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09 Feb 2022, 08:15
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Set M consists of the terms {2, 3, 3, 4, 5, 7, 9, 9}. Which of the following pairs of terms, if added to Set M, would ensure that Set M has exactly two modes?
A. {2, 3}
B. {9, 9}
C. {1, 6}
D. {4, 5}
E. {10, 10}
A. {2, 3}
B. {9, 9}
C. {1, 6}
D. {4, 5}
E. {10, 10}
09 Feb 2022, 08:47
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I think no answer will ensure that Set M has exactly two modes
If added {2, 3}, the mode of the set {2, 2, 3, 3, 3, 4, 5, 7, 9, 9} will be (3+4)/2=3,5
If added {9, 9}, the mode of the set {2, 3, 3, 4, 5, 7, 9, 9, 9, 9} will be (5+7)/2=6
If added {1, 6}, the mode of the set {1, 2, 3, 3, 4, 5, 6, 7, 9, 9} will be (4+5)/2=4,5
If added {4, 5}, the mode of the set {2, 3, 3, 4, 4, 5, 5, 7, 9, 9} will be (4+5)/2=4,5
If added {10, 10}, the mode of the set {2, 3, 3, 4, 5, 7, 9, 9, 10, 10} will be (5+7)/2=6
If added {2, 3}, the mode of the set {2, 2, 3, 3, 3, 4, 5, 7, 9, 9} will be (3+4)/2=3,5
If added {9, 9}, the mode of the set {2, 3, 3, 4, 5, 7, 9, 9, 9, 9} will be (5+7)/2=6
If added {1, 6}, the mode of the set {1, 2, 3, 3, 4, 5, 6, 7, 9, 9} will be (4+5)/2=4,5
If added {4, 5}, the mode of the set {2, 3, 3, 4, 4, 5, 5, 7, 9, 9} will be (4+5)/2=4,5
If added {10, 10}, the mode of the set {2, 3, 3, 4, 5, 7, 9, 9, 10, 10} will be (5+7)/2=6
kungfury42
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09 Feb 2022, 14:19
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gmatcafe
I think no answer will ensure that Set M has exactly two modes
If added {2, 3}, the mode of the set {2, 2, 3, 3, 3, 4, 5, 7, 9, 9} will be (3+4)/2=3,5
If added {9, 9}, the mode of the set {2, 3, 3, 4, 5, 7, 9, 9, 9, 9} will be (5+7)/2=6
If added {1, 6}, the mode of the set {1, 2, 3, 3, 4, 5, 6, 7, 9, 9} will be (4+5)/2=4,5
If added {4, 5}, the mode of the set {2, 3, 3, 4, 4, 5, 5, 7, 9, 9} will be (4+5)/2=4,5
If added {10, 10}, the mode of the set {2, 3, 3, 4, 5, 7, 9, 9, 10, 10} will be (5+7)/2=6
If added {2, 3}, the mode of the set {2, 2, 3, 3, 3, 4, 5, 7, 9, 9} will be (3+4)/2=3,5
If added {9, 9}, the mode of the set {2, 3, 3, 4, 5, 7, 9, 9, 9, 9} will be (5+7)/2=6
If added {1, 6}, the mode of the set {1, 2, 3, 3, 4, 5, 6, 7, 9, 9} will be (4+5)/2=4,5
If added {4, 5}, the mode of the set {2, 3, 3, 4, 4, 5, 5, 7, 9, 9} will be (4+5)/2=4,5
If added {10, 10}, the mode of the set {2, 3, 3, 4, 5, 7, 9, 9, 10, 10} will be (5+7)/2=6
Hi gmatcafe, it seems you have mistakenly calculated the median, the middle element or the average of middle elements (in case of even number of elements in the set) for all the cases.
However, we are required to find the mode - the number which occurs with the greatest instances of repetition (also called frequency) in the set.
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