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If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

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If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75.
(2) None of the six numbers is greater than 75.

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Re: Average of 6 numbers  [#permalink]

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If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

Given: sum of six numbers = 6*75

(1) None of the six numbers is less than 75 --> all 6 numbers must be 75, because if even one of them is more than 75 then the sum will be more than 6*75. Sufficient.

(2) None of the six numbers is greater than 75 --> the same here: all 6 numbers must be 75, because if even one of them is less than 75 then the sum will be less then than 6*75. Sufficient.

Answer: D.
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Re: Average of 6 numbers  [#permalink]

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GMATD11 wrote:
104) If the average of six numbers is 75, how many of the numbers are equal to 75?

a) None of the six numbers is less than 75
b) None of the six numbers is greater than 75

a)none is less than 75 so all numbers are 75 as averagege is 75
b) Noe is greater than 75 so all numbers are 75 as average is 75. If any number become less than 75 then average will not 75 it will less than 75.
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Re: If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

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sum of all numbers is 6*75 = 450

a1+a2+a3+a4+a5+a6 = 450

1) none is less than 75 , if any one will go more than 75 then other have to go less than 75 which is not possible, hence all must be 75, so A or D
2) none is more than 75, again if anyone is less than 75 then other have to more than 75 which is again not possible. so again all are 75 so D
Note this is because 75*6=450
D is the answer
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Re: If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

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If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75?

$$Sum = 75 * 6$$

(1) None of the six numbers is less than 75.

If none of the six numbers is less than 75, then we can have only one possibility that all the 6 numbers are 75

Hence, (1) ===== is SUFFICIENT

(2) None of the six numbers is greater than 75.

If none of the six numbers is greater than 75, then we can have only one possibility that all the 6 numbers are 75

Hence, (2) ===== is SUFFICIENT

Hence, Answer is D
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Re: If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

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GMATD11 wrote:
If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75.
(2) None of the six numbers is greater than 75.

I actually found this to be a bit harder than a 500 level question but anyways 1 must be true on the same basis as 2 and vice versa. Logically, one of the numbers must be greater than 75 if any of the numbers are less than 75. If none of the six numbers are greater than 75 then all six numbers must be 75. The same holds true if none of the numbers are less than 75.

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Re: If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

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GMATD11 wrote:
If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75.
(2) None of the six numbers is greater than 75.

We are given that the average of 6 numbers in a list is 75. Using this information we see that the sum of the 6 numbers is 6 x 75 = 450. We need to determine how many numbers in the list are equal to 75.

Statement One Alone:

None of the six numbers is less than 75.

Recall that the sum of the 6 numbers is 6 x 75 = 450.

Using the information in statement one we know that all the numbers in the list must be greater than or equal to 75.

However, if any of the numbers in our list are greater than 75, we would need another number to be less than 75 in order for the 6 numbers to sum to 450.

For example, let’s say we had the following 6 numbers:

75, 75, 75, 75, 75, 76

The sum of these numbers is 451, which is greater than the required sum of 450.

The only way to get our list to sum to 450 is if one of the 75s were reduced to 74. However, this is not possible, according to the information provided in statement one. Thus, all the numbers in the list must equal 75. Statement one is sufficient to answer the question.

Statement Two Alone:

None of the six numbers is greater than 75.

We can apply similar logic to the information provided in statement two as we did with the information in statement one.

Once again, we know that the sum of the 6 numbers is 6 x 75 = 450.

Using the information in statement two we know that all the numbers in the list must be less than or equal to 75.

Thus, if any of the numbers in our list are less than 75, we would need another number to be greater than 75 in order for the 6 numbers to sum to 450.

For instance, let’s say we had the following 6 numbers:

75, 75, 75, 75, 75, 74

The sum of these numbers is 449, which is less than the required sum of 450.

The only way to get our list to sum to 450 is if one of the 75s were increased to 76. However, this is not possible, according to the information provided in statement two. Thus, all the numbers in the list must equal 75. Statement two is sufficient to answer the question.

Answer: D
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If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

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GMATD11 wrote:
If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75.
(2) None of the six numbers is greater than 75.

Target question: How many of the numbers are equal to 75 ?

Given: The average (arithmetic mean) of six numbers is 75

Statement 1: None of the six numbers is less than 75
One possible scenario is that the 6 number are {75, 75, 75, 75, 75, 75}. This satisfies the conditions that none of the six numbers is less than 75, AND the average is 75
Notice that if we increase ANY of the 6 values, the resulting average will be greater than 75
So, it must be the case that the 6 number are {75, 75, 75, 75, 75, 75}.
The answer to the target question is all 6 numbers are equal to 75
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: None of the six numbers is greater than 75.
One possible scenario is that the 6 number are {75, 75, 75, 75, 75, 75}. This satisfies the conditions that none of the six numbers is greater than 75, AND the average is 75
Notice that if we decrease ANY of the 6 values, the resulting average will be less than 75
So, it must be the case that the 6 number are {75, 75, 75, 75, 75, 75}.
The answer to the target question is all 6 numbers are equal to 75
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

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