frac{15y+12x}{xy}$

This is the same as Quantity B. They are equal!

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Question

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Tap to reveal answer

Answer

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

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Question

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Tap to reveal answer

Answer

Simplify expressions inside parentheses first: $\dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}$ and $\dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}$

Now we have: $\frac{1}{4} + \frac{1}{2} - \frac{2}{3}$

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

$\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}$

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Question

Car A traveled 120 miles with 5 gallons of fuel.

Car B can travel 25 miles per gallon of fuel.

Quantity A: The fuel efficiency of car A

Quantity B: The fuel efficiency of car B

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Answer

Let's make the two quantities look the same.

Quantity A: 120 miles / 5 gallons = 24 miles / gallon

Quantity B: 25 miles / gallon

Quantity B is greater.

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Question

Quantity A:

The -value of the equation $y = \frac{3}{4}x-2$ when $y = \frac{-1}{3}$

Quantity B:

$\frac{3}{4}$

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Answer

In order to solve quantitative comparison problems, you must first deduce whether or not the problem is actually solvable. Since this consists of finding the solution to an -coordinate on a line where nothing too complicated occurs, it will be possible.

Thus, your next step is to solve the problem.

Since $y = \frac{3}{4}x-2$ and $y = \frac{-1}{3}$ , you can plug in the -value and solve for :

$y = \frac{3}{4}x-2$

Plug in y:

$\frac{-1}{3} = \frac{3}{4}x-2$

Add 2 to both sides:

$\frac{5}{3} = \frac{3}{4}x$

Divide by 3/4. To divide, first take the reciprocal of 3/4 (aka, flip it) to get 4/3, then multiply that by 5/3:

$\frac{20}{9} = x$

Make the improper fraction a mixed number:

$2\tfrac{2}{9}$

Now that you have what x equals, you can compare it to Quantity B.

Since $2\tfrac{2}{9}$ is bigger than 2, the answer is that Quantity A is greater

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Question

What is equivalent to $\frac{\frac{1}{5}}{\frac{4}{15}}$ ?

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Answer

Remember that when you divide by a fraction, you multiply by the reciprocal of that fraction. Therefore, this division really is:

$\frac{1}{5}\cdot \frac{15}{4}$

At this point, it is merely a matter of simplification and finishing the multiplication:

$\frac{1}{5}\cdot\frac{15}{4}=\frac{15}{20}=\frac{3}{4}$

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Question

Which of the following is equivalent to $\frac{7}{\frac{4}{5}}$ ?

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Answer

To begin with, most students find it easy to remember that...

$\frac{7}{\frac{4}{5}}=\frac{\frac{7}{1}}{\frac{4}{5}}$

From this, you can apply the rule of division of fractions. That is, multiply by the reciprocal:

Therefore,

$\frac{\frac{7}{1}}{\frac{4}{5}} = \frac{7}{1} \cdot \frac{5}{4}=\frac{35}{4}$

Since nothing needs to be reduced, this is your answer.

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Question

Car A traveled 120 miles with 5 gallons of fuel.

Car B can travel 25 miles per gallon of fuel.

Quantity A: The fuel efficiency of car A

Quantity B: The fuel efficiency of car B

Tap to reveal answer

Answer

Let's make the two quantities look the same.

Quantity A: 120 miles / 5 gallons = 24 miles / gallon

Quantity B: 25 miles / gallon

Quantity B is greater.

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Question

Quantity A:

The -value of the equation $y = \frac{3}{4}x-2$ when $y = \frac{-1}{3}$

Quantity B:

$\frac{3}{4}$

Tap to reveal answer

Answer

In order to solve quantitative comparison problems, you must first deduce whether or not the problem is actually solvable. Since this consists of finding the solution to an -coordinate on a line where nothing too complicated occurs, it will be possible.

Thus, your next step is to solve the problem.

Since $y = \frac{3}{4}x-2$ and $y = \frac{-1}{3}$ , you can plug in the -value and solve for :

$y = \frac{3}{4}x-2$

Plug in y:

$\frac{-1}{3} = \frac{3}{4}x-2$

Add 2 to both sides:

$\frac{5}{3} = \frac{3}{4}x$

Divide by 3/4. To divide, first take the reciprocal of 3/4 (aka, flip it) to get 4/3, then multiply that by 5/3:

$\frac{20}{9} = x$

Make the improper fraction a mixed number:

$2\tfrac{2}{9}$

Now that you have what x equals, you can compare it to Quantity B.

