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# A set of thirteen numbers has an average (arithmetic mean) equal to 3.

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Math Expert
Joined: 02 Sep 2009
Posts: 59674
A set of thirteen numbers has an average (arithmetic mean) equal to 3.  [#permalink]

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19 Sep 2019, 21:51
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Difficulty:

45% (medium)

Question Stats:

69% (02:29) correct 31% (01:54) wrong based on 48 sessions

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A set of thirteen numbers has an average (arithmetic mean) equal to 3. If two numbers are removed from the set and replaced with the number 7, the new average of the set is equal to 4. What could be the two numbers which were removed from the set?

A. 1.5 and -0.5
B. -1.5 and 0.5
C. 0 and 1.0
D. -1.0 and 0
E. -1.5 and -0.5

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Re: A set of thirteen numbers has an average (arithmetic mean) equal to 3.  [#permalink]

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19 Sep 2019, 22:06
x1+x2.....+x13=39, now remove any two numbers and add 7 to the series , I will remove x1,x2 and replace it with 7 , so now there are 12 numbers, avg=4 given ,so x3+x4....+x13=48-7=41,sub in first eq x1+x2+41=39,x1+x2=-2 , so answer is e

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Re: A set of thirteen numbers has an average (arithmetic mean) equal to 3.  [#permalink]

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19 Sep 2019, 22:15
1
Average of 13 numbers is 3.
Thus, sum of all 13 numbers is 13×3 = 39

After, Removal of 2 numbers and replacing them with 7, the average of (new 12 numbers) is 4.

Sum of all 12 numbers is 12×4=48

Sum of 11 numbers = 48-7 = 41

Hence, Remaining 2 numbers should sum upto 39-41= -2

The only option that satisfies the above condition is E.

Hence, E.

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Re: A set of thirteen numbers has an average (arithmetic mean) equal to 3.  [#permalink]

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19 Sep 2019, 22:34
(X1+x2+.....+x13)/13 = 3

(X1+x2+.....+x13)=39
(X1+x2+.....+x13 -x1-x2 +7)=39-x1-x2 +7
= 46-x1-x2

After performing the removal of two num and addition of 7 the avg is 4

(x3+x4+......+x13+7)/12 = 4
(x3+x4+......+x13+7)=48
So
48= 46-x1-x2
x1+x2= -2

So E

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A set of thirteen numbers has an average (arithmetic mean) equal to 3.  [#permalink]

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21 Nov 2019, 02:15
1
Question is poorly worded imho, it would be much clearer to mention that only one seven is added

"If two numbers are removed from the set and replaced with the number 7"

At the first run through it sounded to me as if two 7's were added, which would lead to two possible solutions.
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Re: A set of thirteen numbers has an average (arithmetic mean) equal to 3.  [#permalink]

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24 Nov 2019, 19:06
Bunuel wrote:
A set of thirteen numbers has an average (arithmetic mean) equal to 3. If two numbers are removed from the set and replaced with the number 7, the new average of the set is equal to 4. What could be the two numbers which were removed from the set?

A. 1.5 and -0.5
B. -1.5 and 0.5
C. 0 and 1.0
D. -1.0 and 0
E. -1.5 and -0.5

The sum of the 13 numbers is 13 x 3 = 39. When two numbers are removed and replaced with a single 7, we have:

(39 - x - y + 7)/12 = 4

46 - x - y = 48

-2 = x + y

Since -1.5 + (-0.5) = -2, answer E is correct.

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Re: A set of thirteen numbers has an average (arithmetic mean) equal to 3.   [#permalink] 24 Nov 2019, 19:06
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