PROGRAMA GMAT GRE SAT MATEMÁTICA claudio hurtado gmatchile.cl
GMAT Problem Solving Divisibility Multiples Factors Difficulty: 600 Level
Understanding divisibility, multiples, and factors is essential for mastering GMAT Problem Solving questions, especially at the 600 difficulty level. These concepts form the backbone of many quantitative problems and are frequently tested in both GMAT and GRE exams. For students preparing through specialized programs like GMATCHILE.cl, led by Claudio Hurtado, developing a strong foundation in number properties is a strategic advantage.
Divisibility refers
Divisibility refers to the ability of one integer to be divided by another without leaving a remainder. For example, 24 is divisible by 6 because 24 ÷ 6 = 4. On the GMAT, divisibility rules are often embedded in word problems or algebraic expressions. Knowing rules for divisibility by 2, 3, 5, 9, and 10 can help eliminate answer choices quickly and efficiently.
Multiples are the result of multiplying a number by an integer
Multiples are the result of multiplying a number by an integer. For instance, the multiples of 4 include 4, 8, 12, 16, and so on. GMAT questions may ask for the least common multiple (LCM) of two numbers, which is the smallest number that is a multiple of both. This concept is particularly useful when solving problems involving rates, cycles, or scheduling.
Factors numbers
Factors are numbers that divide another number evenly. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The greatest common factor (GCF) is the largest number that divides two or more numbers without a remainder. GMAT questions often require identifying common factors to simplify fractions or solve equations.
At the 600 level
At the 600 level, GMAT Problem Solving questions involving these concepts may include layered logic, requiring test-takers to combine multiple rules or manipulate algebraic expressions. For example, a question might ask whether a certain expression is divisible by a given number, requiring knowledge of prime factorization and modular arithmetic.
Programs like GMATCHILE.cl
Programs like GMATCHILE.cl emphasize replicable strategies and structured problem-solving techniques. Claudio Hurtado’s approach focuses on semantic clarity and granular control, ensuring that students not only understand the theory but also apply it consistently across different question types. This methodology is particularly effective for students aiming to improve their quantitative scores on the GMAT, GRE, SAT, or other standardized math exams.
In summary, mastering divisibility, multiples, and factors is not just about memorizing rules—it’s about applying them strategically. With the right guidance and practice, students can confidently tackle 600-level GMAT questions and build the skills needed for higher-level problem solving.
1) If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2^k is a
factor of n?
A. 10
B. 12
C. 15
D. 18
E. 20
2) What is the remainder when n^2+7 is divided by 8, where n is an odd prime number?
A. 0
B. 2
C. 3
D. 4
E. 6
3)If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1
does n have?
(A) four
(B) five
(C) six
(D) seven
(E) eight
4) The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following
must be a factor of x + y?
(A) 6
(B) 9
(C) 10
(D) 11
(E) 14
5) The 180 students in a group are to be seated in rows so that there is an equal number of students in each
row. Each of the following could be the number of rows EXCEPT
(A) 4
(B) 20
(C) 30
(D) 40
(E) 90
6) If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the
following is NOT necessarily an integer?
(A) (x+z)/z
(B) (y+z)/x
(C) (x+y)/z
(D) (xy)/z
(E) (yz)/x
Answer: 1)D 2)A 3)A 4)D 5)D 6)B
clasesgmatchile@gmail.com whatsapp +56 937780070
Suggested Video Title
Video Analysis: A GMAT 600-Level Number Properties Question
Suggested Explanatory Text
«After reviewing the theory, the best way to solidify your knowledge is by seeing how it’s applied in practice. In this video, instructor Claudio Hurtado walks you step-by-step through a solution to a data sufficiency question on number properties, similar to the ones you’ll find at the 600 level.
Pay close attention to the strategies he uses to simplify the problem and arrive at the correct answer efficiently.»
FAQ GMAT Problem Solving Divisibility Multiples Factors Difficulty: 600 Level
Answer: At the 600-level, GMAT questions on divisibility, multiples, and factors go beyond basic definitions. You need a solid understanding of prime factorization, recognizing number properties, and applying concepts like the least common multiple (LCM) and greatest common divisor (GCD). Questions often require you to infer properties of a number from given statements, such as determining if an integer is divisible by 12 when you know it’s divisible by both 6 and 8.
Answer: Easier questions test your basic knowledge of rules and definitions. 600-level questions, on the other hand, require you to synthesize multiple concepts. You’ll need to manipulate algebraic expressions to identify divisibility, work with multiple variables, and apply logical reasoning to data sufficiency problems. The focus shifts from direct calculation to conceptual understanding and analytical thinking.
Answer: The most effective strategy is to use prime factorization. Break down all numbers in the problem into their prime factors. This allows you to clearly see the components of a number and determine divisibility rules and relationships between multiples and factors. This approach is more reliable and efficient than testing numerous numbers, especially under time pressure.
Answer: Yes, a common trap is assuming a property that isn’t explicitly stated. For example, if a question states that an integer is divisible by 4 and 6, a common mistake is to assume it is divisible by their product, 24. However, the correct approach is to find the LCM, which in this case is 12, as the prime factors are 2² and 2×3. Always rely on prime factorization to avoid these pitfalls.
Answer: To master 600-level questions, you should use official GMAT materials, reputable question banks like GMAT Club or Manhattan Prep, and video tutorials that break down problem-solving strategies. Look for resources that categorize questions by difficulty level and provide detailed explanations of both correct and incorrect answers.
Answer: To improve speed and accuracy, focus on mastering the fundamentals first. Then, practice timed sets of 600-level questions. Analyze your mistakes to identify patterns in your errors, whether they are conceptual gaps or careless mistakes. Developing a systematic approach to each problem type, such as using prime factorization for divisibility, will help you work more efficiently and confidently.
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