Analytical Ability Set 3:
Answer key Word Problems
1 . Answer: B
Explanation:
Using diagram:
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, Analytical Ability Set 3:
Answer key Word Problems
Using algebraic expression:
Let x be Freddie’s age
Since Eric is 12 years older than Freddie, then Eric’s age can be expressed as 𝑥 + 12
The sum of the ages of Freddie and Eric is 52. Thus,
𝑥 + (𝑥 + 12) = 52
2𝑥 + 12 = 52
2𝑥 = 40
𝑥 = 20
Freddie is 20 years old.
To determine how old is Eric, we substitute x = 20 to 𝑥 + 12
𝑥 + 12
(20) + 12 = 32
Therefore, Eric is 32 years old.
2. Answer: D
Explanation:
We let x be Mark’s age five years ago. Since five years ago, Pat is 15 years younger than Mark,
then we can express Pat’s age five years ago as x - 5.
To obtain their ages in the current year, we just add 5 to the expressions representing the ages
of Mark and Pat.
In solving age problems such that the ages are given in the current year and in previous years
(past), it is helpful for us to use a table to organize the ideas.
PAST Present (+ 5 years)
Pat x - 15 x - 10
Mark x x+5
This year, Mark’s age is twice Pat's age. Thus, we are now going to focus on the respective
ages of Pat and Mark in the present. If Mark’s age is x + 5 in the present, then this is equal to
twice of Pat’s age in the present which is 2(x - 10).
𝑥 + 5 = 2(𝑥 − 10)
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, Analytical Ability Set 3:
Answer key Word Problems
𝑥 + 5 = 2𝑥 − 20
𝑥 − 2𝑥 = − 5 − 20
− 𝑥 = − 25
𝑥 = 25
Looking from the table, x represents Mark’s age five years ago. Thus, Mark was 25 years old
five years ago. To determine Pat’s age five years ago, we substitute x = 25 to x - 15.
𝑥 − 15
(25) − 15 = 10
Five years ago, Pat was 10 years old.
3. Answer: A
Explanation: In solving work problems, it is important to remember the relationship between the
rates it takes to finish a task if the persons will work alone and the rate it takes to finish the
same task if these persons will work together.
𝑡 𝑡
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑝𝑒𝑟𝑠𝑜𝑛 𝐴
+ 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑝𝑒𝑟𝑠𝑜𝑛 𝐵
= 1
In the formula above, t represents the time it takes to finish the task if persons A and B work
together.
Now, let’s apply this formula to the problem.
It takes 2 hours for Sylvia to finish the task.
Meanwhile, it takes 3 hours for Mike to finish the same task.
We need to find the time it takes to finish the task if Sylvia and Mike work together. We let this
time be t.
We can use the formula above to solve for t.
𝑡 𝑡
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑆𝑦𝑙𝑣𝑖𝑎
+ 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑀𝑖𝑘𝑒
= 1
𝑡 𝑡
3
+ 2
= 1
Now that we have set up the equation, we just need to solve for the value of t.
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Answer key Word Problems
1 . Answer: B
Explanation:
Using diagram:
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review materials, visit To God be the glory!
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, Analytical Ability Set 3:
Answer key Word Problems
Using algebraic expression:
Let x be Freddie’s age
Since Eric is 12 years older than Freddie, then Eric’s age can be expressed as 𝑥 + 12
The sum of the ages of Freddie and Eric is 52. Thus,
𝑥 + (𝑥 + 12) = 52
2𝑥 + 12 = 52
2𝑥 = 40
𝑥 = 20
Freddie is 20 years old.
To determine how old is Eric, we substitute x = 20 to 𝑥 + 12
𝑥 + 12
(20) + 12 = 32
Therefore, Eric is 32 years old.
2. Answer: D
Explanation:
We let x be Mark’s age five years ago. Since five years ago, Pat is 15 years younger than Mark,
then we can express Pat’s age five years ago as x - 5.
To obtain their ages in the current year, we just add 5 to the expressions representing the ages
of Mark and Pat.
In solving age problems such that the ages are given in the current year and in previous years
(past), it is helpful for us to use a table to organize the ideas.
PAST Present (+ 5 years)
Pat x - 15 x - 10
Mark x x+5
This year, Mark’s age is twice Pat's age. Thus, we are now going to focus on the respective
ages of Pat and Mark in the present. If Mark’s age is x + 5 in the present, then this is equal to
twice of Pat’s age in the present which is 2(x - 10).
𝑥 + 5 = 2(𝑥 − 10)
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review materials, visit To God be the glory!
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, Analytical Ability Set 3:
Answer key Word Problems
𝑥 + 5 = 2𝑥 − 20
𝑥 − 2𝑥 = − 5 − 20
− 𝑥 = − 25
𝑥 = 25
Looking from the table, x represents Mark’s age five years ago. Thus, Mark was 25 years old
five years ago. To determine Pat’s age five years ago, we substitute x = 25 to x - 15.
𝑥 − 15
(25) − 15 = 10
Five years ago, Pat was 10 years old.
3. Answer: A
Explanation: In solving work problems, it is important to remember the relationship between the
rates it takes to finish a task if the persons will work alone and the rate it takes to finish the
same task if these persons will work together.
𝑡 𝑡
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑝𝑒𝑟𝑠𝑜𝑛 𝐴
+ 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑝𝑒𝑟𝑠𝑜𝑛 𝐵
= 1
In the formula above, t represents the time it takes to finish the task if persons A and B work
together.
Now, let’s apply this formula to the problem.
It takes 2 hours for Sylvia to finish the task.
Meanwhile, it takes 3 hours for Mike to finish the same task.
We need to find the time it takes to finish the task if Sylvia and Mike work together. We let this
time be t.
We can use the formula above to solve for t.
𝑡 𝑡
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑆𝑦𝑙𝑣𝑖𝑎
+ 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑀𝑖𝑘𝑒
= 1
𝑡 𝑡
3
+ 2
= 1
Now that we have set up the equation, we just need to solve for the value of t.
To get more Civil Service Exam
review materials, visit To God be the glory!
https://filipiknow.net/civil-service-
reviewer/
