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In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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10 Feb 2015, 08:42
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Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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10 Feb 2015, 09:06
Bunuel wrote: In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?
I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above.
A. I only B. I and II C. II and III D. I, II, and III E. IV only
Kudos for a correct solution. I. consider T (1, 2, 3) median=mean=2. Consider T (5, 9, 2, 19, 10) median=mean=9 II. Consider T (1, 2, 3) median=mean=2. Consider T (1, 1, 1, 1) median=mean=1 III. Consider T (1, 2, 3) mean=median=2 and there is no mode. Consider T (1, 1, 1) median=mean=1 and mode is 1. Answer E.
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Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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16 Feb 2015, 05:45
Bunuel wrote: In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?
I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above.
A. I only B. I and II C. II and III D. I, II, and III E. IV only
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTIONCorrect Answer: E None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3)
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Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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29 Dec 2015, 19:50
Bunuel wrote: In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?
I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above.
A. I only B. I and II C. II and III D. I, II, and III E. IV only
Kudos for a correct solution. This is a very good 'trap question'. Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0 Eliminates 1,2 and 3 OR Consider Set B= {1,2,2,3 } Mean=Median=Mode=2 Eliminates 1,2 and 3 If you think that only in 'consecutive integers' the average is equal to the median you might fall for 'D'. Ans: E



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In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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18 Dec 2016, 13:45
This is an Excellent Question. Here is my take on this one =>
Firstly,
Quote: For any evenly spaced set => Mean = Median = Average of the first and the last term. Also =>Quote: Sum of deviations around the mean = Zero
Now We are told that a Set T is such that its mean = median We are asked which of the statements must be true.
Statement 1> T is evenly Spaced
Consider two sets => 5,6,7,8,9,10,11 Mean = Median=8 Now Removing 7 and 9 wont affect the mean as 87 will be balanced by 89 and the sum of deviations around 8 will still be zero. Hence 5,6,8,10,11 => Mean = 8 and Median = 8 But the above set isn't every spaced.
Hence this statement is not always true. Statement 2=>
Consider a set => 7,7,7,7 Here => Mean=Median=7 And the number of terms is even. Hence this statement also isn't always true.
Statement 3> Consider a set => 7,7,7,7 Here Mode = 7 Hence Set T will can have a mode=> The statement isn't always true. Statement 4> None of the above => TRUE.
Hence E
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Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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10 Aug 2017, 02:01
Bunuel wrote: Bunuel wrote: In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?
I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above.
A. I only B. I and II C. II and III D. I, II, and III E. IV only
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTIONCorrect Answer: E None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3) So, in conclusion we can takeway from this question that for an evenly spaced set mean=median does not necessarily mean that the vice versa is true. Just because for a set mean = median does not render the set as an evenly spaced one.
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Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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10 Aug 2017, 02:18
ashikaverma13 wrote: Bunuel wrote: Bunuel wrote: In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?
I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above.
A. I only B. I and II C. II and III D. I, II, and III E. IV only
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTIONCorrect Answer: E None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3) So, in conclusion we can takeway from this question that for an evenly spaced set mean=median does not necessarily mean that the vice versa is true. Just because for a set mean = median does not render the set as an evenly spaced one. _______________ Yes, that's true.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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15 Aug 2017, 10:56
Bunuel wrote: In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?
I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above.
A. I only B. I and II C. II and III D. I, II, and III E. IV only
Kudos for a correct solution. Let’s analyze each Roman numeral statement. I. Set T consists of evenly spaced numbers. This is not necessarily true. For example, if set T = {1, 2, 4, 4, 9}, we see that average = median, but T is not an evenly spaced set. II. Set T consists of an odd number of terms. This is not necessarily true. For example, if set T = {3, 3}, we see that average = median, but T has an even number of terms. III. Set T has no mode. This is not necessarily true. For example, if we use the same set T as in Roman numeral I, we see that average = median, but T does have a mode. Answer: E
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Re: In Set T, the average (arithmetic mean) equals the median. Which of th
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