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GMAT - Problem Solving - Geometry

The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length l and width w. (more)

The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length l and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles? 
A. 15 
B. 20 
C. 25 
D. 30 
E. 40

from the figure

length of one single rectangle = 3w

width of the complete painting = w + 3w = 4w

area of the painting = l*total width = 3w*4w = 12w2

4800 = 12w2

w2 = 400

w = 20 inches

B is correct

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be (more)

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

There are three faces of the rectangular box

6 x 8, 8 x 10 and 10 x 6

Case 1

If 6 x 8 is the base of the cylinder, 10 will be the height and 6 will be the diameter

Volume = πr2h = π32*10 = 90π cubic inch

Case 2

If 8 x 10 is the base of the cylinder, 6 will be the height and 8 will be the diameter

Volume = πr2h = π42*6 = 96π cubic inch

Case 3

If 10 x 6 is the base of the cylinder, 8 will be the height and 6 will be the diameter

Volume = πr2h = π32*8 = 72π cubic inch

 

For maximum volume case 2 is valid. Diameter = 8 and radius = 4

B is correct

A rectangular garden is to be twice as long as it is wide. If 360 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards? (more)

A rectangular garden is to be twice as long as it is wide. If 360 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?

(A) 120
(B) 140
(C) 160
(D) 180
(E) 200

let the length of the garden be L and width be L/2

Perimeter = Length of the fencing = 360 yards

2(L + L/2) = 360

3L = 360

L = 120 yards

A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet (more)

A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

Assume the length of the box be L, width be W and height be H

The Volume of the sandbox = LWH = 10 cubic feet

The carpenter doubles the Length, Width and Height

New Length = 2L

New Width = 2W

New Height = 2H

New Volume = 2L*2W*2H = 8 LWH

but we know that LWH = 10 cubic feet

hence new volume = 10*8 cubic feet = 80 cubic feet

 

A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box? (more)

A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

Greatest possible distance between two points = distance between two opposite vertices = length of body diagonal

\sqrt { { length }^{ 2 }+{ width }^{ 2 }+{ height }^{ 2 } }

\sqrt { { 10 }^{ 2 }+{ 10 }^{ 2 }+{ 5 }^{ 2 } } =\sqrt { 225 } =\quad 15