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# If the median of Set A above is one less than the mode of Set A, which

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If the median of Set A above is one less than the mode of Set A, which  [#permalink]

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18 Jul 2018, 21:17
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Difficulty:

25% (medium)

Question Stats:

70% (01:28) correct 30% (01:31) wrong based on 40 sessions

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Set A = {3, 1, 7, 5, 11, x}
If the median of Set A above is one less than the mode of Set A, which of the following is a possible value of x ?

A. 3
B. 5
C. 6
D. 7
E. 9

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Re: If the median of Set A above is one less than the mode of Set A, which  [#permalink]

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18 Jul 2018, 21:31
Ascending order of the set:
{1,3,5,7,11}

D) 7
Median = 7+5/2 = 6
Mode = 7
Median is one less than Mode

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If the median of Set A above is one less than the mode of Set A, which  [#permalink]

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18 Jul 2018, 21:32
Set A = {3, 1, 7, 5, 11, x}

Plugging in option values for x

x = 3

=> mode = 3

=> median of {1,3,3,5,7,11} = 4 $$\neq$$ mode - 1 INCORRECT

__________________________________________________________________________________________________

x = 5

=> mode = 5

=> median of {1,3,5,5,7,11} = 5 $$\neq$$ mode - 1 INCORRECT

__________________________________________________________________________________________________

x = 6

=> mode can be 1, 3, 5, 6, 7, 11

=> median of {1,3,5,6,7,11} = 5.5 $$\neq$$ mode - 1 INCORRECT

__________________________________________________________________________________________________

x = 7

=> mode is 7

=> median of {1,3,5,7,7,11} = 6 = mode - 1 CORRECT

__________________________________________________________________________________________________

x = 9

=> mode can be 1, 3, 5, 7, 9, 11

=> median of {1,3,5,7,9,11} = 6 $$\neq$$ mode - 1 INCORRECT

Hence option D
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If the median of Set A above is one less than the mode of Set A, which &nbs [#permalink] 18 Jul 2018, 21:32
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