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# If the average (arithmetic mean) of three integers is 76, what is the

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If the average (arithmetic mean) of three integers is 76, what is the  [#permalink]

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04 Jan 2018, 23:58
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35% (medium)

Question Stats:

85% (01:41) correct 15% (00:51) wrong based on 34 sessions

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If the average (arithmetic mean) of three integers is 76, what is the value of the least of the integers?

(1) The median of the integers is 82.
(2) The range of the integers is 54.

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If the average (arithmetic mean) of three integers is 76, what is the  [#permalink]

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05 Jan 2018, 00:30
Bunuel wrote:
If the average (arithmetic mean) of three integers is 76, what is the value of the least of the integers?

(1) The median of the integers is 82.
(2) The range of the integers is 54.

Say three integers are a, b, and c in order a < b < c

Given = a + b + c / 3 = 76

a + b+ c = 76 * 3

a + b+ c = 228 -----> (I)

From st 1: b = 82 ------> (II)

Use in (I) a + c = 228 - 82 = 146 (No info about a & c (Insufficient)

From st 2: c - a = 54 -------> (III)

Combining 1 & 2 we get

c + a = 146

c - a = 54

c = 100

Cancelling out "a" we get c = 100

Putting c = 100 in any of the three equations we get a = 46 Sufficient (C)
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If the average (arithmetic mean) of three integers is 76, what is the   [#permalink] 05 Jan 2018, 00:30
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