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

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Bunuel
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A list of five integers has the following criteria: I. The median of [#permalink] New post   06 Jun 2017, 10:02
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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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E
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mohshu
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Re: A list of five integers has the following criteria: I. The median of [#permalink] New post   08 Jun 2017, 08:34
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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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A list of five integers has the following criteria: I. The median of [#permalink] New post   06 Jun 2017, 13:07
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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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A list of five integers has the following criteria: I. The median of [#permalink] New post   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 __ __


Quote:
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.

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

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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Re: A list of five integers has the following criteria: I. The median of [#permalink] New post   17 Oct 2020, 07:41
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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.

Solution:

Since the mean is 5 and there are 5 integers, the sum of the integers is 25. Therefore, we can see both A and B are false. Since the mode is 2 and the median is 6, we see that the five integers are 2, 2, 6, x, y where 6 < x < y. Since the sum of the integers is 25, the sum of x and y is 25 - (2 + 2 + 6) = 15. Therefore, x must be 7 and y must be 8 since 6 < x < y and x + y = 15. We see that the largest of the integers is 8.

Answer: E
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Re: A list of five integers has the following criteria: I. The median of [#permalink] New post   17 Oct 2020, 09:32
We have five integers. We are told the median of the list is 6:

_ _ 6 _ _

The mode of the list is 2. Since 6 is the median, this indicates that 2 appears twice:

2 2 6 _ _

The mean of the list is 5. This means the five numbers total up to 25:

2 2 6 7 8

The only way for the numbers to total 25 is to have one number as 7 and one number as 8. By going through the answer choices, only E fits the criteria. Answer is E.
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Re: A list of five integers has the following criteria: I. The median of [#permalink] New post   25 Apr 2022, 07:20
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Re: A list of five integers has the following criteria: I. The median of [#permalink]
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