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Difficulty:
25%
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Question Stats:
65% (00:46) correct
35%
(01:02)
wrong
based on 77
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The set Q consists of 15 numbers whose arithmetic mean is zero. Which of the following quantities must also be zero?
I. The median of the numbers in Q
II. The mode of the numbers in Q
III. The sum of the numbers in Q
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
I. The median of the numbers in Q
II. The mode of the numbers in Q
III. The sum of the numbers in Q
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
22 Aug 2023, 08:33
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The set Q consists of 15 numbers whose arithmetic mean is zero. Which of the following quantities must also be zero?
I. The median of the numbers in Q
II. The mode of the numbers in Q
III. The sum of the numbers in Q
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
Since nothing is mentioned clearly as in the whether the numbers are integers or not, or anything else, testing(mentally only) values can help. Also, it's a must condition thus it makes our work a little easy.
Mean being zero means numbers can be either equally distributed i.e. for example 7 are negative and 7 positive with each being equidistant from each other(-7,-6,5...0, ... 6, 7) or may be not(-50, -5, -2, 1, 2, 5, ... 20 such that positive ones sum 57). So, we have median being '0' in first case and it not being '0'.
So, anything that has I is not the answer.
Only B is left.
IMO Answer B.
I. The median of the numbers in Q
II. The mode of the numbers in Q
III. The sum of the numbers in Q
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
Since nothing is mentioned clearly as in the whether the numbers are integers or not, or anything else, testing(mentally only) values can help. Also, it's a must condition thus it makes our work a little easy.
Mean being zero means numbers can be either equally distributed i.e. for example 7 are negative and 7 positive with each being equidistant from each other(-7,-6,5...0, ... 6, 7) or may be not(-50, -5, -2, 1, 2, 5, ... 20 such that positive ones sum 57). So, we have median being '0' in first case and it not being '0'.
So, anything that has I is not the answer.
Only B is left.
IMO Answer B.
22 Aug 2023, 10:36
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The set Q consists of 15 numbers whose arithmetic mean is zero. Which of the following quantities must also be zero?
I. The median of the numbers in Q
II. The mode of the numbers in Q
III. The sum of the numbers in Q
If set, Q = {-7,-6,-5,-4,-3-2,-1,-1,1,2,3,4,5,6,8} then the set satisfies the given condition in the problem and only the condition III i.e. The sum of the numbers in Q is zero
Hence B
I. The median of the numbers in Q
II. The mode of the numbers in Q
III. The sum of the numbers in Q
If set, Q = {-7,-6,-5,-4,-3-2,-1,-1,1,2,3,4,5,6,8} then the set satisfies the given condition in the problem and only the condition III i.e. The sum of the numbers in Q is zero
Hence B
