GRE Math : GRE Quantitative Reasoning

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Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Parallelogram gre

Using the parallelogram shown above, find the length of side

Possible Answers:

Correct answer:

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of and two base sides each with a length of 18. Since the perimeter and one base length is provided in the question, work backwards using the perimeter formula:

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

68=2(18+b)

68=36+2b

2b=68-36=32

$b=\frac{32}{2}=16$

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Example Question #1342 : Gre Quantitative Reasoning

A parallelogram has a base of . The perimeter of the parallelogram is . Find the sum of the two adjacent sides to the base.

Possible Answers:

Correct answer:

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of and two base sides each with a length of . In this question, you are provided with the information that the parallelogram has a base of and a total perimeter of . Thus, work backwards using the perimeter formula in order to find the sum of the two adjacent sides to the base.

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

72=2(22+b)

72=44+2b

2b=72-44=28

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Example Question #1343 : Gre Quantitative Reasoning

A parallelogram has a base of . An adjacent side to the base has a length of . Find the perimeter of the parallelogram.

Possible Answers:

47.5

Correct answer:

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of and two base sides each with a length of 28. To find the perimeter of the parallelogram apply the formula:

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

p=2(28+18)

p=2(46)

p=92

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Example Question #25 : Quadrilaterals

A parallelogram has a base of $95\textup{mm}$ . The perimeter of the parallelogram is $338\textup{mm}$ . Find the length for an adjacent side to the base.

Possible Answers:

$36\textup{mm}$

$74\textup{mm}$

$148\textup{mm}$

$42\textup{mm}$

$72\textup{mm}$

Correct answer:

$74\textup{mm}$

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of $74\textup{mm}$ and two base sides each with a length of $95\textup{mm}$ . To solve for the missing side, work backwards using the perimeter formula:

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

338=2(95+b)

338=190+2b

2b=338-190=148

$b=\frac{148}{2}=74$

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Example Question #1341 : Gre Quantitative Reasoning

A quadrilateral has equal sides, each with a length of .

Quantity A: The area of the quadrilateral.

Quantity B: The perimeter of the quadrilateral.

Possible Answers:

The relationship cannot be determined.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

Correct answer:

The relationship cannot be determined.

Explanation:

We are told that the shape is a quadrilateral and that the sides are equal; beyond that, we do not know what specific kind of kind of quadrilateral it is, outside of the fact that it is a rhombus. The perimeter, the sum of the sides, is .

If this shape were a square, the area would also be ; however, if the interior angles were not all equivalent, the area would be smaller than this.

The relationship cannot be determined.

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Example Question #151 : Plane Geometry

A rectangle has an area of 48 and a perimeter of 28. What are its dimensions?

Possible Answers:

2 x 24

0.25 x 192

1 x 48

6 x 8

16 x 3

Correct answer:

6 x 8

Explanation:

We can set up our data into the following two equations:

(Area) LH = 48

(Perimeter) 2L + 2H = 28

Solve the area equation for one of the two variables (here, length): L = 48 / H

Place that value for L into ever place you find L in the perimeter equation: 2(48 / H) + 2H = 28; then simplify:

96/H + 2H = 28

Multiply through by H: 96 + 2H² = 28H

Get everything on the same side of the equals sign: 2H² - 28H + 96 = 0

Divide out the common 2: H² - 14H + 48 = 0

Factor: (H - 6) (H - 8) = 0

Either of these multiples can be 0, therefore, consider each one separately:

H - 6 = 0; H = 6

H - 8 = 0; H = 8

Because this is a rectangle, these two dimensions are the height and width. If you choose 6 for the "height" the other perpendicular dimension would be 8 and vice-versa. Therefore, the dimensions are 6 x 8.

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Example Question #31 : Quadrilaterals

The length of a rectangle is three times its width, and the perimeter is . What is the width of the rectangle?

Possible Answers:

Correct answer:

Explanation:

For any rectangle, $\dpi{100} \small P=2L+2W$ , where $\dpi{100} \small P=perimeter$ , $\dpi{100} \small L=length$ , and $\dpi{100} \small W=width$ .

In this problem, we are given that $\dpi{100} \small L=3W$ (length is three times the width), so replace $\dpi{100} \small L$ in the perimeter equation with $\dpi{100} \small 3W$ : $\dpi{100} \small P=2(3W)+2W$

Plug in our value for the perimeter, $\dpi{100} \small P$ :

$\dpi{100} \small 16=2(3W)+2W$

Simplify:

$\dpi{100} \small 16=6W+2W$

$\dpi{100} \small 16=8W$

$\dpi{100} \small W=2$

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Example Question #1 : Rectangles

The area of a rectangle is $70\:in^2$ . Its perimeter is $38\:in$ . What is the length of its shorter side?

Possible Answers:

$12\:in$

$5\:in$

$8\:in$

$14\:in$

$7\:in$

Correct answer:

$5\:in$

Explanation:

We know that the following two equations hold for rectangles. For area:

A=WL

For perimeter:

P=2W+2L

Now, for our data, we know:

70=WL

38=2W+2L

Now, solve the first equation for one of the variables:

$W=\frac{70}{L}$

Now, substitute this value into the second equation:

$38=2(\frac{70}{L})+2L$

Solve for :

$38=\frac{140}{L}+2L$

Multiply both sides by :

38L=140+2L^2

Solve as a quadratic. Divide through by :

19L=70+L^2

Now, get the equation into standard form:

L^2-19L+70=0

Factor this:

(L-14)(L-5)=0

This means that (or ) would equal either $5\:in$ or $14\:in$ . Therefore, your answer is $5\:in$ .

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Given Rectangle ABCD.

Quantity A: The length of diagonal AC times the length of diagonal BD

Quantity B: The square of half of ABCD's perimeter

Possible Answers:

Quantity A is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

Correct answer:

Quantity B is greater.

Explanation:

Suppose ABCD has sides a and b.

The length of one of ABCD's diagonals is given by a²+ b² = c^2,where c is one of the diagonals.

Note that both diagonals are of the same length.

Quantity A: The length of diagonal AC times the length of diagonal BD

This is c * c = c^2.

Quantity A = c² = a²+ b²

Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).

Half of Perimeter = (a + b)

Square Half of Perimeter = (a + b)²

Use FOIL: (a + b)² = a²+ 2ab + b²

Quantity B = (a + b)² = a²+ 2ab + b²

The question is asking us to compare a²+ b² with a²+ 2ab + b^2.

Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.

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Example Question #152 : Geometry

If rectangle ABCD has a perimeter of , and the longer edge is 2.4 times longer than the shorter edge, then how long is the diagonal ?

Possible Answers:

Correct answer:

Explanation:

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

2L+2W=68 .

We also have that

L=2.4W .

If we then plug this into our equation for perimeter, we get 6.8W=68 .

Therefore, W=10 and L=24 . Using the Pythagorean Theorem, we have 10^2+24^2=676=D^2 so D=26 .

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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 #1 : How To Find The Length Of The Side Of A Parallelogram

Example Question #1342 : Gre Quantitative Reasoning

Example Question #1343 : Gre Quantitative Reasoning

Example Question #25 : Quadrilaterals

Example Question #1341 : Gre Quantitative Reasoning

Example Question #151 : Plane Geometry

Example Question #31 : Quadrilaterals

Example Question #1 : Rectangles

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #152 : Geometry

All GRE Math Resources

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