All SAT Math Resources
Example Questions
Example Question #741 : Arithmetic
What's the fourth smallest prime number?
The order of the prime numbers start from . is not prime as it's a unit. is a composite number. So our fourth smallest prime number is .
Example Question #742 : Arithmetic
Which is not prime?
Since all the numbers are odd and don't end with a , let's check the basic divisbility rule. The divisibility rule for is if the digits have a sum divisible by , then it is.
Based on this analysis, only is divisible by and therefore not prime and is our answer.
Example Question #13 : Prime Numbers
Say is a prime number. Which operation could possibly also lead to a prime number?
Prime numbers are integers. So doing division and square roots will not generate integers. By doing multiplication and exponents, we involve more factors. The only possibility is subtraction. If was and we subtracted we get which is also prime.
Example Question #12 : Prime Numbers
Say is a number. has, other than one and itself, only prime factors. is not a perfect square. What is the smallest prime number can be?
Other than the number itself and one, we also need to have prime factors in that number. Since it's not a perfect square, we need to find the smallest possible prime numbers. That will be or which is our answer.
Example Question #12 : Prime Numbers
Which of the following is not prime?
Since all the numbers are odd and don't end with a , let's check the basic divisbility rule. The divisibility rule for is if the digits have a sum divisible by , then it is.
Based on this analysis, only is divisible by and therefore not prime and is our answer.
Example Question #44 : Factors / Multiples
What's the largest prime number less than ?
Let's work backwards. All even numbers are not prime so we skip . is clearly divisible by . is definitely a composite number as it's divisible by . is divisible by because of the divisibility rule . is divisbile by . The divisibility rule for is double the last digit and subtract from the rest . From the remaining answers, is prime and is the largest prime number under and is our answer.
Example Question #13 : Prime Numbers
Which is prime?
This will require us to know the divisibility rule of . The reason for this choice is that some of the numbers are palindromes like so we eliminate . For the three digit numbers, the divisibility rule for is add the outside digits and if the sum matches the sum then it is divisible. Let's see.
Based on this test, is not divisible by and is our answer.
Example Question #1631 : Sat Mathematics
If is a prime number, what could also be prime?
Plug in a prime number such as and evaluate all the possible solutions. Note that the question asks which value COULD be prime, not which MUST BE prime. As soon as your number-picking yields a prime number, you have satisfied the "could be prime" standard and know that you have a correct answer.