GRE Math : GRE Quantitative Reasoning

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Example Questions

Example Question #125 : Geometry

Parallelogram gre

Using the parallelogram shown above, find the area.

Possible Answers:

$4\textup{,}312\textup{mm}^{2}$

$980\textup{mm}^{2}$

$3\textup{,}256\textup{mm}^{2}$

$3\textup{,}156\textup{mm}^{2}$

$988\textup{mm}^{2}$

Correct answer:

$4\textup{,}312\textup{mm}^{2}$

Explanation:

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:

$area=base\times height$

The solution is:

$area=98\times44=4,312$

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Example Question #2 : Quadrilaterals

A parallelogram has a base of meters and a height measurement that is $\frac{1}{4}$ the base length. Find the area of the parallelogram.

Possible Answers:

$18\textup{m}^{2}$

$36\textup{m}^{2}$

$27\textup{m}^{2}$

$48\textup{m}^{2}$

$52\textup{m}^{2}$

Correct answer:

$36\textup{m}^{2}$

Explanation:

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:

$area=base\times height$
Before applying the formula you must find $\frac{1}{4}$ of .

$\frac{1}{4}\times12=\frac{12}{4}=12\div4=3$

The solution is:

$area=12\times 3=36$

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Example Question #3 : Quadrilaterals

A parallelogram has a base of $8\frac{1}{2}$ and a height of $6\frac{2}{4}$ . Find the area of the parallelogram.

Possible Answers:

$52.25\textup{ units}^{2}$

$60\textup{ units}^{2}$

$54\textup{ units}^{2}$

$55.5\textup{ units}^{2}$

$55.25\textup{ units}^{2}$

Correct answer:

$55.25\textup{ units}^{2}$

Explanation:

A parallelogram must have two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:

$area=base\times height$

The solution is:

$area=8.5\times 6.5=55.25$

Note: prior to applying the formula, the answer choices require you to be able to convert $8\frac{1}{2}$ to 8.5 , as well as $6\frac{2}{4}$ to 6.5 . Or, you could have converted the mixed numbers to improper fractions and then multiplied the two terms:

$8\frac{1}{2}=\frac{17}{2}$

$6\frac{2}{4}=\frac{26}{4}=\frac{13}{2}$

$\frac{17}{2}\times \frac{13}{2}=\frac{221}{4}=55.25$

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Example Question #131 : Plane Geometry

Parallelogram gre

Find the area of the parallelogram shown above, excluding the interior space occupied by the blue rectangle.

Possible Answers:

$58\textup{ units}^{2}$

$50\textup{ units}^{2}$

$24\textup{ units}^{2}$

$38\textup{ units}^{2}$

$42\textup{ units}^{2}$

Correct answer:

$42\textup{ units}^{2}$

Explanation:

A parallelogram must have two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:

$area=base\times height$

Additionally, this problem requires you to find the area of the interior rectangle. This can be simply found by applying the formula: $area=length\times width$

Thus, the solution is:

$area=10\times 5=50$

$4\times2=8$

50-8=42

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Example Question #132 : Plane Geometry

A parallelogram has a base of 140 and a height measurement that is $\frac{1}{2}$ the base length. Find the area of the parallelogram.

Possible Answers:

$4\textup{,}900$

$9\textup{,}800\textup{ units}^{2}$

$1\textup{,}800\textup{ units}^{2}$

$8\textup{,}200\textup{ units}^{2}$

Not enough information is provided.

Correct answer:

$9\textup{,}800\textup{ units}^{2}$

Explanation:

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:

$area=base\times height$
Before applying the formula you must find $\frac{1}{2}$ of $140=\frac{140}{2}=70$ .

The solution is:

$area=140\times 70=9,800$

Note: when working with multiples of ten remove zeros and then tack back onto the product.

$14\times7=98$

There were two total zeros in the factors, so tack on two zeros to the product:
9,800

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Example Question #2 : Quadrilaterals

Parallelogram gre

Find the area for the parallelogram shown above.

