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# If the mode of Set A is equal to the median of Set A, Set A could be

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Math Expert
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If the mode of Set A is equal to the median of Set A, Set A could be  [#permalink]

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11 Feb 2015, 05:43
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Difficulty:

35% (medium)

Question Stats:

70% (01:25) correct 30% (01:23) wrong based on 159 sessions

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If the mode of Set A is equal to the median of Set A, Set A could be

A. [0, 1, 2, 2, 3, 4, 5, 6]
B. [2, 2, 5, 7, 9]
C. [x, x+1, x+2, x+2, x+3, x+3]
D. [10, 102, 105, 105]
E. [4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]

Kudos for a correct solution.

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Re: If the mode of Set A is equal to the median of Set A, Set A could be  [#permalink]

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11 Feb 2015, 06:42
Bunuel wrote:
If the mode of Set A is equal to the median of Set A, Set A could be

A. [0, 1, 2, 2, 3, 4, 5, 6]
B. [2, 2, 5, 7, 9]
C. [x, x+1, x+2, x+2, x+3, x+3]
D. [10, 102, 105, 105]
E. [4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]

Kudos for a correct solution.

It has to be C because mode and median are unequal in every other set.

A. mode=2 median=2,5
B. mode=2 median=5
D. mode=105 median=103,5
E. mode=51 median=13

In C x+2 and x+3 have the same frequency. median is x+2=mode

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Re: If the mode of Set A is equal to the median of Set A, Set A could be  [#permalink]

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11 Feb 2015, 21:30
1
Answer = C. [x, x+1, x+2, x+2, x+3, x+3]

Mode = (x+2) & (x+3)

Median $$= \frac{x+2+x+2}{2} = x+2$$

x+2 hold true for both mode & median
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Re: If the mode of Set A is equal to the median of Set A, Set A could be  [#permalink]

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11 Feb 2015, 23:20
OA = C

mode = mean = "x+2"
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Re: If the mode of Set A is equal to the median of Set A, Set A could be  [#permalink]

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12 Feb 2015, 22:27
Ans C

Using PoE, mode and median are unequal in every other set.
Math Expert
Joined: 02 Sep 2009
Posts: 53020
Re: If the mode of Set A is equal to the median of Set A, Set A could be  [#permalink]

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16 Feb 2015, 05:03
Bunuel wrote:
If the mode of Set A is equal to the median of Set A, Set A could be

A. [0, 1, 2, 2, 3, 4, 5, 6]
B. [2, 2, 5, 7, 9]
C. [x, x+1, x+2, x+2, x+3, x+3]
D. [10, 102, 105, 105]
E. [4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set C is equal to the median of set C.
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Re: If the mode of Set A is equal to the median of Set A, Set A could be  [#permalink]

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16 Mar 2015, 01:21
C is the answer as both the median as well as the median are x+2 because there 6 items and the median is 3rd and 4th item sum divided by 2 which is equal to x+2 also the frequency is x+2 and x+3 hence mode is x+2 and x+3 but equal median is x+2 hence it is the answer.
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Re: If the mode of Set A is equal to the median of Set A, Set A could be  [#permalink]

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08 Oct 2018, 09:12
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Re: If the mode of Set A is equal to the median of Set A, Set A could be   [#permalink] 08 Oct 2018, 09:12
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