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# If the average (arithmetic mean) of 16, 20, and n is between 18 and 21

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If the average (arithmetic mean) of 16, 20, and n is between 18 and 21  [#permalink]

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07 Aug 2018, 04:05
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88% (01:06) correct 12% (01:11) wrong based on 52 sessions

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If the average (arithmetic mean) of 16, 20, and n is between 18 and 21, inclusive, what is the greatest possible value of n ?

(A) 18

(B) 21

(C) 27

(D) 54

(E) 63

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Re: If the average (arithmetic mean) of 16, 20, and n is between 18 and 21  [#permalink]

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07 Aug 2018, 04:17
Bunuel wrote:
If the average (arithmetic mean) of 16, 20, and n is between 18 and 21, inclusive, what is the greatest possible value of n ?

(A) 18

(B) 21

(C) 27

(D) 54

(E) 63

what is the greatest possible value of n ?

Greatest possible value of n is possible when mean is 21

So 21*3 = 63

63-(16+20) = 27

Hence C

Another Approach,

By logic D & E are not possible bcoz mean = between 18 and 21

and if you take n= 18 it will be not greatest possible value of n
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If the average (arithmetic mean) of 16, 20, and n is between 18 and 21  [#permalink]

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07 Aug 2018, 04:35
Bunuel wrote:
If the average (arithmetic mean) of 16, 20, and n is between 18 and 21, inclusive, what is the greatest possible value of n ?

(A) 18

(B) 21

(C) 27

(D) 54

(E) 63

Note : we must take such a value of n for which the average must be in between 18 to 21, inclusive. It means 21 can be the average . We are looking fro greatest value of n. So, we must take 21 as average of this 3 numbers.

16 + 20 + n = 3*21

36 + n = 63

n = 27.

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Re: If the average (arithmetic mean) of 16, 20, and n is between 18 and 21  [#permalink]

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07 Aug 2018, 07:29
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(16 + 20 + n) / 3 = 21
36 + n = 21*3
n = 63 - 36
n =27

Hence, C.
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Re: If the average (arithmetic mean) of 16, 20, and n is between 18 and 21  [#permalink]

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07 Aug 2018, 07:35
Bunuel wrote:
If the average (arithmetic mean) of 16, 20, and n is between 18 and 21, inclusive, what is the greatest possible value of n ?

(A) 18

(B) 21

(C) 27

(D) 54

(E) 63

$$18 < \frac{16 + 20 + n}{3} < 21$$

Or, $$54 < 36 + n < 63$$

Or, $$18 < n < 27$$, Among the given options only (B) fits it, Hence Answer must be (B)
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Re: If the average (arithmetic mean) of 16, 20, and n is between 18 and 21   [#permalink] 07 Aug 2018, 07:35
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