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04 Jan 2018, 23:58
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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.
(1) The median of the integers is 82.
(2) The range of the integers is 54.
05 Jan 2018, 00:30
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Bunuel
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)
No information about "b" (Insufficient)
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)
07 Oct 2022, 09:24
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Given that If the average (arithmetic mean) of three integers is 76 and we need to find what is the value of the least of the integers?
============================================================
Theory
============================================================
=> There are three people = Median = Middle term
STAT 1: The median of the integers is 82.
=> Middle value = 82
=> Sum of other two values + 82 = 76*3 = 228
=> Sum of other two ages = 228 - 82 = 146
=> Lowest + Highest = 146
But we don't know exactly what is the value of the largest term. So, we cannot find the value of the least of the integers.
=> NOT SUFFICIECT
STAT 2: The range of the integers is 54.
=> Range = Highest - Lowest = 54
=> Lowest = Highest - 54
But we don't know exactly what is the value of the largest term. So, we cannot find the value of the least of the integers.
=> NOT SUFFICIECT
Taking BOTH of them we get
Highest + Lowest = 146
Highest - Lowest = 54
Subtracting both of them we get
Highest + Lowest - Highest + Lowest = 146 - 54
=> Lowest = \(\frac{92}{2}\) = 46
=> SUFFICIENT
So, Answer will be C.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
============================================================
Theory
- ‣‣‣ Mean or Average = (Sum Of All The Numbers) / (Total Number Of Numbers)
‣‣‣ In case of odd number of values: Median is the middle value of the set
‣‣‣ Range of a set is the difference between the highest and lowest value of the set.
============================================================
=> There are three people = Median = Middle term
STAT 1: The median of the integers is 82.
=> Middle value = 82
=> Sum of other two values + 82 = 76*3 = 228
=> Sum of other two ages = 228 - 82 = 146
=> Lowest + Highest = 146
But we don't know exactly what is the value of the largest term. So, we cannot find the value of the least of the integers.
=> NOT SUFFICIECT
STAT 2: The range of the integers is 54.
=> Range = Highest - Lowest = 54
=> Lowest = Highest - 54
But we don't know exactly what is the value of the largest term. So, we cannot find the value of the least of the integers.
=> NOT SUFFICIECT
Taking BOTH of them we get
Highest + Lowest = 146
Highest - Lowest = 54
Subtracting both of them we get
Highest + Lowest - Highest + Lowest = 146 - 54
=> Lowest = \(\frac{92}{2}\) = 46
=> SUFFICIENT
So, Answer will be C.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