Since $2\tfrac{2}{9}$ is bigger than 2, the answer is that Quantity A is greater

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Question

What is equivalent to $\frac{\frac{1}{5}}{\frac{4}{15}}$ ?

Tap to reveal answer

Answer

Remember that when you divide by a fraction, you multiply by the reciprocal of that fraction. Therefore, this division really is:

$\frac{1}{5}\cdot \frac{15}{4}$

At this point, it is merely a matter of simplification and finishing the multiplication:

$\frac{1}{5}\cdot\frac{15}{4}=\frac{15}{20}=\frac{3}{4}$

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Question

Which of the following is equivalent to $\frac{7}{\frac{4}{5}}$ ?

Tap to reveal answer

Answer

To begin with, most students find it easy to remember that...

$\frac{7}{\frac{4}{5}}=\frac{\frac{7}{1}}{\frac{4}{5}}$

From this, you can apply the rule of division of fractions. That is, multiply by the reciprocal:

Therefore,

$\frac{\frac{7}{1}}{\frac{4}{5}} = \frac{7}{1} \cdot \frac{5}{4}=\frac{35}{4}$

Since nothing needs to be reduced, this is your answer.

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Question

Car A traveled 120 miles with 5 gallons of fuel.

Car B can travel 25 miles per gallon of fuel.

Quantity A: The fuel efficiency of car A

Quantity B: The fuel efficiency of car B

Tap to reveal answer

Answer

Let's make the two quantities look the same.

Quantity A: 120 miles / 5 gallons = 24 miles / gallon

Quantity B: 25 miles / gallon

Quantity B is greater.

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Question

Quantity A:

The -value of the equation $y = \frac{3}{4}x-2$ when $y = \frac{-1}{3}$

Quantity B:

$\frac{3}{4}$

Tap to reveal answer

Answer

In order to solve quantitative comparison problems, you must first deduce whether or not the problem is actually solvable. Since this consists of finding the solution to an -coordinate on a line where nothing too complicated occurs, it will be possible.

Thus, your next step is to solve the problem.

Since $y = \frac{3}{4}x-2$ and $y = \frac{-1}{3}$ , you can plug in the -value and solve for :

$y = \frac{3}{4}x-2$

Plug in y:

$\frac{-1}{3} = \frac{3}{4}x-2$

Add 2 to both sides:

$\frac{5}{3} = \frac{3}{4}x$

Divide by 3/4. To divide, first take the reciprocal of 3/4 (aka, flip it) to get 4/3, then multiply that by 5/3:

$\frac{20}{9} = x$

Make the improper fraction a mixed number:

$2\tfrac{2}{9}$

Now that you have what x equals, you can compare it to Quantity B.

Since $2\tfrac{2}{9}$ is bigger than 2, the answer is that Quantity A is greater

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Question

What is equivalent to $\frac{\frac{1}{5}}{\frac{4}{15}}$ ?

Tap to reveal answer

Answer

Remember that when you divide by a fraction, you multiply by the reciprocal of that fraction. Therefore, this division really is:

$\frac{1}{5}\cdot \frac{15}{4}$

At this point, it is merely a matter of simplification and finishing the multiplication:

$\frac{1}{5}\cdot\frac{15}{4}=\frac{15}{20}=\frac{3}{4}$

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Knew It

Operations - GRE Quantitative Reasoning

Quantity A: Quantity B: Which of the following is true?

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications: This is the same as: , or This is the same as Quantity B. They are equal!

What is the result of adding of to ?

Reduce to simplest form:

Simplify expressions inside parentheses first: and Now we have: Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

Quantity A: Quantity B: Which of the following is true?

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications: This is the same as: , or This is the same as Quantity B. They are equal!

What is the result of adding of to ?

Reduce to simplest form:

Simplify expressions inside parentheses first: and Now we have: Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

Quantity A: Quantity B: Which of the following is true?

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications: This is the same as: , or This is the same as Quantity B. They are equal!

What is the result of adding of to ?

Reduce to simplest form:

Simplify expressions inside parentheses first: and Now we have: Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

Car A traveled 120 miles with 5 gallons of fuel. Car B can travel 25 miles per gallon of fuel. Quantity A: The fuel efficiency of car A Quantity B: The fuel efficiency of car B

Let's make the two quantities look the same. Quantity A: 120 miles / 5 gallons = 24 miles / gallon Quantity B: 25 miles / gallon Quantity B is greater.

Quantity A: The -value of the equation when Quantity B:

What is equivalent to ?

Remember that when you divide by a fraction, you multiply by the reciprocal of that fraction. Therefore, this division really is: At this point, it is merely a matter of simplification and finishing the multiplication:

Which of the following is equivalent to ?

To begin with, most students find it easy to remember that... From this, you can apply the rule of division of fractions. That is, multiply by the reciprocal: Therefore, Since nothing needs to be reduced, this is your answer.

Car A traveled 120 miles with 5 gallons of fuel. Car B can travel 25 miles per gallon of fuel. Quantity A: The fuel efficiency of car A Quantity B: The fuel efficiency of car B

Let's make the two quantities look the same. Quantity A: 120 miles / 5 gallons = 24 miles / gallon Quantity B: 25 miles / gallon Quantity B is greater.

Quantity A: The -value of the equation when Quantity B:

What is equivalent to ?

Remember that when you divide by a fraction, you multiply by the reciprocal of that fraction. Therefore, this division really is: At this point, it is merely a matter of simplification and finishing the multiplication:

Which of the following is equivalent to ?

To begin with, most students find it easy to remember that... From this, you can apply the rule of division of fractions. That is, multiply by the reciprocal: Therefore, Since nothing needs to be reduced, this is your answer.

Car A traveled 120 miles with 5 gallons of fuel. Car B can travel 25 miles per gallon of fuel. Quantity A: The fuel efficiency of car A Quantity B: The fuel efficiency of car B

Let's make the two quantities look the same. Quantity A: 120 miles / 5 gallons = 24 miles / gallon Quantity B: 25 miles / gallon Quantity B is greater.

Quantity A: The -value of the equation when Quantity B:

What is equivalent to ?

Remember that when you divide by a fraction, you multiply by the reciprocal of that fraction. Therefore, this division really is: At this point, it is merely a matter of simplification and finishing the multiplication:

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

What is the result of adding of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Reduce to simplest form: $\frac{1}{4}+(\frac{4}{3}\times \frac{3}{8})-(\frac{1}{4}\div \frac{3}{8})$

Car A traveled 120 miles with 5 gallons of fuel.

Car B can travel 25 miles per gallon of fuel.

Quantity A: The fuel efficiency of car A

Quantity B: The fuel efficiency of car B

Let's make the two quantities look the same.

Quantity A: 120 miles / 5 gallons = 24 miles / gallon

Quantity B: 25 miles / gallon

Quantity B is greater.

Quantity A:

The -value of the equation $y = \frac{3}{4}x-2$ when $y = \frac{-1}{3}$

Quantity B:

$\frac{3}{4}$

What is equivalent to $\frac{\frac{1}{5}}{\frac{4}{15}}$ ?

Which of the following is equivalent to $\frac{7}{\frac{4}{5}}$ ?

Car A traveled 120 miles with 5 gallons of fuel.

Car B can travel 25 miles per gallon of fuel.

Quantity A: The fuel efficiency of car A

Quantity B: The fuel efficiency of car B

Let's make the two quantities look the same.

Quantity A: 120 miles / 5 gallons = 24 miles / gallon

Quantity B: 25 miles / gallon

Quantity B is greater.

Quantity A:

The -value of the equation $y = \frac{3}{4}x-2$ when $y = \frac{-1}{3}$

Quantity B:

$\frac{3}{4}$

What is equivalent to $\frac{\frac{1}{5}}{\frac{4}{15}}$ ?

Which of the following is equivalent to $\frac{7}{\frac{4}{5}}$ ?

Car A traveled 120 miles with 5 gallons of fuel.

Car B can travel 25 miles per gallon of fuel.

Quantity A: The fuel efficiency of car A

Quantity B: The fuel efficiency of car B

Let's make the two quantities look the same.

Quantity A: 120 miles / 5 gallons = 24 miles / gallon

Quantity B: 25 miles / gallon

Quantity B is greater.

Quantity A:

The -value of the equation $y = \frac{3}{4}x-2$ when $y = \frac{-1}{3}$

Quantity B:

$\frac{3}{4}$

What is equivalent to $\frac{\frac{1}{5}}{\frac{4}{15}}$ ?