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Princeton Test question - doubtful approach.

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Princeton Test question - doubtful approach.

by rac.nishu » Tue Jul 09, 2013 9:36 pm
If the average (arithmetic mean) of a group of numbers is 57, how many of the numbers are not equal to 57 ?

(1) None of the numbers is less than 57.

(2) None of the numbers is greater than 57.

The colored part of the Question says that "How many numbers"?
The Official answer is D

But how can we answer a question which asks how many numbers without any numerical data present! I suppose the answer should be E. The question only says " a group of numbers" and not any specific number.

Is my understanding correct? This question was in Princeton Test.
[/spoiler]
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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Jul 10, 2013 1:09 am
rac.nishu wrote:If the average (arithmetic mean) of a group of numbers is 57, how many of the numbers are not equal to 57 ?

(1) None of the numbers is less than 57.

(2) None of the numbers is greater than 57.

The colored part of the Question says that "How many numbers"?
The Official answer is D

But how can we answer a question which asks how many numbers without any numerical data present! I suppose the answer should be E. The question only says " a group of numbers" and not any specific number.

Is my understanding correct? This question was in Princeton Test.
[/spoiler]
Let n = the number of numbers.
Sum = (number of numbers)(average) = 57n.

Statement 1: None of the numbers is less than 57.
Let's say ALL of the numbers are EQUAL to 57:
...57, 57, 57, 57, 57, 57, 57....
If we increase one of the numbers so that it is GREATER THAN 57, then -- to maintain the sum of 57n -- at least one of the numbers must compensate by being LESS THAN 57.
To illustrate:
...56, 57, 57, 57, 57, 57, 58...
But here there are NO numbers less than 57, implying that there can be no numbers GREATER than 57.
Since there are no numbers LESS than 57, and no numbers GREATER than 57, ALL of the numbers must be EQUAL to 57.
Thus, the number of numbers NOT equal to 57 = 0.
SUFFICIENT.

Statement 2: None of the numbers is greater than 57.
We can apply the same line of reasoning applied in statement 1.
SUFFICIENT.

The correct answer is D.
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