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Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60

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cmugeria
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Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  17 Aug 2010, 08:45
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Is \(7 < \sqrt n < 8\)?

(1) n > 50

(2) n < 60
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Bunuel
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  17 Aug 2010, 08:54
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cmugeria wrote:
IS 7 < SQRT N < 8?

1) N>50
2) N<60


Is \(7<\sqrt{n}<8\) --> or is \(49<n<64\).

(1) \(n>50\). Not sufficient as \(n\) can be more than 64.

(2) \(n<60\). Not sufficient as \(n\) can be less than 49.

(1)+(2) \(50<n<60\). Sufficient.

Answer: C.
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  17 Aug 2010, 22:28
Consider 1)+2) we have (50;60) interval.

_______49__50_______60____64

But what to do with highlighted parts?
Virtually we are asked if 49<N<64?
we miss 2 intervals: (49;50) and (60;64)
Having (50;60) we can't say that (49;64) is true.
Looks like (E).
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  18 Aug 2010, 04:19
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ulm wrote:
Consider 1)+2) we have (50;60) interval.

_______49__50_______60____64

But what to do with highlighted parts?
Virtually we are asked if 49<N<64?
we miss 2 intervals: (49;50) and (60;64)
Having (50;60) we can't say that (49;64) is true.
Looks like (E).


OA for this question is C.

Question: is \(49<n<64\)? or is \(n\) in the range (49,64), not inclusive.

(1)+(2) \(50<n<60\) --> ANY \(n\) (any number) from this range IS in the range (49,64), so the answer to the question "is \(49<n<64\)" is YES.

Hope it's clear.
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  27 Dec 2020, 04:05
7<n<8
or 49<n<64
1) n>50 then can be greater than 64
2) n<60, any value can be below 49
if 50<n<60
then it is in between 49 and 64.
Therefore answer c
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  27 Dec 2020, 06:04
Given Inequality: \(7< \sqrt{n} < 8\).
Squaring the entire equation => \(49 < n < 64\).

1) \(n > 50\) = n is greater than 50 but the value of n can be greater than 64 also, therefore exceeding the range of the inequality. (Not Sufficient)

2)\( n < 60\) = n is less 60 but the value of n can be lesser than 49 also. (Not Sufficient)

(1)+(2) = \( 50<n<60\) Therefore, the condition is sufficient, as any expression falling in this range its \(\sqrt{n}\) will be \(>7\) and \(<8\).

The OA is C.
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  15 May 2021, 10:17
Hi Bunuel

I have a question about this problem. Should we consider the negative square roots of N?
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  15 May 2021, 10:20
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signyc wrote:
Hi Bunuel

I have a question about this problem. Should we consider the negative square roots of N?


\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.


The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT (and generally in math) provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  15 May 2021, 10:30
Asked: Is \(7 < \sqrt n < 8\)?

(1) n > 50
In all cases \(\sqrt{n} > 7\) since \(\sqrt{49}= 7\) and 50>49
If n = 81; \(\sqrt{n} = 9 > 8\)
But if n < 64; \(\sqrt{n} <8\)
NOT SUFFICIENT

(2) n < 60
In all cases \(\sqrt{n} <8\) since \(\sqrt{64}= 8\) and 60<64
If n = 4; \(\sqrt{n} = 2 < 7\)
But if n > 49; \(\sqrt{n} >7\)
NOT SUFFICIENT

(1) + (2)
(1) n > 50
(2) n < 60
49 < 50 < n < 60 < 64
\(7 < \sqrt{50} < \sqrt{n} < \sqrt{60} < 8\)
SUFFICIENT

IMO C
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink] New post  21 Jan 2022, 11:09
cmugeria wrote:
Is \(7 < \sqrt n < 8\)?

(1) n > 50

(2) n < 60


Explanantion
(1) n > 50
Not sufficient as n can be a value greater than 64

(2) n < 60
Not sufficient as n can be a value less than 49

Using both 1 and 2, we get the perfect limits.
Sufficient

Correct Answer is C
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Re: Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 [#permalink]
21 Jan 2022, 11:09
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