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# A list of five integers has the following criteria: I. The median of

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Math Expert
Joined: 02 Sep 2009
Posts: 58332
A list of five integers has the following criteria: I. The median of  [#permalink]

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06 Jun 2017, 10:02
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45% (medium)

Question Stats:

77% (02:12) correct 23% (01:58) wrong based on 97 sessions

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A list of five integers has the following criteria:

I. The median of the list is 6
II. The mode of the list is 2
III. The mean of the list is 5

Which of the following must true?

A. The sum of the five integers is 30.
B. The sum of the five integers is 10.
C. The median of the three largest integers is 6.
D. The largest of the integers is 9.
E. The largest of the integers is 8.

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Joined: 07 Dec 2014
Posts: 1222
A list of five integers has the following criteria: I. The median of  [#permalink]

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06 Jun 2017, 13:07
1
Bunuel wrote:
A list of five integers has the following criteria:

I. The median of the list is 6
II. The mode of the list is 2
III. The mean of the list is 5

Which of the following must true?

A. The sum of the five integers is 30.
B. The sum of the five integers is 10.
C. The median of the three largest integers is 6.
D. The largest of the integers is 9.
E. The largest of the integers is 8.

let list=2,2,6,7,8
largest of integers must be 8
E
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Joined: 21 Mar 2016
Posts: 510
Re: A list of five integers has the following criteria: I. The median of  [#permalink]

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08 Jun 2017, 08:34
the list should be 2,2,6,x,y.
given mean = 5.. so total = 25
median = 6
x+y = 15..
x and y cud be 6,9 or 7,8
since given mode is 2,, then the possible set is 2,2,6,7,8
ans E
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Joined: 24 Sep 2018
Posts: 137
A list of five integers has the following criteria: I. The median of  [#permalink]

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25 Sep 2018, 23:09
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If 6 is the median of a series of 5 numbers, then it is the third number in the series.

__ __ 6 __ __

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If 2 is the mode, then 2 is the most frequent and thus the first two elements in the series.

2 2 6 __ __

Quote:
Since (average) x (quantity) = sum, then (5)(5) = 25 is the sum

Quote:
The first three elements total 10. Thus the final two elements must total 15 (25-10 = 15).

For 6 to me the median, it has to be the 3rd element in the list and hence, the next integer needs to be bigger than 6. Which n least case is 7.

Quote:
SO, The only two elements that total 15 and that satisfy the conditions are 7 and 8
.

Quote:
The most common mistake that one needs to avoid here is is to account for this scenario: For 6 to me the median, it has to be the 3rd element in the list and hence, the next integer needs to be bigger than 6. Which n least case is 7.

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A list of five integers has the following criteria: I. The median of   [#permalink] 25 Sep 2018, 23:09
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