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Is the average age of a class of 60 students more than 30 years?  [#permalink]

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Is the average age of a class of 60 students more than 30 years?

(1) 59 students in the class are exactly 30 years of age each.
(2) The average age of 5 of the students in the class is less than 30 years.

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Is the average age of a class of 60 students more than 30 years?  [#permalink]

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Gnpth wrote:
Is the average age of a class of 60 students more than 30 years?

(1) 59 students in the class are exactly 30 years of age each.
(2) The average age of 5 of the students in the class is less than 30 years.

It should be C.

Statement 1- Suppose the 60th student is 30 or less, average age will not be greater than 30. However, if 60th student is greater than 90, average age will be 30+ which makes statement 1 insufficient.

Statement 2- Average age of 5 students is less than 30 but we do not know if average of remaining 55 is greater or more importantly average of 55 adjusted with these 5 students makes for an overall average age of more than 30.

1+ 2 - We know 59 are 30 and say we split them in 12 groups of 5. 11 groups will have students aged 30. 12th group will have 4 students aged 30 and if its average is less than 30, then the 5th student, or overall 60th student is less than 30. Hence group's age cannot be more than 30.
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Re: Is the average age of a class of 60 students more than 30 years?  [#permalink]

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For 1+2, an easier way to think it :
If the average of 5 students is less than 30, it cannot be 5 among the 59 who have 30 years old each (statement 1). So among the 5, there is the student number 60, who is necessary less than 30.

Finally, with this student less than 30, the mean will be less than 30.

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Re: Is the average age of a class of 60 students more than 30 years?  [#permalink]

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1
1. 59 students in the class are exactly 30 years of age each.
Knowing the average age of 59 students, will not clearly tell us the average age of the
60 students. We will need the age of the 60th student to compute the average
Hence, insufficient

2. The average age of 5 of the students in the class is less than 30 years.
If the average age of 5 students is less than 30, without the information
about the other students in the class, we cannot clearly tell anything about the overall average.
Hence insufficient.

If we combine the information given in both the statements,
Since we are given the ages of 59 students, which is 30 years and we know that the average
of 5 students is below 30 years, the age of the other student, must be less than 30.
Also, overall average will be lesser than 30 years. (Sufficient) (Option C)
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Re: Is the average age of a class of 60 students more than 30 years?  [#permalink]

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Gnpth wrote:
Is the average age of a class of 60 students more than 30 years?

(1) 59 students in the class are exactly 30 years of age each.
(2) The average age of 5 of the students in the class is less than 30 years.

Target question: Is the average age of a class of 60 students more than 30 years?

Statement 1: 59 students in the class are exactly 30 years of age each.
OBSERVE:
i) If the 60th person is also 30 years old, then the average age = 30
ii) If the 60th person is YOUNGER THAN 30 years old, then the average age = LESS THAN 30
iii) If the 60th person is OLDER THAN 30 years old, then the average age = GREATER THAN 30

Consider these two scenarios (that satisfy statement 1):
Case a: the ages are {30, 30, 30, 30, 30, 30, ......30, 31}, in which case the average age is greater than 30
Case b: the ages are {30, 30, 30, 30, 30, 30, ......30, 29}, in which case the average age is less than 30
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The average age of 5 of the students in the class is less than 30 years.
There are several values of x and y that satisfy statement 2. Here are two:
Consider these two scenarios (that satisfy statement 2):
Case a: {five people are 29 years old and the other fifteen people are 100 years old}, in which case the average age is greater than 30
Case b: five people are 25 years old and the other fifteen people are 26 years old}, in which case the average age is less than 30
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 59 people are exactly 30 years old
Statement 2 tells us that there is at least 1 person who is less than 30 years old.
So, we have case ii here, which means the average age is less than 30
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
_________________ Re: Is the average age of a class of 60 students more than 30 years?   [#permalink] 28 Aug 2018, 14:13
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