Question: If f(x) is defined as the largest integer N such that x is divisible by, which f the following numbers is the greatest?

1. f (24)
2. f (42)
3. f (62)
4. f (76)
5. f (84)

Answer:

Approach Solution (1):

We have an integer x. It has some power of 2 in its prime factorization \((2^n)\)and f(x) is the value of that n. basically f(x) is the power of 2 in prime factorization of x.

For example: if x is say 40, then f(x) = 3. Why? Because the largest integer n such that 40 is \((2^n)\) divisible byis 3: \(\frac{40}{2^3}=5 or40=2^3*5\) - the power of 2 in prime factorization of 40 is 3.

Hence all we need to do to answer the question is to factorize all options and see which one has 2 in highest power.

1. f (24): factorize 24: \(24=2^3*3\) , thus f (24) = 3
2. f (42): factorize 42: \(42=2*21\) , thus f (42) = 1
3. f (62): factorize 62: \(62=2*31\) , thus f (62) = 1
4. f (76): factorize 76: \(76=2^2*19\) , thus f (76) = 2
5. f (84): factorize 84: \(84=2^2*21\) , thus f (84) = 2

Correct option: A

“If f(x) is defined as the largest integer N such that x is divisible by, which f the following numbers is the greatest?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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