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# A list of positive numbers 'L' has all integer values. What is the

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A list of positive numbers 'L' has all integer values. What is the  [#permalink]

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15 Jan 2019, 22:04
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A list of positive numbers 'L' has all integer values. What is the arithmetic mean of the numbers in this list?

(1) Least number in L is 12 and highest number in L is 15.

(2) There are four distinct values in L.
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15 Jan 2019, 22:18
From statement 1:

Least number in L is 12 and highest number is 15.
But, we don't the frequency of these and also we don't know how many numbers are there.
Hence 1 is Insufficient.

From statement 2:

Statement 2 is insufficient as it only mentions the number of numbers in set L.
Hence 2 is Insufficient.

Combining both:
The only possible set is 12, 13, 14, 15.
Hence sufficient.

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Updated on: 17 Jan 2019, 01:22
amanvermagmat wrote:
A list of positive numbers 'L' has all integer values. What is the arithmetic mean of the numbers in this list?

(1) Least number in L is 12 and highest number in L is 15.

(2) There are four distinct values in L.

#1:
values in L can be repetitive or not
so in sufficient
#2:
it can be any integer value ; in sufficient

from 1 & 2
L = 12,13,14,15 or
L = 12,12,13,14,15
both sets of L have different mean/avg.
IMO E

Originally posted by Archit3110 on 16 Jan 2019, 01:53.
Last edited by Archit3110 on 17 Jan 2019, 01:22, edited 1 time in total.
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Re: A list of positive numbers 'L' has all integer values. What is the  [#permalink]

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16 Jan 2019, 02:53
doubt cant the numbers be 12,12,12,15 or 12,12,13,15 as its not mentioned that numbers are identical
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Re: A list of positive numbers 'L' has all integer values. What is the  [#permalink]

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16 Jan 2019, 02:55
sameeruce08 wrote:
doubt cant the numbers be 12,12,12,15 or 12,12,13,15 as its not mentioned that numbers are identical

Hey sameeruce08, as mentioned in statement 2, numbers are distinct. Hence it can't repeat.
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Re: A list of positive numbers 'L' has all integer values. What is the  [#permalink]

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16 Jan 2019, 22:26
amanvermagmat wrote:
A list of positive numbers 'L' has all integer values. What is the arithmetic mean of the numbers in this list?

(1) Least number in L is 12 and highest number in L is 15.

(2) There are four distinct values in L.

Individually neither of the two statements is sufficient. When we combine, we know that smallest number is 12, largest number is 15, AND there are four distinct values. So the list could be either:
12, 13, 14, 15 Or 12, 12, 13, 14, 15 Or 12, 13, 14, 14, 14, 15 etc.
All the above examples are of lists where there are 'four distinct values only', and they satisfy the first statement also. But the arithmetic mean is different.

So even after combining, the statements are not sufficient. Hence E.
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Re: A list of positive numbers 'L' has all integer values. What is the  [#permalink]

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16 Jan 2019, 22:36
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amanvermagmat wrote:
A list of positive numbers 'L' has all integer values. What is the arithmetic mean of the numbers in this list?

(1) Least number in L is 12 and highest number in L is 15.

(2) There are four distinct values in L.

Statement A
Number of terms are not given.

Statement B
4 distinct values are present, still number of terms are not given.

On combining
We just get to know about the Range and a condition of the series

The other integers can be same.
12 12 12 13 14 15
12 12 13 14 15

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Re: A list of positive numbers 'L' has all integer values. What is the  [#permalink]

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17 Jan 2019, 00:31
amanvermagmat wrote:
amanvermagmat wrote:
A list of positive numbers 'L' has all integer values. What is the arithmetic mean of the numbers in this list?

(1) Least number in L is 12 and highest number in L is 15.

(2) There are four distinct values in L.

Individually neither of the two statements is sufficient. When we combine, we know that smallest number is 12, largest number is 15, AND there are four distinct values. So the list could be either:
12, 13, 14, 15 Or 12, 12, 13, 14, 15 Or 12, 13, 14, 14, 14, 15 etc.
All the above examples are of lists where there are 'four distinct values only', and they satisfy the first statement also. But the arithmetic mean is different.

So even after combining, the statements are not sufficient. Hence E.

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Re: A list of positive numbers 'L' has all integer values. What is the   [#permalink] 17 Jan 2019, 00:31
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