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# If it is true that -6 =< n =<10, which of the

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Director
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If it is true that -6 =< n =<10, which of the [#permalink]

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09 Sep 2004, 07:14
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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
[Reveal] Spoiler: OA

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08 Apr 2010, 03:56
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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

The stem says that $$-6\leq{n}\leq{10}$$. This info is given to be true. The question asks which of the following MUST be true?

A. $$n<8$$ --> n can be 9, hence this might be wrong.
B. $$n=-6$$ --> we don't know the exact value of n, we just know that n is in the range $$-6\leq{n}\leq{10}$$. Hence this might be wrong.
C. $$n>-8$$ --> ANY value of n from the range $$-6\leq{n}\leq{10}$$ is more than -8, hence this info is ALWAYS true. Correct answer.
D. $$-10<n<7$$ --> n can be 8, hence this might be wrong.
E. None.

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07 Apr 2010, 23:06
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rohitgoel15 wrote:

n can be -6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10
1: n<8, False as n can be any value less than -6
2: n = -6 True as possible value
3: n>-8, False as n can be -7 which is incorrect
4: -10<n<7, False as n can be -9, -8,-7 which is incorrect
5: Not possible as (2) is correct.

The OA marked is impossible with the question given.
What is the source of question?

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Re: Problem solving - inequality - 700 level [#permalink]

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04 Aug 2011, 05:06
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shashankp27 wrote:
bschool83 wrote:
agdimple333 and zuberahmed,

What if n = -5, 0, or 5? Then answer choice B (n = –6) will fall apart.

–6 <= n <= 10 means all values between and equal to -6 and 10.

Answer choice C, n > –8 holds true for all available values of n. Hence answer is C.

how does it 'fall apart' ? could you please elaborate...

Focus on the question's wording:
If it is true that –6 <= n <= 10, which of the following [highlight]must be true[/highlight]?

'must be true' implies that no matter what value n takes (out of the given range), 'which of the following will definitely hold?'
We have to find that option that will remain true. It is different from 'which of the following CAN be true?' i.e. which of the following is possible...
Given -6 <= n <= 10

n = -6 is possible. But it will not hold for all possible values of n i.e. if n = 5, then n is not equal to -6. So 'n = -6' is not a 'must be true' condition.

On the other hand, n > -8 will always be true.
If n = -6, then n > -8
If n = 0, then n > -8
If n = 4, then n > -8
If n = 10, then n > -8
Hope you got the point. No matter which value n takes out of the available values, n > -8 will always be true. For every value of n, n will be more than -8.

GMAT loves to lay this trap. Be very careful. Make sure you understand exactly what the question is asking.
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06 Mar 2006, 15:15
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bewakoof wrote:
-6<= n <= 10

this may sound really stupid for me to ask.. but what if n = -7..

-7 > -8 right??

As the saying goes, "there are no stupid questions" period.
We already know that n>=-6. So n cannot be =-7.

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Re: Problem solving - inequality - 700 level [#permalink]

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24 Jul 2011, 07:56
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kp1811,

I think your interpretation of the question is incorrect.

Let's revisit the question.

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

In other words... if the value of n is given to be -6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10 which of the following must be true.

Can you infer/say with 100% confidence that all given values of n are greater than -8?

Hope this helps you.

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09 Sep 2004, 07:38
I am intrigued to say E - none of the above. But I have seen a similar one in OG (q.210) and using the (il)logic there, I will say

C.

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09 Sep 2004, 07:44
I have my doubts between C and E.

A) n < 8
Not a must, because n still can be 8, 9 or 10
B) n = -6
Not a must, because n still can be -5 till 10
D) -10 < n < 7
Not a must because n still can be 7, 8, 9 or 10

C) n > -8
Yes it must be greater than -8, but we still have -7 which is not valid for n.

Hmmmm, I would pick E as answer.

Please correct me if I am wrong.

Regards,

Alex

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09 Sep 2004, 07:59
It's questions like these that make one wonder what is this exam really testing. I'll bet the answer if C because the question doesn't ask if the answer choice will fall within the established perameters. It only asks which must be true and all numbers in that set will be greater than -8. It stinks but I think the answer is C.

