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Unable to understand the solution, kindly explain

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Unable to understand the solution, kindly explain

by sabiha » Mon Jun 21, 2010 7:18 am
If it is true that -6 < equal to n < equal to 10, which of the following must be true?

A. n < 8

B. n = -6

C. n > -8

D. -10 < n < 7

E. none of the above


The correct choice is C i.e. n > -8.

I am unable to understand this coz if n > -8, then n = -7, -6...
It is not any where mentioned in the stem that n = -7 whereas n has all the values from -6 to 10.

Kindly explain.
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by sk818020 » Mon Jun 21, 2010 7:27 am
According to the parameters -6<n<10.

Any number in that particular set will be greater than any number less than -6. Thus, if in must be in this particular range, then n will always be greater than any number less than -6. You can conclude that C is the correct answer.

"It is not any where mentioned in the stem that n = -7 whereas n has all the values from -6 to 10."

The question stem specifically mentions that n is not equal to -7, but that doesn't change the fact that because n is greater than or equal to -6 and less than or equal to 10, it must also always be greater than -8 because n must exist in the given range.

Hope this helps.

Thanks,

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by Rich@VeritasPrep » Mon Jun 21, 2010 7:50 am
Nice explanation Jared.

To that I would add the following...

There's a difference between saying "n > -8 must be true" and "n > -8 is the range of all possible values of n". I think that's where the confusion is coming from.

We're not saying that all possible values of n > -8 fit the inequality given in the prompt. We're just saying that no matter what value of n we pick from -6<=n<=10, it will DEFINITELY be greater than -8.

Another example:

If we say that the value of x is positive, then it is definitely true that x > -10, because any positive number is bigger than a negative number. We're not saying that x can be ANY value greater than -10; we're just saying it is definitely greater than -10.

Hopefully that makes sense!
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by sabiha » Mon Jun 21, 2010 8:24 am
Thanks for explaining the difference.

I have another question.

This one was with a diagram, where A,B,C,D,E are 5 points on the number line for -2,-1,0,1, 2 respectively. The question asks which of these points has highest absolute value?
The answer is A (-2)

But my question here is that isn't it that both -2 and 2 have the same absolute values? How can we distinguish between the absolute values of a positive and negative of the same no.?

Thanks in advance
raz1024 wrote:Nice explanation Jared.

To that I would add the following...

There's a difference between saying "n > -8 must be true" and "n > -8 is the range of all possible values of n". I think that's where the confusion is coming from.

We're not saying that all possible values of n > -8 fit the inequality given in the prompt. We're just saying that no matter what value of n we pick from -6<=n<=10, it will DEFINITELY be greater than -8.

Another example:

If we say that the value of x is positive, then it is definitely true that x > -10, because any positive number is bigger than a negative number. We're not saying that x can be ANY value greater than -10; we're just saying it is definitely greater than -10.

Hopefully that makes sense!
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by amising6 » Mon Jun 21, 2010 9:43 am
sabiha wrote:Thanks for explaining the difference.

I have another question.

This one was with a diagram, where A,B,C,D,E are 5 points on the number line for -2,-1,0,1, 2 respectively. The question asks which of these points has highest absolute value?
The answer is A (-2)

But my question here is that isn't it that both -2 and 2 have the same absolute values? How can we distinguish between the absolute values of a positive and negative of the same no.?

Thanks in advance
raz1024 wrote:Nice explanation Jared.



To that I would add the following...

There's a difference between saying "n > -8 must be true" and "n > -8 is the range of all possible values of n". I think that's where the confusion is coming from.

We're not saying that all possible values of n > -8 fit the inequality given in the prompt. We're just saying that no matter what value of n we pick from -6<=n<=10, it will DEFINITELY be greater than -8.

Another example:

If we say that the value of x is positive, then it is definitely true that x > -10, because any positive number is bigger than a negative number. We're not saying that x can be ANY value greater than -10; we're just saying it is definitely greater than -10.

Hopefully that makes sense!



ye you are right the absolut value will be 2
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by sabiha » Mon Jun 21, 2010 10:22 am
amising6 wrote:
sabiha wrote:Thanks for explaining the difference.

I have another question.

This one was with a diagram, where A,B,C,D,E are 5 points on the number line for -2,-1,0,1, 2 respectively. The question asks which of these points has highest absolute value?
The answer is A (-2)

But my question here is that isn't it that both -2 and 2 have the same absolute values? How can we distinguish between the absolute values of a positive and negative of the same no.?

Thanks in advance
raz1024 wrote:Nice explanation Jared.



To that I would add the following...

There's a difference between saying "n > -8 must be true" and "n > -8 is the range of all possible values of n". I think that's where the confusion is coming from.

We're not saying that all possible values of n > -8 fit the inequality given in the prompt. We're just saying that no matter what value of n we pick from -6<=n<=10, it will DEFINITELY be greater than -8.

Another example:

If we say that the value of x is positive, then it is definitely true that x > -10, because any positive number is bigger than a negative number. We're not saying that x can be ANY value greater than -10; we're just saying it is definitely greater than -10.

Hopefully that makes sense!



ye you are right the absolut value will be 2
yes that is right, but the question asked is which of the points has highest absolute value and the answer is -2.
I don't understand how can they distinguish between the absolute value of 2 and -2?
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by singhpreet1 » Tue Jun 22, 2010 9:48 am
sabiha wrote:If it is true that -6 < equal to n < equal to 10, which of the following must be true?

A. n < 8

B. n = -6

C. n > -8

D. -10 < n < 7

E. none of the above


The correct choice is C i.e. n > -8.

I am unable to understand this coz if n > -8, then n = -7, -6...
It is not any where mentioned in the stem that n = -7 whereas n has all the values from -6 to 10.

Kindly explain.
really sorry to reopen this discussion but i still dont understand why we cant choose B, which is the ideal option as per the information given: -6 < equal to n < equal to 10, we know for sure that n could be -6, for n > -8 it could be-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9 but there is no certainty of the value, though we know it does fulfill the condition as does answer choice B. i would really appreciate a expert opinion on this problem to clarify this to me.

thanks a ton.
Preet
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by Testluv » Tue Jun 22, 2010 2:54 pm
Hi preet,

if the question asked for what COULD be true, then you would be correct.

But the question asks for what MUST be true. It doesn't HAVE to be true that n = -6.

However, it must be true that any value within the range of -6 to 10 (inclusive) is larger than -8.
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by sabiha » Tue Jun 22, 2010 11:06 pm
Could you please also explain the question below:


This one was with a diagram, where A,B,C,D,E are 5 points on the number line for -2,-1,0,1, 2 respectively. The question asks which of these points has highest absolute value?
The answer is A (-2)

But my question here is that isn't it that both -2 and 2 have the same absolute values? How can we distinguish between the absolute values of a positive and negative of the same no.?

Testluv wrote:Hi preet,

if the question asked for what COULD be true, then you would be correct.

But the question asks for what MUST be true. It doesn't HAVE to be true that n = -6.

However, it must be true that any value within the range of -6 to 10 (inclusive) is larger than -8.
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by Testluv » Wed Jun 23, 2010 12:15 am
I know the question you are referring to. In some early printings of the OG, E is above "2". But in later printings it is before "2". (I mean printings not editions).

Rest easy. You've encountered a rare thing indeed: a typo in the OG.
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