PSAT Math : PSAT Mathematics
Study concepts, example questions & explanations for PSAT Math
All PSAT Math Resources
Example Questions
Example Question #61 : Factors / Multiples
If 
4
5
3
7
6
5
We will essentially have to represent 180 as a product of prime factors, because 2, 3, 5, and 7 are all prime numbers. The easiest way to do this will be to find the prime factorization of 180.
180 = 18(10)= (9)(2)(10) = (3)(3)(2)(10)=(3)(3)(2)(2)(5) = 
In order for 
The answer is 5.
Example Question #11 : How To Factor A Number
What is the product of the distinct prime factors of 24?
The prime factorization of 24 is (2)(2)(2)(3). The distinct primes are 2 and 3, the product of which is 6.
Example Question #12 : How To Factor A Number
How many prime factors does 
Since 7 is prime, its only prime factor is itself.
Example Question #301 : Arithmetic
What is the smallest positive multiple of 12?
Multiples of 12 are found by multiplying 12 by a whole number. Some examples include:
Clearly, the smallest positive value obtainable is 12. Do not confuse the term multiple with the term factor!
Example Question #31 : Factors / Multiples
How many prime factors of 210 are greater than 2?
one
three
two
four
five
three
Begin by identifying the prime factors of 210. This can be done easily using a factoring tree (see image).
The prime factors of 210 are 2, 3, 5 and 7. Of these factors, three of them are greater than 2.
Example Question #32 : Factors / Multiples
How many integers between 50 and 100 are divisible by 9?
8
7
6
9
5
6
The smallest multiple of 9 within the given range is 
The largest multiple of 9 within the given range is 
Counting the numbers from 6 to 11, inclusive, yields 6.
Example Question #31 : Factors / Multiples
Factor each number into prime roots:
Example Question #1 : Basic Operations
Kacey works 5 hours per day on Monday, Tuesday, and Wednesday, as well as 9 hours on Thursday and Friday. She does not work on Saturday or Sunday. Her total earnings per week is $363. How much does she earn per hour in dollars?
8
9
12
11
11
Kacey works 5 hours a day for 3 days and 9 hours a day for 2 days. (5)(3) = 15 and (2)(9) = 18. 15 + 18 = 33 hours worked a week. $363/33 hours = $11/hr.
Example Question #1861 : Psat Mathematics
When k is divided by 2, the remainder is 1. If k is divided by 3, the remainder is 0. And if k is divded by 5, the remainder is 3. Which of the following is a possible value for k?
Since the remainder when k is divided by 2 is 1, this means that k is not an even number. Therefore, we can immediately eliminate 30 from our possible answer choices.
Because the remainder when k is divded by 3 is 0, we know that k must be a multiple of 3. This means we can eliminate 23 from our answer choices.
The only choices left are 63, 27, and 57. When 27 and 57 are divded by five, the remainder is two. Thus, only 63 works, because when 63 is divded by five, the remainder is three.
The answer is 63.
Example Question #1 : How To Divide Integers
The result of a number divided by 2 is the same as the result of that number divided by 10. What is that number?
1
0
2
10
0
0 is the only choice that yields the same answer (0) when divided by 2 and 10. You can check this easily by plugging a few of the answer choices into a fraction:
1/2 ≠ 1/10
2/2 ≠ 2/10 etc.
Certified Tutor
All PSAT Math Resources
