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Please help explain

by tinyturtle » Sat Aug 03, 2013 1:14 am
"A list kept at Town Hall contains that town's average daily temperature in Fahren­
heit, rounded to the nearest integer, for each day of a particular completed month.
Does this month have 30 or 31 days?
(1) The median temperature is 73.5.
(2) The sum of the average daily temperatures is divisible by 3."

Source: Manhattan Guide 3 - Word problem

(1) I determine that there is an even number on the list. The list can have 28 (February) or 30 elements. So, (1) is insufficient.

Please help explain why (1) is sufficient!
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Source: — Data Sufficiency |
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by melguy » Sat Aug 03, 2013 5:13 am
The question is asking you does this month have 30 or 31 days and does not mentions to 28 days. So we need to focus only on the things within the scope.

Also, if you take mean of odd number of integers its an integer

2+3+4 / 3 = 3

if you take mean of even number of integers its not an integer

2+3+4+5 / 4 = 3.5

Hope that helps.
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by Brent@GMATPrepNow » Sat Aug 03, 2013 6:13 am
tinyturtle wrote:"A list kept at Town Hall contains that town's average daily temperature in Fahren­heit, rounded to the nearest integer, for each day of a particular completed month.
Does this month have 30 or 31 days?
(1) The median temperature is 73.5.
(2) The sum of the average daily temperatures is divisible by 3"
Target question: Does this month have 30 or 31 days?

IMPORTANT: Notice that the question does not ask "How many days are in this month?" If that were the case, then we'd have to consider February. Instead, the question is ruling out February by basically telling us that the month in question has EITHER 30 days OR 31 days. So, we need not consider February as a possibility.

Statement 1: The median temperature is 73.5
Since all of the temperatures in question were ROUNDED TO THE NEAREST INTEGER, the median will be a non-integer ONLY IF there is an even number of temperatures to consider.
In other words, the month must have an even number of days.
So, the month must have 30 days
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of the average daily temperatures is divisible by 3
Consider these two conflicting cases that both meet this condition:
Case a: the month has 30 days, and the temperature is 3 degrees everyday. This will result in the sum of the average daily temperatures being divisible by 3
Case b: the month has 31 days, and the temperature is 3 degrees everyday. This will result in the sum of the average daily temperatures being divisible by 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Sun Aug 04, 2013 6:27 am, edited 1 time in total.
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by Uva@90 » Sun Aug 04, 2013 6:20 am
tinyturtle wrote:"A list kept at Town Hall contains that town's average daily temperature in Fahren­
heit, rounded to the nearest integer, for each day of a particular completed month.
Does this month have 30 or 31 days?
(1) The median temperature is 73.5.
(2) The sum of the average daily temperatures is divisible by 3."

Source: Manhattan Guide 3 - Word problem

(1) I determine that there is an even number on the list. The list can have 28 (February) or 30 elements. So, (1) is insufficient.

Please help explain why (1) is sufficient!
TinyTurtle
Question ask "Does this month have 30 or 31 days?" So, List can't have 28(Feb). It can only have 30 days. So, Statement 1 is sufficient.
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