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# If the average (arithmetic mean) of five different integers is 1, whi

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Joined: 02 Sep 2009
Posts: 52295
If the average (arithmetic mean) of five different integers is 1, whi  [#permalink]

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06 Feb 2018, 21:51
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Difficulty:

35% (medium)

Question Stats:

73% (01:39) correct 27% (01:27) wrong based on 88 sessions

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If the average (arithmetic mean) of five different integers is 1, which of the following must be true?

I. 1 is one of the integers.
II. At least one of the integers is negative.
III. 0 is not one of the integers.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

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Re: If the average (arithmetic mean) of five different integers is 1, whi  [#permalink]

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06 Feb 2018, 22:18
Bunuel wrote:
If the average (arithmetic mean) of five different integers is 1, which of the following must be true?

I. 1 is one of the integers.
II. At least one of the integers is negative.
III. 0 is not one of the integers.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

We need one case each to disprove each of the statements.

I. 1 is one of the integers.
If the 5 integers are -3,-2,-1,5,6 the sum of the integers is 5. Therefore, average = 1
Also, 1 is not one of the integers.

II. At least one of the integers is negative.
Since the integers are all different, the minimum sum we will have if none of the
number is negative is 10(0+1+2+3+4) whose average is 2. So, we have to have a
negative integer.

III. 0 is not one of the integers.
Consider the 5 numbers to be -1,0,1,2,3.
Here the average of 1 and 0 is also part of the number

Therefore Option B(II only) will always be true.
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Re: If the average (arithmetic mean) of five different integers is 1, whi  [#permalink]

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09 Feb 2018, 10:01
Bunuel wrote:
If the average (arithmetic mean) of five different integers is 1, which of the following must be true?

I. 1 is one of the integers.
II. At least one of the integers is negative.
III. 0 is not one of the integers.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

Since the average of 5 integers is 1, the sum of all the integers must be 5.

Let’s analyzer each Roman numeral:

I. 1 is one of the integers.

This is not necessarily true.

The numbers could be, 2, 3, 5, -1, and -4.

II. At least one of the integers is negative.

Since we have all different integers, there is not way to get five numbers to sum to 5 unless (at least) one of the integers is negative.

This must be true.

III. 0 is not one of the integers.

This is not necessarily true.

The numbers could be 0, -3, 4, -2, and 6.

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Re: If the average (arithmetic mean) of five different integers is 1, whi &nbs [#permalink] 09 Feb 2018, 10:01
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