Question 1 :
The density of an object is equal to the mass of the object divided by the volume of the object. Find the mass of an object in grams with a volume of 0.01 m3 and a density of 4.54 grams per cubic centimeters? (1 m = 100 cm)
Question 2 :
Jason and Donny painted a house and received $1,200. To complete the painting job Jason painted 4 hours 25 minutes and Donny spent 2 hours and 15 minutes. If they split the $1,200 in proportion to the amount of time each spent painting, how much did Donny receive?
Question 3 :
The tennis balls in a bag are either white or yellow. If the ratio of white balls to yellow balls is ³⁄₁₀, which of the following could not be the number of balls in the bag?
(A) 26
(B) 39
(C) 42
(D) 52
Question 4 :
A car is traveling at a constant rate of x miles per hour. How many miles will the car travel in y minutes?
Question 5 :
A tree is 8 feet tall and grows 8 inches each year. In how many years will the tree reach a height of 30 feet?
Question 6 :
Aaron reads x pages of a science fiction book in m minutes. If he continues reading at this rate, what will be the number of pages he reads in 20m seconds?
Question 7 :
If ˣ⁄y = 1, what is the value of x - y - 1?
Question 8 :
In a certain room the ratio of males to females is 4 to 5. After 8 males enter the room, the ratio of males to females is 6 to 5. What is the total number of people in the room before the additional males enter the room?
Question 9 :
A person is born every 5 seconds and a person dies every 12 seconds. How many seconds does it take for the population to grow by one person?
Question 10 :
Steve is going to paint a wall that measures 9 feet by 12 feet. If one gallon of paint is needed for each s square foot of wall and each gallon costs g dollars, in terms of s and g how much does it cost to paint the entire wall?
(A) ¹⁰⁸⁄gs
(B) ᵍˢ⁄₁₀₈
(B) ¹⁰⁸ˢ⁄g
(B) ¹⁰⁸ᵍ⁄s
Question 11 :
If 2 inches are equivalent to 5 centimeters, how many square centimeters are in one square inch?
Question 12 :
A large painting has a length of 18 inches and a width of 12 inches. If each dimension is reduced by x inches to make the ratio of length to width 5 to 3, what is the value of x?
1. Answer :
1 m = 100 cm
(1 m)3 = (100 cm)3
1 m3 = 1,000,000 cm3
0..01 ⋅ 1 m3 = 0.01 ⋅ 1,000,000 cm3
0..01 m3 = 10,000 cm3
Mass = (10000 cm3)(4.54 grams/cm3)
Mass = 45,400 grams
2. Answer :
Time spent by Jason :
= 4 hours 25 minutes
= 4²⁵⁄₆₀ hours
= 4⁵⁄₁₂ hours
Time spent by Donny :
= 2 hours 15 minutes
= 2¹⁵⁄₆₀ hours
= 2¼ hours
Ratio of time spent by Jason and Donny :
= 4⁵⁄₁₂: 2¼
= ⁵³⁄₁₂ : ⁹⁄₄
= 12(⁵³⁄₁₂) : 12( ⁹⁄₄)
= 53 : 27
Jason and Donny have to share the total money in the ratio 53 : 27.
Jason's share = 53x
Donny's share = 27x
Given : Total money received $1,200.
53x + 27x = 1200
80x = 1200
x = 15
Money received by Donny :
= 27(15)
= $405
3. Answer :
Given : The ratio of white balls to yellow balls is ³⁄₁₀.
white : yellow = 3 : 10
number of white balls = 3x
number of yellow balls = 10x
Total number of balls in the bag :
= 3x + 10x
= 13x
So, total number of balls in the bag is a multiple of 13.
In the given choices, 42 is not a multiple of 13.
Therefore, the correct answer is option (C).
4. Answer :
Given : The car is traveling at a constant rate of x miles per hour.
1 hour ----> x miles
60 minutes ----> x miles
y(1 minute) ----> y(ˣ⁄₆₀) miles
y minutes ----> ˣʸ⁄₆₀ miles
The the car will travel ˣʸ⁄₆₀ miles in yminutes.
5. Answer :
Let x be the number of years required for the tree to reach a height of 30 feet.
Given : The tree grows 8 inches each year.
