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Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?
I. The maximum possible range of the set is greater than 33.
II. The median can never be an even number.
III. If y = 37, the average of the set will be greater than the median.
  • a)
    I only
  • b)
    I and II only
  • c)
    I and III only
  • d)
    III only
  • e)
    I, II, and III
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and...
Step 1: Key Data from the Question Stem
Set S has 6 elements.
The elements of set S are distinct.
x and y are prime numbers. Because 2 is already an element in S, both x and y have to be odd.
0 < x < 40 and 0 < y < 40
Step 2: Check Statement I
I. The maximum possible range of the set is greater than 33.
The key word in this entire statement is maximum. We have to determine whether the maximum value possible for the range exceeds 33.
We know x and y are prime numbers. The largest prime number less than 40 is 37.
If either x or y is 37, the largest number in the set will be 37 and the smallest number is 2.
Therefore, the maximum range of the set will be 37 - 2 = 35. It is greater than 33.
Statement I is true. So, eliminate choices that do not contain I.
Eliminate choice D
Step 3: Check Statement II
II. The median can never be an even number.
There are 6 numbers in the set. Therefore, the median is the arithmetic mean of the 3rd and the 4th term when the numbers are written in ascending or descending order.
The elements are {2, 4, 6, 8, x, y}, where x and y are prime numbers.
If x and y take 3 and 5 as values, the median is 4.5
If x = 3, y = 7 or greater, the median is 5.
If x = 5, y = 7 or greater, the median is 5.5
If x = 7, y = 11 or greater, the median is 6.5
If x = 11 or greater and y = 13 or greater, the median is 7.
It is quite clear that the median is either an odd number or is not an interger. So, the median can never be an even integer.
Statement II is true. Eliminate choices that do not contain II.
Eliminate choices A and C as well.
Step 4: Check Statement III
III. If y = 37, the average of the set will be greater than the median.
If y = 37, the set will be {2, 4, 6, 8, x, 37}, where x is a prime number greater than 2 and less than 37.
The average will be
If x = 3, median = 5 and average = 10. Average > median.
If x = 5, median = 5.5 and average = 10.33. Average > median
If x = 7, median = 6.5 and average = 10.66. Average > medain
If x = 11 or greater, the median = 7. Average will be definitely greater than 10. So, Average > Median.
It is true that the average is greater than the median if y = 37.
Statement III is also true.
Statements I, II, and III are true.
Choice E is the correct answer.
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Community Answer
Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and...
Step 1: Key Data from the Question Stem
Set S has 6 elements.
The elements of set S are distinct.
x and y are prime numbers. Because 2 is already an element in S, both x and y have to be odd.
0 < x < 40 and 0 < y < 40
Step 2: Check Statement I
I. The maximum possible range of the set is greater than 33.
The key word in this entire statement is maximum. We have to determine whether the maximum value possible for the range exceeds 33.
We know x and y are prime numbers. The largest prime number less than 40 is 37.
If either x or y is 37, the largest number in the set will be 37 and the smallest number is 2.
Therefore, the maximum range of the set will be 37 - 2 = 35. It is greater than 33.
Statement I is true. So, eliminate choices that do not contain I.
Eliminate choice D
Step 3: Check Statement II
II. The median can never be an even number.
There are 6 numbers in the set. Therefore, the median is the arithmetic mean of the 3rd and the 4th term when the numbers are written in ascending or descending order.
The elements are {2, 4, 6, 8, x, y}, where x and y are prime numbers.
If x and y take 3 and 5 as values, the median is 4.5
If x = 3, y = 7 or greater, the median is 5.
If x = 5, y = 7 or greater, the median is 5.5
If x = 7, y = 11 or greater, the median is 6.5
If x = 11 or greater and y = 13 or greater, the median is 7.
It is quite clear that the median is either an odd number or is not an interger. So, the median can never be an even integer.
Statement II is true. Eliminate choices that do not contain II.
Eliminate choices A and C as well.
Step 4: Check Statement III
III. If y = 37, the average of the set will be greater than the median.
If y = 37, the set will be {2, 4, 6, 8, x, 37}, where x is a prime number greater than 2 and less than 37.
The average will be
If x = 3, median = 5 and average = 10. Average > median.
If x = 5, median = 5.5 and average = 10.33. Average > median
If x = 7, median = 6.5 and average = 10.66. Average > medain
If x = 11 or greater, the median = 7. Average will be definitely greater than 10. So, Average > Median.
It is true that the average is greater than the median if y = 37.
Statement III is also true.
Statements I, II, and III are true.
Choice E is the correct answer.
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Directions: Read the given passage carefully and answer the question as follow.Among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint, the origin of number is one that has provoked much lively discussion, and has led to a great amount of learned research among the primitive and savage languages of the human race. A few simple considerations will, however, show that such research must necessarily leave this question entirely unsettled, and will indicate clearly that it is, from the very nature of things, a question to which no definite and final answer can be given. Among the barbarous tribes whose languages have been studied, even in a most cursory manner, none have ever been discovered which did not show some familiarity with the number concept. The knowledge thus indicated has often proved to be most limited; not extending beyond the numbers 1 and 2, or 1, 2, and 3. At first thought it seems quite inconceivable that any human being should be destitute of the power of counting beyond 2. But such is the case; and in a few instances languages have been found to be absolutely destitute of pure numeral words.These facts must of necessity deter the mathematician from seeking to push his investigation too far back toward the very origin of number. Philosophers have endeavoured to establish certain propositions concerning this subject, but, as might have been expected, have failed to reach any common ground of agreement. Whewell has maintained that “such propositions as that two and three make five are necessary truths, containing in them an element of certainty beyond that which mere experience can give.” Mill, on the other hand, argues that any such statement merely expresses a truth derived from early and constant experience; and in this view he is heartily supported by Tylor.But why this question should provoke controversy, it is difficult for the mathematician to understand. Either view would seem to be correct, according to the standpoint from which the question is approached. We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language. They express ideas which are, at first, wholly concrete, which are of the greatest possible simplicity, and which seem in many ways to be clearly understood, even by the higher orders of the brute creation. The origin of number would in itself, then, appear to lie beyond the proper limits of inquiry; and the primitive conception of number to be fundamental with human thought.Q.The author of the passage would most probably agree with each of the following EXCEPT

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Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?I. The maximum possible range of the set is greater than 33.II. The median can never be an even number.III. If y = 37, the average of the set will be greater than the median.a)I onlyb)I and II onlyc)I and III onlyd)III onlye)I, II, and IIICorrect answer is option 'E'. Can you explain this answer?
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Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?I. The maximum possible range of the set is greater than 33.II. The median can never be an even number.III. If y = 37, the average of the set will be greater than the median.a)I onlyb)I and II onlyc)I and III onlyd)III onlye)I, II, and IIICorrect answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?I. The maximum possible range of the set is greater than 33.II. The median can never be an even number.III. If y = 37, the average of the set will be greater than the median.a)I onlyb)I and II onlyc)I and III onlyd)III onlye)I, II, and IIICorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?I. The maximum possible range of the set is greater than 33.II. The median can never be an even number.III. If y = 37, the average of the set will be greater than the median.a)I onlyb)I and II onlyc)I and III onlyd)III onlye)I, II, and IIICorrect answer is option 'E'. Can you explain this answer?.
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