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inequality problem

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inequality problem

by akhilsaini2001 » Thu Jul 15, 2010 1:05 am
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


Analyze the Question:

In this question we are told that n is between -6 and 10 which limits our options for variables.

Identify the Task:

We need to attack each answer choice strategically looking for the answer choice that must be true and eliminating ones that may not be true.

Approach Strategically:

We should start with answer choice (D) and move up the choices to see if any must be true. If answers (A) through (D) are false or only could be true, we would choose answer choice(E). Choice (D) may be true, but if 7 ≤ n ≤ 10 then this statement is not true. Choice (C) must be true because all possible values of n specified by the inequality in the question stem are greater than -8, -8 < -6 ≤ n ≤ 10. We can stop here. Answer Choice (C) is correct.

Confirm your Answer:
Since the correct answer choice must be true, wrong answer choices are either false or could be true.

i DIDN'T GET THE EXPLANATION. I THINK CHOICE "B" IS CORRECT ANSWER. CAN SOMEONE PLZ HELP ME OUT.[/u]
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by Testluv » Thu Jul 15, 2010 1:17 am
The question is asking for something that must be true. So, the right answer is something that must be true.

Thus, the four wrong answers are things that could be false.

It could be true that n = -6 but it could also be false. (Because n could also be -5 or -4 or any other number in the range). So, choice B is wrong.

Choice C must be true. If n is somewhere between -6 and 10, then of course it is always going to be greater than -8. It also must be true that it is greater than -800. That it is less than 100, etc. (Look at it on the number line).
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by haidgmat » Thu Jul 15, 2010 7:00 am
Answer has to be B. See comments below next to each option
akhilsaini2001 wrote:If it is true that -6 ≤ n ≤ 10, which of the following must be true?

A n < 8:: n can be -7 hence may not be always true
B n = -6:: n is always -6 so it is always between -6 and 10 as the original states
C n > -8:: n may be -7 and so may not always be true
D -10 < n < 7:: n may be -9 to -7 and so may not always be true
E none of the above


Analyze the Question:

In this question we are told that n is between -6 and 10 which limits our options for variables.

Identify the Task:

We need to attack each answer choice strategically looking for the answer choice that must be true and eliminating ones that may not be true.

Approach Strategically:

We should start with answer choice (D) and move up the choices to see if any must be true. If answers (A) through (D) are false or only could be true, we would choose answer choice(E). Choice (D) may be true, but if 7 ≤ n ≤ 10 then this statement is not true. Choice (C) must be true because all possible values of n specified by the inequality in the question stem are greater than -8, -8 < -6 ≤ n ≤ 10. We can stop here. Answer Choice (C) is correct.

Confirm your Answer:
Since the correct answer choice must be true, wrong answer choices are either false or could be true.

i DIDN'T GET THE EXPLANATION. I THINK CHOICE "B" IS CORRECT ANSWER. CAN SOMEONE PLZ HELP ME OUT.[/u]
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by kmittal82 » Thu Jul 15, 2010 7:43 am
haidgmat wrote:Answer has to be B. See comments below next to each option
akhilsaini2001 wrote:If it is true that -6 ≤ n ≤ 10, which of the following must be true?

A n < 8:: n can be -7 hence may not be always true
B n = -6:: n is always -6 so it is always between -6 and 10 as the original states
C n > -8:: n may be -7 and so may not always be true
D -10 < n < 7:: n may be -9 to -7 and so may not always be true
E none of the above


Analyze the Question:

In this question we are told that n is between -6 and 10 which limits our options for variables.

Identify the Task:

We need to attack each answer choice strategically looking for the answer choice that must be true and eliminating ones that may not be true.

Approach Strategically:

We should start with answer choice (D) and move up the choices to see if any must be true. If answers (A) through (D) are false or only could be true, we would choose answer choice(E). Choice (D) may be true, but if 7 ≤ n ≤ 10 then this statement is not true. Choice (C) must be true because all possible values of n specified by the inequality in the question stem are greater than -8, -8 < -6 ≤ n ≤ 10. We can stop here. Answer Choice (C) is correct.

Confirm your Answer:
Since the correct answer choice must be true, wrong answer choices are either false or could be true.

i DIDN'T GET THE EXPLANATION. I THINK CHOICE "B" IS CORRECT ANSWER. CAN SOMEONE PLZ HELP ME OUT.[/u]
I think you've understood the question the wrong way.

It is given to us that -6 <= n <= 10, which means some possible values for n are -6, -5, -4 ..... 9, 10

One of your reasoning says:
(C) n > -8:: n may be -7 and so may not always be true

n cannot be -7, since n has to be between -6 and 10 (both inclusive) as given in the question. Any number between -6 and 10 has to be greater than -8, hence (C) is correct.
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by selango » Thu Jul 15, 2010 8:01 am
The trick here s all the values of n must satisfy the condition.

Since -6>=n<=10,n can be any value.n can be -6 or -5 or so.So we cannot say that n=-6 only.

But look at option C,all the values of n(ie from -6 to 10) satisfy the condition n>-8

Hope this clarify.
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by Testluv » Thu Jul 15, 2010 9:10 am
Answer has to be B. See comments below next to each option
No, the answer is C.

You are using the choices to verify the truth of the information in the question stem--this is the reverse of task. We have to treat the information in the question stem as true and use it to evaluate the truth of the choices.
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by this_time_i_will » Thu Jul 15, 2010 6:36 pm
what is wrong with D
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by barcebal » Thu Jul 15, 2010 8:50 pm
The problem with D is as follows:

If -6 <= n <= 10 is true then N COULD be 8 and then D would be false.

Inequalities with if, then set-ups are a little tricky but one thing I have found helpful is to read the question carefully:

FIRST, rephrase the question, if necessary: "IF A is true, THEN is B true?"
SECOND, DO NOT reverse the logic. The question is not, "IF B is true, then is A true" or "IF A is true, COULD B be true"

Another problem that may help you see another example is posted here in the forums

https://www.beatthegmat.com/ps-inequalit ... tml#273139
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