If it is true that –6 <= n <=10, which of the following must be true?

Hi, so I got this question on my practice tests. I read it as n could also be -7, which would be false. What am I missing?

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The question tells us that x is GREATER THAN or equal to -6
-7 is LESS than -6

Cheers,
Brent

\(–6 <= n <=10\)

Value of \(n\) can range from \(-6\) to \(10\).

Among the answer choices.

C. \(n > –8\) --> \(n\) must be greater than \(-8\).

Answer C

GMATPrepNow This question is confusing. If we say C (n > -8) is the OA, but -7 is greater than -8 so it wouldn't satisfy -6<=n<=10. What did I miss? Thanks.

Let's examine a similar question.

To gain admission to the Richy Rich Club, one's net worth must be greater than 1 billion dollars.
If Joe is a member of the Richy Rich Club, which of the following statements MUST BE TRUE about Joe's net worth?

A) Joe's net worth is greater than 10 billion dollars.
B) Joe's net worth is less than 10 billion dollars.
C) Joe's net worth greater than 52 dollars.
.
.
.
The correct answer is C. If Joe's net worth is greater than 1 billion dollars, he MUST have more than $52.

Does this mean that Joe could have $55?
No.
If Joe is in the Richy Rich Club, his net worth must be greater than 1 billion dollars.


ASIDE: You are reversing the direction of the IF-THEN statement.
TRUE STATEMENT: IF Joe's net worth is greater than 1 billion dollars, THEN he must have more than $52.

You are reversing the statement to get: IF Joe has more than $52, THEN he must have more than 1 billion dollars (not a true statement)


Does that help?

Cheers,
Brent

If -6 ≤ v ≤ 10, 'n' needs to satisfy both conditions.

A. n < 8 - Not necessarily 'n' will be greater than -6
B. n = –6 - Not necessarily
C. n > –8 - Yes satisfy both conditions
D. -10 < n < 7 - Not necessarily 'n' will be greater than -6
E. none of the above


Answer C

Given

• –6 <= n <=10

To Find

• The option that is always true.

Approach and Working Out

• n < 8

o n can be 9 as well so not always true.


• n = –6

o n can be 0, 1, 2 many other values.

• n > –8

o The least value of n can be – 6 and hence it is always more than – 8.
o Always true

• - 10 < n < 7

o n can be 8, 9 as well. So not always true.

• None of the above

Correct Answer: Option C

Bunuel sir

in option c n can be -7

but n lies between -6<n<10

can you pls explain

It's the other way around. n cannot be -7 because we are given as a fact that –6 <= n <=10. So, if –6 <= n <=10, then n, whatever it is -6, ..., -5,5, ..., 0, ..., 1, ..., \(\pi\), ..., 7.7, ..10, will for sure be more than -8 or say more than -100, or say more than -6.1, ....

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.

Hope it helps.

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