Counting - ACT Math
Card 0 of 5
How many irrational numbers are there between 3 and 7?
How many irrational numbers are there between 3 and 7?
There is an infinite amount of irrational numbers between any two "real" (whole) numbers. 3 and 7 are both real numbers
There is an infinite amount of irrational numbers between any two "real" (whole) numbers. 3 and 7 are both real numbers
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How many prime numbers are between 20 and 50?
How many prime numbers are between 20 and 50?
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.
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.
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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?
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?
Increasing 2 bags of potato chips increases the cost by $2. Therefore, they cost $1 per bag.
Increasing 2 bags of potato chips increases the cost by $2. Therefore, they cost $1 per bag.
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How many integers are between 
and 
(not including 
and 
)?
How many integers are between
The integers are 
.
So there are 8 integers total
The integers are
So there are 8 integers total
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What is the average of all prime numbers in between 7 and 23 (not including 7 or 23)?
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.
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.
Compare your answer with the correct one above