pappueshwar wrote:If it is true that -6 =< n =<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

OA IS E why is C incorrect?

Hi pappueshwar!

I'll take both of your questions in turn, but can you also provide the ORIGINAL source. Remember that we only want to study from material that is known to be high quality!

pappueshwar wrote:A)
The list of possible values of N are -6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10. so obviously all these values are greater than -8 right?
should we consider -7 ? but -7 is not a part of the list. so obviously C is correct. let m e know

Your understanding of this problem is perfect as it is written so again I would be VERY suspect of the source.

Choice (A) is not good because n could be 9, 10, or any non-integer between 8 and 10.
Choice (B) is not good because we have no clue that n is that 1 specific value in the list
Choice (D) is not good because n could be 8, 9, 10, or any non-integer between 7 and 10.

Now Choice (C). You are exactly right that n will always be greater than -8 because the entire range is greater han -8.

In fact, the rule for generalizing ranges is that we can always claim a wider range than we are given. For example, if we know that x is between 2 and 3, then I can claim it is between 1-->3, or 1-->4, or -100-->100.

We CANNOT go smaller: if we know that x is between 5 and 10, we cannot claim it is between 6-->9 or 5-->6, or specify a single number.

So, as the problem is written, (C) is the correct answer - I would check the wording to make sure you didn't type it incorrectly, and if not, I would NOT study from this source unless they have published an errata update for this question.

pappueshwar wrote:B) in the wordings that i have written :

The list of possible values of N are= is this sentence correct?
or
should the sentence be "The list of possible values of N is"..... "list" is singular and "values" is plural.

Your second choice (singular) is the correct one. "of possible values of N" is just the prepositional phrase describing "list". Therefore the subject is just "list".

The list...IS n=___, ___, ___, ___, and ___.

Hope this helps!

Whit