Number properties and number theory include concepts such as Least Common Multiple (LCM), Highest Common Factor (HCF), tests of divisibility, prime numbers, factors and divisors, remainders, odd and even numbers, and operations on these numbers. This is an important topic and you will get questions in the SAT exam from this topic. The following is a selection of questions that typically appear in the SAT from Number Properties and Number Theory.

1. What is the remainder when 16³ + 17³ + 18³ + 19³ is divided by 70?

   1. 0
   2. 69
   3. 1
   4. 34
   5. 47
   • Correct AnswerChoice (A).
     The remainder is 0. Correct answer
   • Explanatory Answer
   • Remainders
   • Medium

2. Which of the following is the smallest positive integer that when divided by 4, 6 and 8 leaves a remainder of ‘2’ but is perfectly divisible by 37?

   1. 146
   2. 666
   3. 296
   4. 74
   5. 242
   • Correct AnswerChoice (D).
     The smallest number to satisfy the conditions is 74. Correct answer
   • Explanatory Answer
   • Divisibility & Remainders
   • Easy

3. Two positive integers are in the ratio 3 : 4. If their LCM is 192, what is the difference between the squares of the numbers?

   1. 1792
   2. 1790
   3. 1798
   4. 1796
   5. 1794
   • Correct AnswerChoice (A).
     The difference between the squares of the numbers is 1792. Correct answer
   • Explanatory Answer
   • LCM
   • Easy

4. If K is divisible by 3, 4 and 5, which of the following will also divide K?

   I. 3, 4 and 15
   II. 12, 15, and 18
   III. 5, 20, and 30

   1. I only
   2. II only
   3. I and II only
   4. I and III only
   5. II and III only
   • Correct AnswerChoice (D).
     K is also divisible by I and III. Correct answer
   • Explanatory Answer
   • Divisibility
   • Easy