GMAT Exam > GMAT Questions > Set X is given by {a, 2a, 3a, 4a, 5a} where &...
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Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. If element ‘a’ in Set X is replaced by ‘b’ and b < a, then which of the following must be true?
I.Mean would not change.
II.Median would not change.
III. Standard deviation would not change
- a)I only
- b)II only
- c)III only
- d)Both I and II
- e)Both II and III
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a posit...
Solution:
Given, Set X = {a, 2a, 3a, 4a, 5a}
If element a in Set X is replaced by b and b < a,="" then="" the="" set="" becomes="" {b,="" 2b,="" 3b,="" 4b,="" />
To find out which of the given options is true, we need to calculate the mean, median, and standard deviation of both sets and compare them.
Mean:
Mean of Set X = (a + 2a + 3a + 4a + 5a)/5 = 3a
Mean of {b, 2b, 3b, 4b, 5b} = (b + 2b + 3b + 4b + 5b)/5 = 3b
Since a > b, the mean of the second set is less than the mean of the first set. Therefore, option I is not true.
Median:
Median of Set X = 3a
Median of {b, 2b, 3b, 4b, 5b} = 3b
Since the median of both sets is the third element, which is 3a and 3b respectively, the median does not change. Therefore, option II is true.
Standard deviation:
Standard deviation of Set X can be calculated as follows:
σ = √[(1/5) * {(a - 3a)² + (2a - 3a)² + (3a - 3a)² + (4a - 3a)² + (5a - 3a)²}]
= √[(1/5) * {4a² + a² + a² + 4a² + 16a²}]
= √(26a²/5)
Standard deviation of {b, 2b, 3b, 4b, 5b} can be calculated as follows:
σ = √[(1/5) * {(b - 3b)² + (2b - 3b)² + (3b - 3b)² + (4b - 3b)² + (5b - 3b)²}]
= √[(1/5) * {4b² + b² + b² + 4b² + 16b²}]
= √(26b²/5)
Since a > b, the standard deviation of the first set is greater than the standard deviation of the second set. Therefore, option III is not true.
Hence, the correct answer is option II only.
Given, Set X = {a, 2a, 3a, 4a, 5a}
If element a in Set X is replaced by b and b < a,="" then="" the="" set="" becomes="" {b,="" 2b,="" 3b,="" 4b,="" />
To find out which of the given options is true, we need to calculate the mean, median, and standard deviation of both sets and compare them.
Mean:
Mean of Set X = (a + 2a + 3a + 4a + 5a)/5 = 3a
Mean of {b, 2b, 3b, 4b, 5b} = (b + 2b + 3b + 4b + 5b)/5 = 3b
Since a > b, the mean of the second set is less than the mean of the first set. Therefore, option I is not true.
Median:
Median of Set X = 3a
Median of {b, 2b, 3b, 4b, 5b} = 3b
Since the median of both sets is the third element, which is 3a and 3b respectively, the median does not change. Therefore, option II is true.
Standard deviation:
Standard deviation of Set X can be calculated as follows:
σ = √[(1/5) * {(a - 3a)² + (2a - 3a)² + (3a - 3a)² + (4a - 3a)² + (5a - 3a)²}]
= √[(1/5) * {4a² + a² + a² + 4a² + 16a²}]
= √(26a²/5)
Standard deviation of {b, 2b, 3b, 4b, 5b} can be calculated as follows:
σ = √[(1/5) * {(b - 3b)² + (2b - 3b)² + (3b - 3b)² + (4b - 3b)² + (5b - 3b)²}]
= √[(1/5) * {4b² + b² + b² + 4b² + 16b²}]
= √(26b²/5)
Since a > b, the standard deviation of the first set is greater than the standard deviation of the second set. Therefore, option III is not true.
Hence, the correct answer is option II only.
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Community Answer
Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a posit...
Say a = 2 -- 2,4,6,8,10 - Mean = 6 Median = 6 .
B = 1,2,3,4,5 - Mean is 3 & Median = 3.
So the mean and median are for both sets! :/
B = 1,2,3,4,5 - Mean is 3 & Median = 3.
So the mean and median are for both sets! :/
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Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. If element ‘a’ in Set X is replaced by ‘b’ and b < a, then which of the following must be true?I.Mean would not change.II.Median would not change.III. Standard deviation would not changea)I onlyb)II onlyc)III onlyd)Both I and IIe)Both II and IIICorrect answer is option 'B'. Can you explain this answer?
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Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. If element ‘a’ in Set X is replaced by ‘b’ and b < a, then which of the following must be true?I.Mean would not change.II.Median would not change.III. Standard deviation would not changea)I onlyb)II onlyc)III onlyd)Both I and IIe)Both II and IIICorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. If element ‘a’ in Set X is replaced by ‘b’ and b < a, then which of the following must be true?I.Mean would not change.II.Median would not change.III. Standard deviation would not changea)I onlyb)II onlyc)III onlyd)Both I and IIe)Both II and IIICorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. If element ‘a’ in Set X is replaced by ‘b’ and b < a, then which of the following must be true?I.Mean would not change.II.Median would not change.III. Standard deviation would not changea)I onlyb)II onlyc)III onlyd)Both I and IIe)Both II and IIICorrect answer is option 'B'. Can you explain this answer?.
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