Part 6 of our Numerical Ability reviewer has 20 practice questions in the style of the Civil Service Exam. Answer them in order, read the explanation after each one, and check your score against the 80% passing mark at the end. Questions and choices are reshuffled every time you retake the part.
Start Part 6Sample questions from Part 6
Here are a few questions from this part. Take the full test to answer all 20 and get your score.
Sample question 1
The length of a rectangle is 8 meters more than twice its width. The perimeter is 112 meters. Find its area.
- 16m
- 24m
- 28 m²
- 640 m²
Answer: 640 m²
To find the area of the rectangle given that its length is 8 meters more than twice its width and the perimeter is 112 meters, we can use the following steps:
Step 1: Define the Variables
Let:
- Width of the rectangle = w meters
- Length of the rectangle = l meters
According to the problem:
l = 2w + 8
Step 2: Set Up the Perimeter Equation
The formula for the perimeter P of a rectangle is given by:
P = 2l + 2w
Given that the perimeter is 112 meters, we can set up the equation:
2l + 2w = 112
Step 3: Substitute the Length Expression
Substituting l = 2w + 8 into the perimeter equation gives:
2(2w + 8) + 2w = 112
Step 4: Simplify the Equation
1. Expand the equation:
4w + 16 + 2w = 112
2. Combine like terms:
6w + 16 = 112
3. Subtract 16 from both sides:
6w = 112 - 16
6w = 96
4. Divide by 6:
w = 96 / 6 = 16
Step 5: Find the Length
Now that we have the width, we can find the length using the expression for length:
l = 2w + 8 = 2(16) + 8 = 32 + 8 = 40
Step 6: Calculate the Area
The area A of a rectangle is given by:
A = l × w
Substituting the values of l and w:
A = 40 × 16 = 640 square meters
Conclusion:
The area of the rectangle is 640 square meters.
Step 1: Define the Variables
Let:
- Width of the rectangle = w meters
- Length of the rectangle = l meters
According to the problem:
l = 2w + 8
Step 2: Set Up the Perimeter Equation
The formula for the perimeter P of a rectangle is given by:
P = 2l + 2w
Given that the perimeter is 112 meters, we can set up the equation:
2l + 2w = 112
Step 3: Substitute the Length Expression
Substituting l = 2w + 8 into the perimeter equation gives:
2(2w + 8) + 2w = 112
Step 4: Simplify the Equation
1. Expand the equation:
4w + 16 + 2w = 112
2. Combine like terms:
6w + 16 = 112
3. Subtract 16 from both sides:
6w = 112 - 16
6w = 96
4. Divide by 6:
w = 96 / 6 = 16
Step 5: Find the Length
Now that we have the width, we can find the length using the expression for length:
l = 2w + 8 = 2(16) + 8 = 32 + 8 = 40
Step 6: Calculate the Area
The area A of a rectangle is given by:
A = l × w
Substituting the values of l and w:
A = 40 × 16 = 640 square meters
Conclusion:
The area of the rectangle is 640 square meters.
Sample question 2
Paula is twice as old as Queenie. Seven years ago the sum of their ages was 16. How old is Queenie now?
- 8
- 10
- 16
- 20
Answer: 10
To find Queenie's current age, let's define the variables based on the information provided:
Let Q be Queenie's current age. Since Paula is twice as old as Queenie, Paula's current age P can be expressed as:
P = 2Q
Step 1: Set Up the Equation for Their Ages Seven Years Ago
Seven years ago, their ages would be:
- Queenie's age: Q - 7
- Paula's age: P - 7 = 2Q - 7
According to the problem, the sum of their ages seven years ago was 16:
(Q - 7) + (2Q - 7) = 16
Step 2: Simplify the Equation
Combine like terms:
Q - 7 + 2Q - 7 = 16
3Q - 14 = 16
Step 3: Solve for Q
1. Add 14 to both sides:
3Q = 16 + 14
3Q = 30
2. Divide by 3:
Q = 30 / 3 = 10
Conclusion:
Queenie is currently 10 years old, which corresponds to option b. 10.
Let Q be Queenie's current age. Since Paula is twice as old as Queenie, Paula's current age P can be expressed as:
P = 2Q
Step 1: Set Up the Equation for Their Ages Seven Years Ago
Seven years ago, their ages would be:
- Queenie's age: Q - 7
- Paula's age: P - 7 = 2Q - 7
According to the problem, the sum of their ages seven years ago was 16:
(Q - 7) + (2Q - 7) = 16
Step 2: Simplify the Equation
Combine like terms:
Q - 7 + 2Q - 7 = 16
3Q - 14 = 16
Step 3: Solve for Q
1. Add 14 to both sides:
3Q = 16 + 14
3Q = 30
2. Divide by 3:
Q = 30 / 3 = 10
Conclusion:
Queenie is currently 10 years old, which corresponds to option b. 10.
Sample question 3
For what value of x will x be the average of 2, 4x, 6, 8, 10?