Possible Answers:

$307\textup{ units}^{2}$

$157.5\textup{ units}^{2}$

$142.5\textup{ units}^{2}$

$285\textup{ units}^{2}$

$305\textup{ units}^{2}$

Correct answer:

$285\textup{ units}^{2}$

Explanation:

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Example Question #11 : How To Find The Area Of A Parallelogram

A parallelogram has a base of $180\textup{mm}^{2}$ and a height measurement that is $\frac{1}{3}$ the base length. Find the area of the parallelogram.

Possible Answers:

$504\textup{mm}^{2}$

$540\textup{mm}^{2}$

$5\textup{,}400\textup{mm}^{2}$

$1\textup{,}800\textup{mm}^{2}$

$10\textup{,800}\textup{mm}^{2}$

Correct answer:

$10\textup{,800}\textup{mm}^{2}$

Explanation:

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:

$area=base\times height$
Before applying the formula you must find $\frac{1}{3}$ of $180=\frac{180}{3}=60$ .

The solution is:

$area=180\times 60=10,800$

Note: when working with multiples of ten remove zeros and then tack back onto the product.

$18\times6=108$

There were two total zeros in the factors, so tack on two zeros to the product:
10,800

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Example Question #12 : How To Find The Area Of A Parallelogram

Grerectangle

ABCD is a rectangle.

Quantity A: The area of AEB

Quantity B: The area BEC

Possible Answers:

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined.

Correct answer:

The two quantities are equal.

Explanation:

The area of a triangle is $\frac{1}{2}bh;b:base,h:height$

Consider the rectangle ABCD
Grerectangle

As a rectangle:

$\overline{AB}=\overline{DC}$

$\overline{AD}=\overline{BC}$

With appearing directly in the center of the rectangle.

The area of $AEB=\frac{1}{2}(\overline{AB})(\frac{1}{2}\overline{BC})=\frac{1}{4}(\overline{AB})(\overline{BC})$

Notice that the $\frac{1}{2}\overline{BC}$ term corresponds to the triangle's height.

The area of $BEC=\frac{1}{2}(\overline{BC})(\frac{1}{2}\overline{AB})=\frac{1}{4}(\overline{BC})(\overline{AB})$

The two quantities are equal.

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Example Question #11 : Quadrilaterals

Parallelogram gre

Using the parallelogram shown above, find the area.

Possible Answers:

$6480\textup{ in}^{2}$

$54 \textup{ ft}^{2}$

$504\textup{ ft}^{2}$

$540\textup{ ft}^{2}$

Not enough information is provided.

Correct answer:

$6480\textup{ in}^{2}$

Explanation:

This problem provides both the base and height measurements, thus apply the formula:

$area=base\times height$

$area=9\times 5=45$ $ft^{2}$

To find an equivalent answer in inches, you must convert the measurements to inches FIRST, and then multiply:

$9\times12=108$

$5\times12=60$

Therefore, our area in square inches is:

$108\times60=6480\ \textup{inches}$

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Example Question #1 : How To Find An Angle In A Parallelogram

In a given parallelogram, the measure of one of the interior angles is 25 degrees less than another. What is the approximate measure rounded to the nearest degree of the larger angle?

Possible Answers:

101 degrees

77 degrees

78 degrees

102 degrees

103 degrees

Correct answer:

103 degrees

Explanation:

There are two components to solving this geometry puzzle. First, one must be aware that the sum of the measures of the interior angles of a parallelogram is 360 degrees (sum of the interior angles of a figure = 180(n-2), where n is the number of sides of the figure). Second, one must know that the other two interior angles are doubles of those given here. Thus if we assign one interior angle as x and the other as x-25, we find that x + x + (x-25) + (x-25) = 360. Combining like terms leads to the equation 4x-50=360. Solving for x we find that x = 410/4, 102.5, or approximately 103 degrees. Since x is the measure of the larger angle, this is our answer.

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GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #125 : Geometry

Example Question #2 : Quadrilaterals

Example Question #3 : Quadrilaterals

Example Question #131 : Plane Geometry

Example Question #132 : Plane Geometry

Example Question #2 : Quadrilaterals

Example Question #11 : How To Find The Area Of A Parallelogram

Example Question #12 : How To Find The Area Of A Parallelogram

Example Question #11 : Quadrilaterals

Example Question #1 : How To Find An Angle In A Parallelogram

All GRE Math Resources

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