Tài liệu Master the Gre 2010 - Part 30 pdf

7. If a square’s sides are each increased by 50%, by what percent does the

square’s area increase?

(A) 75%

(B) 100%

(C) 125%

(D) 150%

(E) 200%

The correct answer is (C). Letting s 5 the length of each side before the

increase, area 5 s2

. If

3

2

s 5 the length of each side after the increase, the new

area 5S

3

2

sD

2

5 9

4

s

2

. The increase from s2 to

9

4

s

2 is

5

4

, or 125%.

GRE questions involving non-square rectangles also come in many possible flavors.

For example, a question might ask you to determine area based on perimeter, or vice

versa.

8. The length of a rectangle with area 12 is three times the rectangle’s width.

What is the perimeter of the rectangle?

inches

Enter a number in the box.

The correct answer is (16). The ratio of length to width is 3:1. The ratio 6:2 is

equivalent, and 6 3 2 5 12 (the area). Thus, the perimeter 5 (2)(6) 1 (2)(2) 5 16.

A question might involve the properties of a square or rectangle as well as those of

another geometric figure, such as a right, isosceles, or equilateral triangle.

9. A rectangular block of wood is to be cut into sections to form

either two triangular enclosures or three rectangular

enclosures. All wood sections must be equal in length on all sides.

Column A Column B

The total area of the two

proposed triangular

enclosures

The total area of the three proposed

rectangular enclosures

(A) The quantity in Column A is greater.

(B) The quantity in Column B is greater.

(C) The quantities are equal.

(D) The relationship cannot be determined from the information given.

The correct answer is (A). Since the sections must all be equal in length, the

triangles must each be equilateral and the rectangles must each be square. The

easiest way to make the comparison is to assign to the length of the original block

a number that is the least common multiple of 6 and 12 (the total number of sides

among the triangles and squares, respectively). That multiple, of course, is 12.

Each triangle side = 2. Applying the area formula for equilateral triangles, the

Chapter 11: Math Review: Geometry 273

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