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02 Mar 2022, 05:30
Kudos
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A
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Difficulty:
55%
(hard)
Question Stats:
61% (01:46) correct
39%
(01:43)
wrong
based on 250
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The average (arithmetic mean) of a set of numbers is 12. How many numbers are there in the set?
(1) Eliminating the number 8 from the set increases the average by 1.
(2) When adding the number 12, the average remains unchanged.
Are You Up For the Challenge: 700 Level Questions
(1) Eliminating the number 8 from the set increases the average by 1.
(2) When adding the number 12, the average remains unchanged.
Are You Up For the Challenge: 700 Level Questions
02 Mar 2022, 23:10
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Bunuel
Let, there are x numbers in the set and their sum is S
i.e \(\frac{S}{x} =12\) (Given)
i.e. S = 12x
Question: How many numbers are in the set? i.e. x = ?
STatement 1: Eliminating the number 8 from the set increases the average by 1.
i.e. \(\frac{S-8 }{ {(x-1)}} = 12+1 = 13\)
i.e. S-8 = 13x - 13
Substituting S = 12 x in the above equation we get
12x-8 = 13x - 13
i.e. x = 5
SUFFICIENT
Statement 2: When adding the number 12, the average remains unchanged.
Adding the average number in the set never changes teh average which is a universal truth hence this statements doesn't help us get a new relation between S and x to find the value of x hence
NOT SUFFICIENT
Answer: Option A
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04 Mar 2022, 13:36
Kudos
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As mean is 12, let us consider all the elements as 12 except the last 2.
Initial Set -
12 12 12 12 ......... n times
(1) Eliminating the number 8 from the set increases the average by 1.
Then original set can be written as 12 12 12 12 .........16 8 --> As mean is 12, hence considering all the elements as 12 except the last 2.
New set becomes 13 13 13 13 13 13 ...... (n-1) times
If we compare with original set minus 8.
then 12 12 12 12 ...... 16
Hence we can write 16 = (n-2)*1 +13
meaning = there are total (n-2) 12s.. to make each of them 13 we add +1 to each (n-2) 12s. This (n-2) is added to 13 to make the last value 16.
16 = (n-2)*1 +13 => n=5
Sufficient
(2) When adding the number 12, the average remains unchanged.
Meaning Original set - 12 12 12 12 12 ...... (n times) . Then new set becomes 12 12 12 12 ... (n times) 12
Of course the average wont change. so we cannot determine n here.
Insufficient
Answer A.
Initial Set -
12 12 12 12 ......... n times
(1) Eliminating the number 8 from the set increases the average by 1.
Then original set can be written as 12 12 12 12 .........16 8 --> As mean is 12, hence considering all the elements as 12 except the last 2.
New set becomes 13 13 13 13 13 13 ...... (n-1) times
If we compare with original set minus 8.
then 12 12 12 12 ...... 16
Hence we can write 16 = (n-2)*1 +13
meaning = there are total (n-2) 12s.. to make each of them 13 we add +1 to each (n-2) 12s. This (n-2) is added to 13 to make the last value 16.
16 = (n-2)*1 +13 => n=5
Sufficient
(2) When adding the number 12, the average remains unchanged.
Meaning Original set - 12 12 12 12 12 ...... (n times) . Then new set becomes 12 12 12 12 ... (n times) 12
Of course the average wont change. so we cannot determine n here.
Insufficient
Answer A.
