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# Is 7 < sqrt(n) < 8? (1) n > 50 (2) n < 60

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Manager
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Is 7 < sqrt(n) < 8? (1) n > 50 (2) n < 60 [#permalink]  06 Mar 2006, 10:49
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Is 7 < sqrt(n) < 8?
(1) n > 50
(2) n < 60
Manager
Joined: 20 Mar 2005
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Location: Colombia, South America
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Re: DS sqrt (n) [#permalink]  06 Mar 2006, 10:52
hellom3p wrote:
Is 7 < sqrt(n) < 8?
(1) n > 50
(2) n < 60

7 < sqrt(n) < 8

square

49 < n < 64

therefore you will need both

so is C
Manager
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-8<sqrt (n)<-7?

49<n<64
Senior Manager
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hellom3p wrote:
-8<sqrt (n)<-7?

49<n<64

Question is not asking for -ve values.
Manager
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I am for E.
Director
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Tricky one)) E for me cause we don't know if n is an integer))
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Manager
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Even if n was a fraction, wouldnt sqrt(n) still lie between 7 and 8 if we take both the statements together? Yurik79 could you elaborate? I mean if n was 55.5 then sqrt(55.5) would still be between 7 and 8 right? Am I missing something here?
SVP
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Gordon wrote:
Even if n was a fraction, wouldnt sqrt(n) still lie between 7 and 8 if we take both the statements together? Yurik79 could you elaborate? I mean if n was 55.5 then sqrt(55.5) would still be between 7 and 8 right? Am I missing something here?

No, you are not missing anything
Even if we consider fractions between 7 & 8, "C" holds good!
Manager
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gmat_crack wrote:
hellom3p wrote:
-8<sqrt (n)<-7?

49<n<64

Question is not asking for -ve values.

why not?

Is sqrt(n) negative?
I. n = 49
II. n = 64
Manager
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What if n = 49.5? sqrt(n) will still be between 7 and 8.
So, shouldn't the domain of n be (49,64) exluding 49 and 64?
SVP
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chuckle wrote:
What if n = 49.5? sqrt(n) will still be between 7 and 8.
So, shouldn't the domain of n be (49,64) exluding 49 and 64?

chuckle,
The question asks whether, 7 < sqrt(n) < 8? given that n>50 & n < 60.
From the given two conditions it lies between that range.

You are right, sqrt(49.5) will still lie between 7 & 8 (it is 7.02..) but that is not what this DS asks, it just wants us to tell,
if n>50 & n < 60, is 7 < sqrt(n) < 8 true?
Manager
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Thanks Vivek. I understood now.
VP
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hellom3p wrote:
gmat_crack wrote:
hellom3p wrote:
-8<sqrt (n)<-7?
49<n<64

Question is not asking for -ve values.

Is sqrt(n) negative?
I. n = 49
II. n = 64

E seems correct to me cuz even if 49<n<64, sqrt(n) can be +ve and -ve. so sqrt can or canot fall between 7 and 8.
Manager
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I will also go with E as
a) n > 50 - obviously insufficient
b) n < 60 - obviously insufficient
a & b) for every n (where 50 < n < 60), sqrt(n) is either +ve or -ve - so insufficient.

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VP
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On the GMAT , the sqrt is always positive. sqrt(4) is always 2 and not -2.
In my opinion, that is $@#%$%$%, but we need to keep that in mind for such problems. Professor wrote: hellom3p wrote: gmat_crack wrote: hellom3p wrote: what about -8<sqrt (n)<-7? 49<n<64 Question is not asking for -ve values. why not? it's like asking: Is sqrt(n) negative? I. n = 49 II. n = 64 E seems correct to me cuz even if 49<n<64, sqrt(n) can be +ve and -ve. so sqrt can or canot fall between 7 and 8. Manager Joined: 16 Sep 2005 Posts: 62 Followers: 1 Kudos [?]: 2 [0], given: 0 [#permalink] 13 Mar 2006, 11:51 lhotseface wrote: On the GMAT , the sqrt is always positive. sqrt(4) is always 2 and not -2. In my opinion, that is$@#%$%$%, but we need to keep that in mind for such problems.

Oh! I did not know about this at all. Any ways can you please tell me is this a general thumb rule for all DS questions or it applies to the whole quantitative section?
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7 < sqrt(n) < 8
49 < n < 64

(1) Insufficient. n could be 100 and sqrt(n) would be out of range

(2) Insufficient for the same reason

Using (1) and (2), we know 50 < n < 60 which lies within the range.

Ans C
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