If a, b, and c are distinct positive integers, and a + b + c = 31, wha GMAT Problem-Solving

Question: If a, b, and c are distinct positive integers, and a + b + c = 31, what is the greatest possible value of a*b*c?

A. 1024
B. 1056
C. 1072
D. 1080
E. 1200

Answer: D

Solution and Explanation:

Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with algebra. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
These three integers must be as close to one another as feasible to get the maximum possible value of the product of a, b, and c.
Their values must be within the range 31/3=10.33
By using the hit-and-miss method, let's set a = 10, b = 9, and c = 12 (c cannot be 11 because 11+10+10 = 31 - there will be repetition).
The product of a, b, and c, therefore, equals 10*9*12 = 1080.
Correct option: D

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with algebra. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
When given a fixed total, any number of positive integers will produce its largest product when the numbers are the closest to one another.
Each number should be around 10 since there are 3 numbers and their aggregate is 31. If the three numbers are not necessarily distinct, the biggest product would be 10 x 10 x 11 = 1100.
Yet since they must be distinct, we can reduce one of the tens to nine and raise one to twelve. As the three numbers are different and their sum is 31, the biggest product is 9 x 10 x 12 = 1080.
Correct option: D

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with algebra. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
The goal is to discover three consecutive numbers that add up to 31.
That is, if an is the largest positive integer, then
a+a-1+a-2=31
3a=34
a=11.333
Consider that the floor function of a-1 and a-2 is 10, while the ceiling function of a has a value of 12. The greatest product is therefore 9*10*12=1080.
Correct option: D

“If a, b, and c are distinct positive integers, and a + b + c = 31, wha" - 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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