GMAT Factors And Multiples Questions

Hii sir, I am Preparing for the GMAT Examination Will you Please Provide me Questions on the Greatest Common Factor And their Solutions for the GMAT Examination ?

[sumit]

The Graduate Management Admission Test is a computer adaptive test intended to assess certain analytical, writing, quantitative, verbal, and reading skills in written English for use in admission to a graduate management program, such as an MBA.


Greatest Common Factor (GCF): The GCF of two numbers is the largest number that is a factor of both numbers.

Rule (How to find the GCF): The GCF of two numbers is the product of all the numbers that appear in the prime factorizations of both numbers

Q: What is the Greatest Common Factor of 24 and 150?

Step 1: Find the prime factorizations of 24 and 150.

In the prime factorization diagram above you see that:
24 = 2 2 2 3
150 = 2 3 5 5

Step 2: Identify the overlap of the two numbers prime factorizations.

Only the numbers 2 and 3 are factors of BOTH 24 and 150; note that 5 is not a factor of 24.

Step 3: To find the GCF of 24 and 150, apply the rule noted above.

The GCF is the product of all the numbers that appear in the prime factorizations of both numbers, in this case one 2 and one 3. Thus, the GCF of 24 and 150 = 2 3 = 6.


Application: GCFs on the GMAT

Question #2 (GMAT Data Sufficiency)
Is z divisible by 6?
(1) The greatest common factor between 12 and z is 3.
(2) The greatest common factor between 15 and z is 15.

Just because this question is a data sufficiency question instead of a problem solving question, what we re trying to do when evaluating each statement is essentially the same as we did in answering the problem solving question above.

The major difference of course is that instead of actually having to solve something, we simply have to determine the sufficiency of each statement.

Remember from the video lesson on “Data Sufficiency Part 2, the first thing you want to do before evaluating the two statements is to ask yourself: What information, if given to me in the statements, would enable me to answer this question?

For z to be divisible by 6, the prime factorization of z must at least have a 2 and a 3 in it, right? Thus, when evaluating the statements, all we really need to know is if the statement gives us enough information to determine whether z has both a 2 and a 3 as factors. Let’s take a closer look:

Statement 1: The prime factorization of 12 = 2 2 3. If the GCF of 12 and z is 3, that means that z does have 3 as a factor, but not 2 (otherwise the GCF would be at least 6). Therefore, the statement is sufficient to definitively answer the question.

Statement 2: The prime factorization of 15 = 3 5. If the GCF of 15 and z is 15, we know that z has a 3 and a 5 as factors, but we don’t know from this statement if it also has 2 as a factor. Therefore we can’t definitively answer the question, so this statement is insufficient.

The answer is A.