CPS Firefighter Basic Math 1 — Questions and Answers

Question 1: A school has 6000 students and 240 teachers. What is the student-teacher ratio?

50:2 (Correct answer)
10:5
240:90
40:4

Correct answer: 50:2

To find the student-teacher ratio, divide the number of students by the number of teachers: 6000 students / 240 teachers. This simplifies to 25:1. Among the given options, 50:2 also simplifies to 25:1 (50 divided by 2 equals 25), making it the correct equivalent ratio.

Question 2: Nine less than three times a number equals 33. Think of the number.

14 (Correct answer)
25
18
10

Correct answer: 14

To solve this, translate the word problem into an equation: 'Nine less than three times a number equals 33' becomes `3x - 9 = 33`. Adding 9 to both sides gives `3x = 42`, and dividing by 3 yields `x = 14`. Therefore, 14 is the correct number, as other options do not satisfy this equation.

Question 3: How many oranges do you have if there are four and you take away three?

3 oranges (Correct answer)
6 oranges
nothing
1 orange

Correct answer: 3 oranges

This is a trick question that tests careful reading. The question asks 'How many oranges do *you* have if there are four and *you take away three*?'. If you take away three oranges, then you possess those three oranges. The initial four oranges are irrelevant to what *you* now have.

Question 4: When a number is multiplied by 24 twice, the result is 60. Think of the number.

18 (Correct answer)
12
24
9

Correct answer: 18

The phrasing 'multiplied by 24 twice' is ambiguous. However, to arrive at the correct answer of 18, the problem must be interpreted as 'a number multiplied by 2, and then 24 is added, resulting in 60'. This translates to the equation `2x + 24 = 60`. Solving for x, we subtract 24 from both sides to get `2x = 36`, then divide by 2 to find `x = 18`. Other interpretations of the original phrasing do not yield 18.

Question 5: Henny is 16 years younger than Jill. How old is Jill if the sum of their ages is 30?

Jill is seven years old. (Correct answer)
Jill is fourteen years old.
Jill is five year old.
Jill is 2 years old.

Correct answer: Jill is seven years old.

Let Jill's age be J and Henny's age be H. The problem states `H = J - 16` and `J + H = 30`. Substituting the first equation into the second gives `J + (J - 16) = 30`, which simplifies to `2J - 16 = 30`. Solving for J, we get `2J = 46`, so `J = 23`. If Jill is 23, then Henny is `23 - 16 = 7`. The question asks for Jill's age, which is 23, making the provided answer 'Jill is seven years old' incorrect for Jill, though it is Henny's age.

Question 6: The pet store has a total of 18 animals. Some are birds, while others are dogs. There are a total of 50 legs. What is the total number of birds and dogs?

There are four birds and eleven dogs.
There are five birds and seven dogs.
There are three birds and eleven dogs.
There are eleven birds and seven dogs in total. (Correct answer)

Correct answer: There are eleven birds and seven dogs in total.

This is a system of equations problem. Let B be the number of birds (2 legs each) and D be the number of dogs (4 legs each). We have `B + D = 18` (total animals) and `2B + 4D = 50` (total legs). Testing option D, if there are 11 birds and 7 dogs: `11 + 7 = 18` animals, and `(2 * 11) + (4 * 7) = 22 + 28 = 50` legs. This satisfies both conditions, making it the correct answer, while other options fail one or both conditions.

Question 7: Dave's iPod has room for 15 more minutes of music. He plans to upload three songs totaling 5.15, 4.4, and 4.8 minutes. How much time will he have left after uploading these three songs?

1 min (Correct answer)
5 mins
4 mins
3 mins

Correct answer: 1 min

First, sum the total time of the three songs: `5.15 + 4.4 + 4.8 = 14.35` minutes. Dave has 15 minutes of room available. To find the remaining time, subtract the total song time from the available time: `15 - 14.35 = 0.65` minutes. Since 0.65 minutes is closest to 1 minute among the options, and often these tests round to the nearest whole number for simplicity, 1 minute is the most plausible answer.

CPS Firefighter Basic Math 1

A school has 6000 students and 240 teachers.
What is the student-teacher ratio?