Problem 11 :
A survey was conducted to determine the types of occupations of the 1,200 residents of a town. The types of occupations are shown in the circle graph.
Based on the circle graph, how many more residents have an occupation in industry than have an occupation in government?
A. 20 B. 360 C. 240 D. 300
Solution:
The sum of percent shares of all the occupations must be 100.
% share of Government = 100 - (25 + 15 + 25 + 30)
= 100 - 95 = 5
Number of residents in industry occupation
= 25% of the total town population
= 25% of 1200
= (25/100) × 1200
= 25 × 12
= 300
Number of residents in Government occupation
= 5% of the total town residency
= 5% of 1200
= (5/100) × 1200
= 5 × 12
= 60
So, the number of residents in industry than in Government jobs as an occupation is:
= Number of residents in industry - Government
= 300 - 60
= 240
Hence, Residents in industry are 240 more than in Government.
So, option (C) is correct.
Problem 12 :
One year on Venus is equivalent to 224.7 days on Earth. How many days on Earth, in decimal form, are equivalent to 9 1/2 years on Venus?
Solution:
x = 9.5 yr × 224.7 days
x = 2134.65 days
A period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.
Problem 13 :
Which measurement is closest to the circumference of the circle in centimeters, when radius of the circle is 3 cm.
A. 154 cm B. 11 cm C. 18.84 cm D. 38 cm
Solution:
Let, radius r = 3 cm
Circumference of circle = 2πr
= 2 × (3.14) × 3
= 18.84 cm
So, option (C) is correct.
Problem 14 :
A bookstore offered mystery bags each containing 12 books. The quantity of each type of book was the same in each mystery bag. A shopper bought 3 mystery bags and found that 6 books were spy novels.
Based on this information, which prediction can the shopper make about buying mystery bags in the future?
A. There will be 4 more spy novels in 8 bags than in 6 bags.
B. There will be 2 more spy novels in 6 bags than in 4 bags.
C. There will be 1 more spy novels in 9 bags than in 8 bags.
D. There will be 6 more spy novels in 10 bags than in 8 bags.
Solution:
A shopper bought 3 mystery bags and found that 6 books were spy novels.
Because the quantity of each type of book was the same in each mystery bag.
So, 6 ÷ 3 = 2 books
Then, 1 mystery bag has 2 spy novels
So,
A. (8 - 6) × 2 = 4; its true
B. (6 - 4) × 2 = 4 ≠ 2; its false
C. (9 - 8) × 2 = 2 ≠ 1; its false
D. (10 - 8) × 2 = 4 ≠ 6; its false
So, option (A) is correct.
Problem 15 :
A dog eats 1.25 cups of dog food twice a day. Which graph best represents this relationship?
Solution:
So, option (C) is correct.
Problem 16 :
The table shows the numbers of different colors of pencils in a pencil case. A student will randomly select one pencil from the pencil case.
Based on the information in the table, which statement is true?
A. The pencil is least likely to be blue.
B. The pencil is 4 times as likely to be purple as it is to be red.
C. The pencil is equally likely to be blue or green.
D. The pencil is more likely to be purple than all other colors combined.
Solution:
According to the probability the pencil is least likely to be red.
So, statement A is false.
The probability of red is 2/19 and the probability of purple is 8/19.
So, statement B is true.
The probability of blue is 4/19 and the probability of green is 5/19.
5/19 ≠ 4/19
So, statement C is false.
The probability of purple is 8/19, the probability of other colors combine is
So, statement D is false.
Problem 17 :
Which number line represents the solution to the inequality 3x - 8 ≥ 7 ?
Solution:
3x - 8 ≥ 7
3x ≥ 7 + 8
3x ≥ 15
Divide both sides by 3,
x ≥ 5
So, option (D) is correct.
Problem 18 :
Angle F and angle H are supplementary angles.
Which equation can be used to find the value of x?
A. 77 = 5x + 18
B. 77 + (5x + 18) = 180
C. 77 + (5x + 18) = 90
D. 77 + (5x + 18) = 360
Solution:
Sum of supplementary angle is 180º.
∠F + ∠H = 180°
77° + (5x + 18)° = 180°
So, option (B) is correct.
Problem 19 :
A spinner with 6 equal sections is shown.
What is the probability of spinning a number greater than 4?
Solution:
So, option (D) is correct.
Problem 20 :
Which equation represents the linear relationship between the x-values and the y-values in the table?
A. y = 2x + 12 B. y = 5x - 6 C. 6x - 5 D. -x - 11
Solution:
y = mx + b
The line passes through (1, 1) and (3, 13).
Substitute m = 6 in above equation
y = 6x + b
1=6(1) + b
6 + b = 1
b = 1 - 6
b = -5
y = 6x - 5
So, option (C) is correct.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM