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PR1012 - Must Be True - Q12

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PR1012 - Must Be True - Q12 [#permalink] New post 27 Nov 2009, 14:39
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

100% (01:37) correct 0% (00:00) wrong based on 3 sessions
The follwing question seems fairly easy to me, but my answer differs from the OA. I believe the OA is wrong as the authors make an unstated assumption in the detailed solution. I would like to have your opinion.

The crew of the Voelkle Mountain Observatory traks the outdoor temperature for x days. If the temperature increases of exactly 1 degree per day, and the sum of all the temperatures is 0, then which of the following must be true?

I. x represents an even number of days.
II. x represents an odd number of days.
II. the average temperature for the x days is 0

(A) I only
(B) II only
(C) I and III
(D) II and III
(E) None of the above

OA
[Reveal] Spoiler:
D


My answer
[Reveal] Spoiler:
E. The solution makes the unstated assumption that the temperature on day 1 is an integer value. The only option that is certainly true is III, but this is not one of the answers.
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Re: PR1012 - Must Be True - Q12 [#permalink] New post 27 Nov 2009, 15:57
Expert's post
Let's deal with the easy statement first.

III. the average temperature for the x days is 0.

We are told that the sum of all temperatures for x days is 0. Average=Sum/x=0/x=0. Hence this statement is always true no matter temperatures are integers or not.

Now, if the temperatures per x days have integer values it means that we have consecutive integers and the number of terms is x. In consecutive integers average=median, and we know that the average=0=median, which means that integers are symmetric to 0. Hence x is odd. So II is always true, again if we assume that temperatures have integer values.

But if we are not told that temperatures have integer values, the above won't be always true. We could have the following temperatures:
-1.5, -0.5, 0.5, 1.5.

The sum is 0, but x=4, so II must not be always true.

I would say that if stem doesn't specify that temperatures have integer values answer should be E. As only III is always true and we don't have this option.
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Re: PR1012 - Must Be True - Q12 [#permalink] New post 28 Nov 2009, 06:35
As the temperature increases uniformly every day by 1 degree and the sum is zero, implies there are equal number of numbers on either side of the zero. So the total number is always odd.

As the sum is zero => mean is also zero (mean=sum/n, where n is the total number of elements).

Hence the answer D
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Re: PR1012 - Must Be True - Q12 [#permalink] New post 28 Nov 2009, 09:35
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jade3 wrote:
As the temperature increases uniformly every day by 1 degree and the sum is zero, implies there are equal number of numbers on either side of the zero. So the total number is always odd.

As the sum is zero => mean is also zero (mean=sum/n, where n is the total number of elements).

Hence the answer D


Check this example: -1.5; -0.5; 0.5; 1.5.

The sum is 0.
The temperature increases by 1 degree.

Number of days is EVEN.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: PR1012 - Must Be True - Q12 [#permalink] New post 28 Nov 2009, 14:00
What is the source? This is the problem with illegitimate sources. Unless you have an innate ability and a good grasp of the field of mathematics, sources only but confuse and aggravate moods. This question is seemingly bad and I am very sure such questions do not come up on the GMAT. There is no scope of pointing out any error with official GMAT questions.
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Re: PR1012 - Must Be True - Q12 [#permalink] New post 28 Nov 2009, 18:51
Bunuel wrote:
jade3 wrote:
As the temperature increases uniformly every day by 1 degree and the sum is zero, implies there are equal number of numbers on either side of the zero. So the total number is always odd.

As the sum is zero => mean is also zero (mean=sum/n, where n is the total number of elements).

Hence the answer D


Check this example: -1.5; -0.5; 0.5; 1.5.

The sum is 0.
The temperature increases by 1 degree.

Number of days is EVEN.


You are right. I wrongly assumed the temperatures to be integer values
Re: PR1012 - Must Be True - Q12   [#permalink] 28 Nov 2009, 18:51
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