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GRE - Quantitative Reasoning - Geometry

What is the length of a diagonal of a rectangle that has width 5 and perimeter 34 ? (more)

What is the length of a diagonal of a rectangle that has width 5 and perimeter 34 ?

perimeter = 2(length + width)

34 = 2(length + 5)

length = 12

diagonal of a rectangle (from pythagorus theorem) = (length2 + width2)1/2 = (122 + 52)1/2 = 13

 

A rectangular floor 18 feet by 10 feet is to be completely covered with carpeting that costs X dollars per square yard. In terms of X, how many dollars will the carpeting cost ? (1 yard = 3 feet) (more)

A rectangular floor 18 feet by 10 feet is to be completely covered with carpeting that costs X dollars per square yard. In terms of X, how many dollars will the carpeting cost ? (1 yard = 3 feet)

(A) 20x
(B) 28x
(C) 60x
(D) 180x
(E) 540x

length of the floor = 18 ft = 6 yards

width of the floor = 10 ft = 10/3 yards

area of the floor = 6*10/3 sq yards = 20 sq yards

cost of carpeting = x per sq. yard

total cost = 20x dollars

If the lengths of two sides of a triangle are 5 and 9, respectively, which of the following could be the length of the third side of the triangle? (more)

If the lengths of two sides of a triangle are 5 and 9, respectively, which of the following could be the length of the third side of the triangle?

Indicate all such lengths.

A. 3
B. 5
C. 8
D. 15

for a triangle sum of two sides >= third side

Option check

A. 3

5 + 3 < 9.. not possible

B. 5

5 + 5 >= 9
and 9 + 5 > = 5
possible
C. 8
5 + 8 >= 9
9 + 8 > = 5
9 + 5 > = 8
possible

D. 15
9 + 5 = 14 < = 15
not possible

A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 40 lots are to h (more)

A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?

A) 400

B) 3,200

C) 3,700

D) 4,400

E) 4,760

let the total number of lots be t

given 1/9th of total number of lots are 80ft

thus (1-1/9)th of total number of lots will be 100 ft = 40

(1 - 1/9)*t = 40

8/9 * t = 40

t = 40*9/8 = 45

Number of lots with 80ft frontage = 1/9 * 45 = 5

Number of lots with 100ft frontage = 40

Total lake frontage = 80*5 + 40*100 =400 + 4000 = 4400

Option D is correct

What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48 meters wide? (more)

What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48
meters wide?

 A 112
 B 152
 C 224
 D 256
 E 304

Area of second playground = length * width = 64*48 = 3072

Given Area of first plaground = area of second playground = 3072

length * width = 3072

length * 24 = 3072

length = 128

perimeter of first plaground = 2* length + 2* width = 2*128 + 2*24 = 256 + 48 = 304

Option E.