ACT Math : Arithmetic
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Example Questions
Example Question #631 : Arithmetic
If the average and median of the group of integers shown below is equal to x, what is the value of x?
40, 11, 62, x, 20, 51, 2
14
26
31
28
31
First, we must find the average of these 6 numbers. This is done by adding all of them and dividing by the number of values we have (in this case, 6).
Next, we have to make sure that this number is also the median. Since the median is the middle number of our values put in ascending order, we have to put our values in increasing order:
2, 11, 20, 31, 40, 51, 62
When we do this, we see that 31 is indeed the “middle number” so we are happy with choosing 31 as our correct answer
Example Question #4 : How To Find The Missing Number In A Set
The following series of numbers follows a rule to progress from number to number. What is the value of Y?
4, 15, 59, Y, 939
789
97
235
329
95
235
Each number from set is:
(Previous Number x 4) – 1
Example: (4 x 4) – 1 = 15
Answer: (59 x 4) – 1 = 235
Example Question #632 : Arithmetic
There is a set of numbers. The mean of this set of numbers is equal to the median. If four of the numbers are 10, 15, 15, and 17, what is the fifth number?
13
16
18
12
15
18
Since the set contains two 15s, along with 10 and 17, the median can only be 15, no matter what the fifth number is. So now we know that the mean is equal to 15, since it is equal to the median. Now an equation can be set up to solve this problem. 15 = (10 + 15 + 15 + 17 + x)/5. Solving for x we get an answer of 18.
Example Question #1 : Counting
How many irrational numbers are there between 3 and 7?
4
8
Infinitely many
10
5
Infinitely many
There is an infinite amount of irrational numbers between any two "real" (whole) numbers. 3 and 7 are both real numbers
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
3 candy bars and 4 bags of potato chips cost $7, and 3 candy bars and 2 bags of potato chips cost $5. What is the price of 1 bag of potato chips?
$1
$.33
$.50
$2
$1
Increasing 2 bags of potato chips increases the cost by $2. Therefore, they cost $1 per bag.
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
What is the average of all prime numbers in between 7 and 23 (not including 7 or 23)?
A prime number is defined as any number that is only divisible by itself and 1 with no remainders. So for example, 7 and 23 are both prime numbers. Seven can only be divided by 7 and 1, any other number would give a fraction or decimal.
The best approach to this problem is to simply list each number starting from 7.
Seven itself is a prime number, but the question specifically says that 7 should not be included. Eight is divisible by 1, 2, 4, and 8, and therefore is not a prime number. Nine is divisible by 3 and so on. Quickly we see that the prime numbers in betwen 7 and 23 include:
Finally, the question asks you to find the average of these numbers:
Concepts such as prime numbers or other definitions should be readily called when taking the ACT with minimal effort.
Example Question #4 : Counting
How many prime numbers are between 20 and 50?
5
3
8
6
7
7
Prime numbers are numbers that cannot be divided evenly by any numbers besides itself and 1. The prime numbers between 20 and 50 are: 23, 29, 31, 37, 41, 43, 47, yielding an answer of 6.
Example Question #5 : Counting
How many integers are between 
The integers are 
So there are 8 integers total
Example Question #1 : Permutation / Combination
A candy shop sells Valentine's Day gift baskets that consist of chocolates, a basket, and a card. If there are five different types of chocolate, three types of baskets, and ten options for cards, how many different gift basket combinations are there?
15
18
180
1500
150
150
The correct answer is 150. Since there are five types of chocolate, three types of baskets, and ten card choices, the correct answer can be found by multiplying 3 x 5 x 10, which is 150. If you got 15 or 1500, you may have made a multiplication error. If you got 18, you may have added instead of multiplying.
Example Question #1 : Permutation / Combination
A locker combination consists of three different numbers from the set of 30 different numbers on the face of the lock. Imagine that you have forgotten the combination. How many times do you have to try to find the right combination?
90
1765
24360
2876
900
24360
It is said that the three numbers are different. So the number of lock combinations is 30P3 = 24 360.
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