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06 Mar 2006, 15:05
-6<= n <= 10

this may sound really stupid for me to ask.. but what if n = -7..

-7 > -8 right??
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08 Apr 2010, 03:46
I agree with bangalorean 2000,

However, IMO, since the question is mentioning " which of the following must be true", we can eliminate answer choice (2), to leave (5) as the only correct option.

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08 Apr 2010, 04:21
Thanks for correcting on this one.
It appears that interpreting the question is more than half the battle won.
In the answer choice (C), there is a tendency in this one to take a value of -7 & mark this choice as incorrect. However, if you look at the larger set of -6=<n=<10, then all the values of n here are greater than -8.

Cheers

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Re: Problem solving - inequality - 700 level [#permalink]

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24 Jul 2011, 07:16
agdimple333 and zuberahmed,

What if n = -5, 0, or 5? Then answer choice B (n = –6) will fall apart.

–6 <= n <= 10 means all values between and equal to -6 and 10.

Answer choice C, n > –8 holds true for all available values of n. Hence answer is C.

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Re: Problem solving - inequality - 700 level [#permalink]

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24 Jul 2011, 07:37
bschool83 wrote:
agdimple333 and zuberahmed,

What if n = -5, 0, or 5? Then answer choice B (n = –6) will fall apart.

–6 <= n <= 10 means all values between and equal to -6 and 10.

Answer choice C, n > –8 holds true for all available values of n. Hence answer is C.

what about -7? n=-7 is not in the range of values mentioned for n

will go with E

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Re: Problem solving - inequality - 700 level [#permalink]

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24 Jul 2011, 11:37
agdimple333,

If you tell me that you took the GMAT 3 times and each time you scored between 710 and 770, and I say "Wow! you scored above 700 each time", will my statement always be true?

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Re: Problem solving - inequality - 700 level [#permalink]

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24 Jul 2011, 14:18
Isn't the answer a clear C? if n > -6, then n > -8 for all n.
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Re: Problem solving - inequality - 700 level [#permalink]

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02 Aug 2011, 17:47
bschool83 wrote:
agdimple333 and zuberahmed,

What if n = -5, 0, or 5? Then answer choice B (n = –6) will fall apart.

–6 <= n <= 10 means all values between and equal to -6 and 10.

Answer choice C, n > –8 holds true for all available values of n. Hence answer is C.

how does it 'fall apart' ? could you please elaborate...

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Re: Problem solving - inequality - 700 level [#permalink]

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05 Aug 2011, 12:44
1. n<8?

n=9 no

n=-6 yes

not true all the time.
2. n=-6

not true all the time as -6<=n<=10

3. n>-8

even minimum value in the range -6<=n<=10, i.e n=-6>-8

so n>-8 all the time. In other words n>-8 must be true.

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Re: Problem solving - inequality - 700 level [#permalink]

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05 Aug 2011, 20:16
bschool83 wrote:
If it is true that –6 <= n <= 10, which of the following must be true?

n < 8
n = –6
n > –8
-10 < n < 7
none of the above

There appears to be a very simple way to understand this problem...Popped into my head after seeing the tedious ways of making all understand, so thought of posting it.

Whenever you see a MUST BE TRUE question of the form IF [X], then [Y] MUST BE TRUE
Visualize/draw as a VENN DIAGRAM the above two conditions X and Y....In this case :

Fact : –6 <= n <= 10 ------- (X)

All the Other Choice -------- (Y)

When will this be a MUST BE TRUE ?

When X is always contained inside Y/ Y is equal to or a superset of Y

Now, you have got this idea....Just plug in the choices for Y putting X constant.
 n < 8 fails for n < -6 and –6 <= n <= 10 n = –6 fails for all values when n <> -6 and –6 <= n <= 10 n > –8 does not fail for any value when n > –8 and –6 <= n <= 10 -10 < n < 7 fails for all values when n = -9,-8,-7 and and –6 <= n <= 10 none of the above

Hope this helps all !!!
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Re: Problem solving - inequality - 700 level [#permalink]

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08 Aug 2011, 22:27
when n > -8 then n = -7 (can be) the criterai -6<=n is not met here

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Re: Problem solving - inequality - 700 level   [#permalink] 08 Aug 2011, 22:27

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