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24 Jan 2022, 02:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:37) correct
36%
(01:23)
wrong
based on 105
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What is the average (arithmetic mean) of n consecutive even integers?
(1) The range of the given integers is 20
(2) When the given integers are arranged in the order of increasing magnitude, the average (arithmetic mean) of the first 3 terms is 12
(1) The range of the given integers is 20
(2) When the given integers are arranged in the order of increasing magnitude, the average (arithmetic mean) of the first 3 terms is 12
24 Jan 2022, 03:08
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(1) Only
n=11. Average can be numerous different values.
Not sufficient.
(2) Only
The first three integers are 2, 4, 6
But we do not know n
Not sufficient.
(1) and (2) together
The 11 numbers are 2, 4, 6, ..., 22.
Sufficient.
Answer is (C).
n=11. Average can be numerous different values.
Not sufficient.
(2) Only
The first three integers are 2, 4, 6
But we do not know n
Not sufficient.
(1) and (2) together
The 11 numbers are 2, 4, 6, ..., 22.
Sufficient.
Answer is (C).
07 Oct 2022, 10:22
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We need to find What is the average (arithmetic mean) of n consecutive even integers?
============================================================
Theory
============================================================
=> To find the average we need to find both the sum of values and the total number of values as we are given the total number as n
STAT 1: The range of the given integers is 20.
=> Range = Highest value - Lowest Value = 20 (given)
And we know that we have n consecutive even numbers
=> Highest value = Lowest Value + (n-1)*2 (Example if we have two consecutive even numbers, then highest value = lowest + 2 = Lowest + (2-1)*2)
=> Highest - Lowest value = (n-1)*2
=> (n-1)*2 = 20
=> n = 11
But we don't any of these 11 numbers to find their sum
=> NOT SUFFICIECT
STAT 2: When the given integers are arranged in the order of increasing magnitude, the average (arithmetic mean) of the first 3 terms is 12
Average of first three terms = middle term = second term = 12
=> First term is 12-2 = 10 and we can find all remaining terms
But, we don't know how many such terms are there
=> NOT SUFFICIECT
Combining, both of them we know both the number of terms and the actual terms.
=> We can find the Average of these n consecutive even integers.
=> SUFFICIENT
So, Answer will be C.
Hope it helps!
Watch the following video to learn How to Sequence problems
============================================================
Theory
- ‣‣‣ Mean or Average = (Sum Of All The Numbers) / (Total Number Of Numbers)
‣‣‣ In case of consecutive terms mean = median = middle term = mean of first and last term.
‣‣‣ Range = Highest value - Lowest Value
============================================================
=> To find the average we need to find both the sum of values and the total number of values as we are given the total number as n
STAT 1: The range of the given integers is 20.
=> Range = Highest value - Lowest Value = 20 (given)
And we know that we have n consecutive even numbers
=> Highest value = Lowest Value + (n-1)*2 (Example if we have two consecutive even numbers, then highest value = lowest + 2 = Lowest + (2-1)*2)
=> Highest - Lowest value = (n-1)*2
=> (n-1)*2 = 20
=> n = 11
But we don't any of these 11 numbers to find their sum
=> NOT SUFFICIECT
STAT 2: When the given integers are arranged in the order of increasing magnitude, the average (arithmetic mean) of the first 3 terms is 12
Average of first three terms = middle term = second term = 12
=> First term is 12-2 = 10 and we can find all remaining terms
But, we don't know how many such terms are there
=> NOT SUFFICIECT
Combining, both of them we know both the number of terms and the actual terms.
=> We can find the Average of these n consecutive even integers.
=> SUFFICIENT
So, Answer will be C.
Hope it helps!
Watch the following video to learn How to Sequence problems
