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Inequalities problem. help!

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Inequalities problem. help!

by Taniuca » Mon Nov 01, 2010 5:46 pm
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

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by Rahul@gurome » Mon Nov 01, 2010 7:11 pm
Solution:
Check the options one by one.
Let n = 9.
-6 <=9<=10, but 9>8.
Or a) is not always true.
Let n = 2.
So -6<=2<=10, but 2=n is not equal to -6.
Or b) is not always true.
Now -8 < -6 <= n.
So -8 < n.
Or c) is always true.
Let n = 8.
So -6<=8<=10, but 8 does not lie between -10 and 7.
Or d) is not always true.

The correct answer is c).
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by Testluv » Mon Nov 01, 2010 9:40 pm
Great solution but after we saw that c was always true there was no need to check any other answer choice (as there can only be one right answer).

When reviewing problem solving be sure to review your right answers too (not just wrong ones). And ask yourself: could I have gotten to the right answer more quickly by using a nontraditional approach (logical reasoning, using the answer choices, perhaps picking some numbers, etc.).

Remember that when we find a way to save time, we have also found a way to raise our score.
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by Taniuca » Tue Nov 02, 2010 10:46 am
Thanks, but I still don't understand why answer c.

If n>-8 then the values could be -7,-6,-5...o infinite.

if I substitute n=-7 into the original inequality -6<=n<=10 , then I get that -6<=-7 <=10 which is not possible. -6 is not greater than -7.

Is there any trick for this?

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by Testluv » Tue Nov 02, 2010 11:55 am
Taniuca wrote:Thanks, but I still don't understand why answer c.

If n>-8 then the values could be -7,-6,-5...o infinite.

if I substitute n=-7 into the original inequality -6<=n<=10 , then I get that -6<=-7 <=10 which is not possible. -6 is not greater than -7.

Is there any trick for this?
The task is to determine what must be true. If the range is -6<=n<=10, then it must be true, for example, that n>-1000 (since all values within the range of -6<=n<=10 are greater than -1000). Or, it must be true that n<1000 (since all values within the range of -6<=n<=10 are less than 1000). Likewise, since we know that the smallest value n can take is -6, it must be true that n>-8.
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by Brian@VeritasPrep » Tue Nov 02, 2010 1:54 pm
Hey Taniuca,

Great follow-up question...let me see if I can help by adding to what Testluv said.

This question asks you which answer choice MUST BE TRUE, which is also something that CANNOT BE FALSE. One way to look at it is this way - say I were to say that:

In order to be admitted to Harvard Business School, one must have:

-a bachelor's degree
-a GMAT score above 500
-three compelling letters of recommendation
-a $125 registration fee
-three essays

Those are all then NECESSARY conditions to be admitted to be admitted to HBS. So if I were to say that:

Taniuca was admitted to HBS.

Then which of the following must be true?

A) Taniuca has a bachelor's degree
B) Taniuca submitted the $125 registration fee
C) Taniuca has a GMAT score above 500
D) All of the above

It's D, right? Because in order to get into HBS you would have had to meet all of those conditions.

Now...just because something is NECESSARY does not mean that it is SUFFICIENT! Meeting those qualifications alone will not get you into Harvard, just as saying that a number is greater than -8 is not sufficient to say that it's between -6 and 10. But we do know that if you get into Harvard then you MUST HAVE met those requirements, the same way that if a number is between -6 and 8 then it MUST BE greater than -8.

Looking at it the other way, if a number is NOT greater than -8, then there's no way that it qualifies to be between -6 and 10. It has to meet that qualification to even have a chance, just like you need to pay that Harvard application fee to even have a chance there.

I hope that helps - keep in mind that the MUST BE TRUE standard in this case just means that we need some thing necessary, not necessarily something sufficient.
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