8 inches = ⁸⁄₁₂ or ⅔ feet
The tree grows ⅔ feet each year.
Present height + Height grow in x years = 30
8 ft. + (⅔)x ft. = 30 ft.
8 + (⅔)x = 30
Multiply both sides by 3.
24 + 2x = 90
Subtract 24 from both sides.
2x = 66
Divide both sides by 2.
x = 33
It will take 33 years for the tree to reach a height of 30 feet.
6. Answer :
Aaron reads 18 pages of a science fiction book in m minutes. If he continues reading at this rate, what will be the number of pages he reads in 20m seconds?
m minutes = 18 pages
1 minute = ¹⁸⁄m pages
60 seconds = ¹⁸⁄m pages
1 second = ¹⁸⁄₆₀m pages
20m(1 second) = 20m(¹⁸⁄₆₀m pages)
20m seconds = 3 pages
Aaron will read 3 pages in 20m seconds.
7. Answer :
ˣ⁄y = 1
Multiply both sides by y.
x = y
Subtract y from both sides.
x - y = 1
Subtract 1 from both sides.
x - y - 1 = 0
8. Answer :
Let m and f be the original number of males and females respectively.
Given : The ratio of males to females is 4 to 5.
m ; f = 4 : 5
ᵐ⁄f = ⅘
5m = 4f ----(1)
Given : After 8 males enter the room, the ratio of males to females is 6 to 5.
(m + 8) : f = 6 : 5
⁽ᵐ ⁺ ⁸⁾⁄f = ⁶⁄₅
5(m + 8) = 6f
5m + 40 = 6f
Substitute 5m = 4f.
4f + 40 = 6f
40 = 2f
20 = f
Substitute f = 20 in (1).
5m = 4(20)
5m = 80
m = 16
The total number of people in the room before the additional males enter the room :
= 16 + 20
= 36
9. Answer :
Every 5 seconds, a person is born :
5 seconds ----> 1 person
12(5 seconds) ----> 12(1 person)
60 seconds ----> 12 people
1 minute ----> 12 people
Every 12 seconds, a person dies :
12 seconds ----> 1 person
5(12 seconds) ----> 5(1 person)
60 seconds ----> 5 people
1 minute ----> 5 people
Every minute, 12 people are born and 5 people die.
Every minute, the population grows by (12 - 5) or 7 people.
7 people ----> 1 minute
7 people ----> 60 seconds
1 person ----> ⁶⁰⁄₇ seconds
1 person ----> 8⁴⁄₇ seconds
It takes 8⁴⁄₇ seconds for the population to grow by one person.
10. Answer :
Total area of the wall :
= 9 ⋅ 12
= 108 ft2
Given : One gallon of paint is needed for each s square foot of wall.
Let x be the number of gallons of paint needed to paint 108 ft2.
1 : s = x : 108
¹⁄s = ˣ⁄₁₀₈
x = ¹⁰⁸⁄s gallons
¹⁰⁸⁄s gallons of paint needed to paint the entire wall with the area 108 ft2.
Given : The cost of 1 gallon of paint is g dollars.
Now, we have to find the cost of ¹⁰⁸⁄s gallons of paint.
1 gallon ----> g dollars
(¹⁰⁸⁄s)(1 gallon) ----> (¹⁰⁸⁄s)(g dollars)
¹⁰⁸⁄s gallons ----> ¹⁰⁸ᵍ⁄s dollars
It costs ¹⁰⁸ᵍ⁄s dollars to paint the entire wall.
Therefore, the correct answer is option (D).
11. Answer :
Given : 2 inches are equivalent to 5 centimeters.
2 in = 5 cm
(2 in)2 = (5 cm)2
22 in2 = 52 cm2
4 in2 = 25 cm2
1 in2 = ²⁵⁄₄ cm2
There are ²⁵⁄₄ square centimeters in 1 square inch.
12. Answer :
From the given information,
(18 - x) : (12 - x) = 5 : 3
⁽¹⁸ ⁻ ˣ⁾⁄₍₁₂ ₋ ₓ₎ = ⁵⁄₃
3(18 - x) = 5(12 - x)
54 - 3x = 60 - 5x
2x = 6
x = 3
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