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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.
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.
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
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.
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.
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.
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.
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
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.
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.
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.
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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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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for GMAT.
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ample number of questions to practice 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? tests, examples and also practice GMAT tests.
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