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If the average of 10, 14, and n is greater than or equal to 8 and less

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If the average of 10, 14, and n is greater than or equal to 8 and less  [#permalink]

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New post 12 Jun 2017, 05:07
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If the average of 10, 14, and n is greater than or equal to 8 and less than or equal to 12, what is the least possible value of n ?

(A) –12
(B) –6
(C) 0
(D) 6
(E) 12

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Re: If the average of 10, 14, and n is greater than or equal to 8 and less  [#permalink]

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New post 12 Jun 2017, 05:26
SajjadAhmad wrote:
If the average of 10, 14, and n is greater than or equal to 8 and less than or equal to 12, what is the least possible value of n ?

(A) –12
(B) –6
(C) 0
(D) 6
(E) 12

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Average of \(10, 14\), and \(n\) is greater than or equal to \(8\).

\(\frac{10+14+n}{3}\) \(\geq\)\(8\)

\(24+n\) \(\geq\) \(8*3\)
\(24+n\) \(\geq\) \(24\)

Least value would be \(24+n = 24\). Therefore least value of \(n\) would be \(0\). Answer C.
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Re: If the average of 10, 14, and n is greater than or equal to 8 and less  [#permalink]

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New post 12 Jun 2017, 09:29
12>=(24+n)>=8
=>12>=n>=0 hence least value = 0 ---(c)
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Re: If the average of 10, 14, and n is greater than or equal to 8 and less  [#permalink]

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New post 14 Jun 2017, 16:07
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SajjadAhmad wrote:
If the average of 10, 14, and n is greater than or equal to 8 and less than or equal to 12, what is the least possible value of n ?

(A) –12
(B) –6
(C) 0
(D) 6
(E) 12


We are given that the average of 10, 14, and n is greater than or equal to 8 and less than or equal to 12.

Thus:

8 ≤ (10 + 14 + n)/3 ≤ 10

24 ≤ 10 + 14 + n ≤ 30

24 ≤ 24 + n ≤ 30

0 ≤ n ≤ 6

The least possible value of n is zero.

Answer: C
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If the average of 10, 14, and n is greater than or equal to 8 and less  [#permalink]

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New post 24 Jun 2017, 07:47
Bunuel wrote:
If the average of 10, 14, and n is greater than or equal to 8 and less than or equal to 12, what is the least possible value of n ?

(A) –12
(B) –6
(C) 0
(D) 6
(E) 12


Avg is (24+n)/3 which ranges between 8 & 12 inclusive
\(8<=(24+n)/3<=12\)
\(24<=24+n<=36\)
\(0<=n<=12\)

Minimum value of n is 0 hence C
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Re: If the average of 10, 14, and n is greater than or equal to 8 and less  [#permalink]

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New post 01 Jul 2017, 03:47
If the average of 10, 14, and n is greater than or equal to 8 and less than or equal to 12, what is the least possible value of n ?

\(Average = \frac{Sum}{Count}\)

\(8 <= \frac{24 + n}{3} <= 12\)


\(24 <= 24 + n <= 36\)


\(0 <= n <= 12\)


Hence, as per above inequality, least value of \(n = 0\)


Hence, Answer is C
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Re: If the average of 10, 14, and n is greater than or equal to 8 and less  [#permalink]

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New post 01 Jul 2017, 08:13
Bunuel wrote:
If the average of 10, 14, and n is greater than or equal to 8 and less than or equal to 12, what is the least possible value of n ?

(A) –12
(B) –6
(C) 0
(D) 6
(E) 12

Average of \(\frac{10 + 14 + n}{3} = 8\)

So, \(10 + 14 + n = 24\)

Or, \(n = 0\)

Checking again -

\(\frac{10 + 14 + n}{3} = 12\)

Or, \(n = 12\)

Thus, we find that the answer must be (C) 0

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Re: If the average of 10, 14, and n is greater than or equal to 8 and less   [#permalink] 01 Jul 2017, 08:13
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