Last visit was: 17 May 2025, 18:13 It is currently 17 May 2025, 18:13
Home
GMAT
MBA Fair
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
Sub 505 Level|   Inequalities|   Roots|         
User avatar
cmugeria
User avatar
Joined: 22 Dec 2009
Last visit: 19 Mar 2011
Posts: 18
Own Kudos:
560
 [10]
Given Kudos: 1
Posts: 18
Kudos: 560
 [10]
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 17 Aug 2010, 08:45
5
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

84% (00:48) correct 16% (00:53) wrong based on 544 sessions

History

Date
Time
Result
Not Attempted Yet
Is \(7 < \sqrt n < 8\)?

(1) n > 50

(2) n < 60
ShowHide Answer
Official Answer
C
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 May 2025
Posts: 101,480
Own Kudos:
725,031
 [1]
Given Kudos: 93,530
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 101,480
Kudos: 725,031
 [1]
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 17 Aug 2010, 08:54
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
cmugeria
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.
avatar
ulm
avatar
Joined: 03 Jun 2010
Last visit: 20 Aug 2019
Posts: 95
Own Kudos:
585
Given Kudos: 40
Location: United States (MI)
Concentration: Marketing, General Management
Schools: Ross '15 (A) Darden '14 (D) Duke '15 (D)
WE:Business Development (Consumer Packaged Goods)
Products:
My Reviews
Schools: Ross '15 (A) Darden '14 (D) Duke '15 (D)
Posts: 95
Kudos: 585
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 17 Aug 2010, 22:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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).
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 May 2025
Posts: 101,480
Own Kudos:
725,031
 [3]
Given Kudos: 93,530
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 101,480
Kudos: 725,031
 [3]
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 18 Aug 2010, 04:19
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
ulm
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.
avatar
ayeshakhosla1718
avatar
Joined: 20 Sep 2020
Last visit: 23 Mar 2021
Posts: 10
Own Kudos:
1
Given Kudos: 93
Posts: 10
Kudos: 1
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 27 Dec 2020, 04:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
kntombat
User avatar
Retired Moderator
Joined: 28 Feb 2020
Last visit: 19 Jan 2023
Posts: 905
Own Kudos:
511
Given Kudos: 839
Location: India
WE:Other (Other)
Posts: 905
Kudos: 511
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 27 Dec 2020, 06:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
avatar
signyc
avatar
Joined: 15 May 2021
Last visit: 25 May 2022
Posts: 9
Given Kudos: 1
Location: Indonesia
Schools: Columbia CBS '24 (S)
Schools: Columbia CBS '24 (S)
Posts: 9
Kudos: 0
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 15 May 2021, 10:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel

I have a question about this problem. Should we consider the negative square roots of N?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 May 2025
Posts: 101,480
Own Kudos:
725,031
 [1]
Given Kudos: 93,530
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 101,480
Kudos: 725,031
 [1]
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 15 May 2021, 10:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
signyc
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 \(x=\sqrt{9}=3\).
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 17 May 2025
Posts: 5,594
Own Kudos:
5,013
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews Forum Quiz
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,594
Kudos: 5,013
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 15 May 2021, 10:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Snehaaaaa
User avatar
Joined: 09 Mar 2021
Last visit: 13 Feb 2025
Posts: 135
Own Kudos:
375
Given Kudos: 161
Location: India
Schools: Booth '24 ISB '23 Ross '24 Sloan '24 Wharton '24 Haas '25 Kellogg '24 Anderson '25
GMAT 1: 640 Q44 V34
GPA: 3.68
Schools: Booth '24 ISB '23 Ross '24 Sloan '24 Wharton '24 Haas '25 Kellogg '24 Anderson '25
GMAT 1: 640 Q44 V34
Posts: 135
Kudos: 375
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 21 Jan 2022, 11:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
cmugeria
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
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 36,868
Own Kudos:
985
Posts: 36,868
Kudos: 985
Is 7 < n^(1/2) < 8? (1) n > 50 (2) n < 60 18 Jun 2024, 02:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderator:
Bunuel
Math Expert
101480 posts