- 4
- 12
- 26
- 39
Answer: 26
To find the value of x such that x is the average of the numbers 2, 4x, 6, 8, and 10, we can use the formula for the average:
Average = Sum of all values / Number of values
Step 1: Set Up the Equation
The numbers we are averaging are 2, 4x, 6, 8, and 10. The sum of these numbers is:
2 + 4x + 6 + 8 + 10
Step 2: Calculate the Number of Values
There are 5 values (2, 4x, 6, 8, and 10).
Step 3: Write the Average Equation
The average is equal to x:
x = (2 + 4x + 6 + 8 + 10) / 5
Step 4: Simplify the Equation
Combine the constant terms:
x = (26 + 4x) / 5
Step 5: Clear the Fraction
Multiply both sides by 5 to eliminate the denominator:
5x = 26 + 4x
Step 6: Solve for x
1. Subtract 4x from both sides:
5x - 4x = 26
x = 26
Conclusion:
The value of x such that x is the average of 2, 4x, 6, 8, and 10 is 26, which corresponds to option c. 26.
Average = Sum of all values / Number of values
Step 1: Set Up the Equation
The numbers we are averaging are 2, 4x, 6, 8, and 10. The sum of these numbers is:
2 + 4x + 6 + 8 + 10
Step 2: Calculate the Number of Values
There are 5 values (2, 4x, 6, 8, and 10).
Step 3: Write the Average Equation
The average is equal to x:
x = (2 + 4x + 6 + 8 + 10) / 5
Step 4: Simplify the Equation
Combine the constant terms:
x = (26 + 4x) / 5
Step 5: Clear the Fraction
Multiply both sides by 5 to eliminate the denominator:
5x = 26 + 4x
Step 6: Solve for x
1. Subtract 4x from both sides:
5x - 4x = 26
x = 26
Conclusion:
The value of x such that x is the average of 2, 4x, 6, 8, and 10 is 26, which corresponds to option c. 26.
Sample question 4
A patient must take his medication every 7 hours starting at 7:00 AM, Sunday.
On what day will the patient first receive his medication at 8 AM?
- Sunday
- Wednesday
- Thursday
- Tuesday
Answer: Tuesday
To determine on which day the patient will first receive his medication at 8 AM, we can calculate the times when the patient takes his medication every 7 hours starting from 7:00 AM on Sunday.
Step 1: Calculate the Medication Times
The patient takes his medication every 7 hours starting at 7:00 AM on Sunday:
1st dose: 7:00 AM, Sunday
2nd dose: 7:00 AM + 7 hours = 2:00 PM, Sunday
3rd dose: 2:00 PM + 7 hours = 9:00 PM, Sunday
4th dose: 9:00 PM + 7 hours = 4:00 AM, Monday
5th dose: 4:00 AM + 7 hours = 11:00 AM, Monday
6th dose: 11:00 AM + 7 hours = 6:00 PM, Monday
7th dose: 6:00 PM + 7 hours = 1:00 AM, Tuesday
8th dose: 1:00 AM + 7 hours = 8:00 AM, Tuesday
Conclusion
The patient will first receive his medication at 8:00 AM on Tuesday.
Answer
d. Tuesday
Step 1: Calculate the Medication Times
The patient takes his medication every 7 hours starting at 7:00 AM on Sunday:
1st dose: 7:00 AM, Sunday
2nd dose: 7:00 AM + 7 hours = 2:00 PM, Sunday
3rd dose: 2:00 PM + 7 hours = 9:00 PM, Sunday
4th dose: 9:00 PM + 7 hours = 4:00 AM, Monday
5th dose: 4:00 AM + 7 hours = 11:00 AM, Monday
6th dose: 11:00 AM + 7 hours = 6:00 PM, Monday
7th dose: 6:00 PM + 7 hours = 1:00 AM, Tuesday
8th dose: 1:00 AM + 7 hours = 8:00 AM, Tuesday
Conclusion
The patient will first receive his medication at 8:00 AM on Tuesday.
Answer
d. Tuesday
Sample question 5
Of the 300 grocery shoppers surveyed, 96 did not have a regular day of the week on which they shop. What percentage of the shoppers did not have a regular day of shopping?
- 32%
- 48%
- 64%
- 96%
Answer: 32%
To find the percentage of grocery shoppers who did not have a regular day of the week on which they shop, use the formula:
Percentage = (Number of shoppers without a regular day / Total number of shoppers) × 100
Step 1: Plug in the Values
- Number of shoppers without a regular day = 96
- Total number of shoppers = 300
Percentage = (96 / 300) × 100
Step 2: Calculate
1. Divide 96 by 300:
96 / 300 = 0.32
2. Multiply by 100 to get the percentage:
0.32 × 100 = 32%
Conclusion:
The percentage of shoppers who did not have a regular day of shopping is 32%.
Answer:
a. 32%
Percentage = (Number of shoppers without a regular day / Total number of shoppers) × 100
Step 1: Plug in the Values
- Number of shoppers without a regular day = 96
- Total number of shoppers = 300
Percentage = (96 / 300) × 100
Step 2: Calculate
1. Divide 96 by 300:
96 / 300 = 0.32
2. Multiply by 100 to get the percentage:
0.32 × 100 = 32%
Conclusion:
The percentage of shoppers who did not have a regular day of shopping is 32%.
Answer:
a. 32%