Question:  If x is a product of 4 consecutive integers, and x is divisible by 11, which of the following is not necessarily a divisor of x?

A) 12
B) 22
C) 24
D) 33
E) None of these

Correct Answer: E
Solution and Explanation:
Approach Solution 1:

Which of the following is not definitely a divisor of x if x is the product of 4 consecutive integers and x is divisible by 11?

The product of four numbers that are multiplied together produces a number that is divisible by 4!
which equals 24, meaning that it is always divisible by both 12 and 24.

In addition, given that it may be divided by 11, as well as by 2 and by 3, the numbers 22 and 33 will both be considered factors of x.
Because 22 = 11 * 2, and 33 = 11 * 3
Here both 11, 2, and 3 are factors of x.

Now we got that 12, 24, 33, and 22 are the factors of x.
The only remaining choice is E.
E is the correct choice.

Approach Solution 2:

Which of the following is not definitely a divisor of x if x is the product of 4 consecutive integers and x is divisible by 11?

The product of four numbers that are multiplied together produces a number that is divisible by 4!

The first set of four numbers may be (8,9,10,11), and the subsequent sets of (12,22,33, and 24) will divide this set of numbers. There may be an endless number of sets of successive integers that, when multiplied, will be a multiple of 11.

P.S. - Listing the first set of numbers is sufficient to determine the solution.

E is the best option.

“If x is a product of 4 consecutive integers, and x is" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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