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Question: If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?
- x is an even integer.
- x is a nonzero integer.
- x is a multiple of 5.
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
Approach Solution 1
This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.
Only one of the five options is correct.
First off, note that the question is which of the following MUST be true, not which of the following COULD be true.
Also note that the median, which is essentially a middle word, is equal to the average of five consecutive even integers. I must thus always be the truth: "even, even, even, even, even."
- x is a positive integer. Contrary to popular belief, x is a multiple of 5, as shown by the following numbers: -4, -2, 0, 2, and 4. Not always the case; take the numbers 0, 2, 4, 6, and 8.
A is the correct choice.
Approach Solution 2
Only one of the five options is correct.
Statement I states that x is an even integer.
Since x is the average of 5 consecutive even integers, the sum of these integers will be divisible by 5. Therefore, the average x will also be divisible by 5.
Additionally, the sum of consecutive even integers will always be even. Dividing an even sum by 5 will yield an even average.
Thus, statement I alone guarantees that x is an even integer.
Therefore, the answer is (A) I only.
Approach Solution 3
This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.
Only one of the five options is correct.
Statement I states that x is an even integer.
Since x is the average of 5 consecutive even integers, the sum of these integers will be divisible by 5. Therefore, the average x will also be divisible by 5.
Additionally, the sum of consecutive even integers will always be even. Dividing an even sum by 5 will yield an even average.
Thus, statement I alone guarantees that x is an even integer.
Therefore, the answer is (A) I only.
“If x is the average (arithmetic mean) of 5 consecutive even integers" - 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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