Author 
Message 
TAGS:

Hide Tags

Intern
Status: GMAT on july 13.
Joined: 10 Feb 2017
Posts: 37

If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
Updated on: 24 May 2018, 21:34
Question Stats:
40% (01:33) correct 60% (01:38) wrong based on 125 sessions
HideShow timer Statistics
If n is a positive integer greater than 1, is \(\sqrt{n+11} = \sqrt{n} + 1\)? (1) n is a perfect square (2) n + 11 is a perfect square.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Viserion99 on 22 May 2018, 22:28.
Last edited by Bunuel on 24 May 2018, 21:34, edited 2 times in total.
Edited the OA.



Manager
Joined: 28 Nov 2017
Posts: 145
Location: Uzbekistan

Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
23 May 2018, 00:27
Viserion99 wrote: If n is a positive integer greater than 1, is \(\sqrt{n+11} = \sqrt{n} + 1\)?
(1) n is a perfect square (2) n + 11 is a perfect square. Even though official answer is \(E\), I will go with \(C\). Because, \((1)\) and \((2)\) taken together, results in \(n=25\). This is sufficient to answer the question.
_________________
Kindest Regards! Tulkin.



Intern
Status: GMAT on july 13.
Joined: 10 Feb 2017
Posts: 37

Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
23 May 2018, 02:29
Tulkin987 wrote: Viserion99 wrote: If n is a positive integer greater than 1, is \(\sqrt{n+11} = \sqrt{n} + 1\)?
(1) n is a perfect square (2) n + 11 is a perfect square. Even though official answer is \(E\), I will go with \(C\). Because, \((1)\) and \((2)\) taken together, results in \(n=25\). This is sufficient to answer the question. Yes. Thanks for the reassurance. Even, I went with C. Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app



Manager
Joined: 24 Nov 2017
Posts: 53
Location: India

Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
24 May 2018, 05:59
Viserion99 wrote: If n is a positive integer greater than 1, is \(\sqrt{n+11} = \sqrt{n} + 1\)?
(1) n is a perfect square (2) n + 11 is a perfect square. The data is sufficient if we can determine whether the equation holds good with the information in the statements. n is a positive integer. Properties of perfect squares. The difference between squares of consecutive positive integers will increase by 2. For instance, 2^2  1^2 = 3; 3^2  2^2 = 5; 4^2  3^2 = 7; 5^2  4^2 = 9; 6^2  5^2 = 11 and so on. Statement 1: n is a perfect square. If n = 4; \(\sqrt{4+11} \neq \sqrt{4} + 1\) If n = 25; \(\sqrt{25+11} = \sqrt{25} + 1\) Cannot determine whether the equality will hold good. Statement 1 alone is not sufficient. Statement 2: n + 11 is a perfect square If n = 14; n + 11 = 25, which is a perfect square. \(\sqrt{14+11} \neq \sqrt{14} + 1\) If n = 25; n + 11 = 36, which is a perfect square. \(\sqrt{25+11} = \sqrt{25} + 1\) Combining the two statements: n is a perfect square and (n + 11) is also a perfect square. If the equation were to hold good, the two numbers n and (n + 11) will have to be squares of two consecutive numbers. From the properties of difference between square of positive integers, there can exist only one set of values where the difference between squares of consecutive numbers is 11. The difference between 6^2 and 5^2 is 11 and we cannot find any other set of two consecutive integers that will satisfy this condition. i.e., the only value that satisfies is when n = 25 and (n + 11) = 36. Choice C is the answer.
_________________
An IIM C Alumnus  Class of '94 GMAT Tutor at Wizako GMAT Classes & Online Courses



Manager
Joined: 26 Dec 2017
Posts: 136

Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
24 May 2018, 06:26
\(\sqrt{n+11} = \sqrt{n} + 1\)? Squaring on both ides and solve for n then we will get n=25.So we need to get a unique value 25 from A or b or both (1) n is a perfect square 25,200,4,9,... (2) n + 11 is a perfect square.25,14,5,.... n=25 is only perfect square with n+11 a perfect square so unique and C is the answer.
_________________
If you like my post pls give kudos



SVP
Joined: 26 Mar 2013
Posts: 1778

Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
24 May 2018, 16:06
Viserion99 wrote: If n is a positive integer greater than 1, is \(\sqrt{n+11} = \sqrt{n} + 1\)?
(1) n is a perfect square (2) n + 11 is a perfect square. Dear Bunuel, I have got same answer C as the above. Can you change the OA?



Intern
Status: GMAT in August 2018
Joined: 05 Mar 2018
Posts: 46
Location: India
Concentration: Leadership, Strategy
WE: Law (Consulting)

Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
10 Jun 2018, 07:57
WizakoBaskar wrote: Viserion99 wrote: If n is a positive integer greater than 1, is \(\sqrt{n+11} = \sqrt{n} + 1\)?
(1) n is a perfect square (2) n + 11 is a perfect square. The data is sufficient if we can determine whether the equation holds good with the information in the statements. n is a positive integer. Properties of perfect squares. The difference between squares of consecutive positive integers will increase by 2. For instance, 2^2  1^2 = 3; 3^2  2^2 = 5; 4^2  3^2 = 7; 5^2  4^2 = 9; 6^2  5^2 = 11 and so on. Statement 1: n is a perfect square. If n = 4; \(\sqrt{4+11} \neq \sqrt{4} + 1\) If n = 25; \(\sqrt{25+11} = \sqrt{25} + 1\) Cannot determine whether the equality will hold good. Statement 1 alone is not sufficient. Statement 2: n + 11 is a perfect square If n = 14; n + 11 = 25, which is a perfect square. \(\sqrt{14+11} \neq \sqrt{14} + 1\) If n = 25; n + 11 = 36, which is a perfect square. \(\sqrt{25+11} = \sqrt{25} + 1\) Combining the two statements: n is a perfect square and (n + 11) is also a perfect square. If the equation were to hold good, the two numbers n and (n + 11) will have to be squares of two consecutive numbers. From the properties of difference between square of positive integers, there can exist only one set of values where the difference between squares of consecutive numbers is 11. The difference between 6^2 and 5^2 is 11 and we cannot find any other set of two consecutive integers that will satisfy this condition. i.e., the only value that satisfies is when n = 25 and (n + 11) = 36. Choice C is the answer. Dear Bunuel, Shouldn't the answer be E? I see a lot of my friends have said C, considering that n=25 and n+11 = 36, would solve the problem. I say that because \sqrt{36} would be +/ 6 and not just =6. Similarly, the \sqrt{25}, will be +/5 and not just +5. Given this, I believe the ans to be E. I note that the restriction to be a positive integer is for n, not on \sqrt{n}. Requesting your expertise! Thanks a lot.



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
10 Jun 2018, 10:19
jayantbakshi wrote: WizakoBaskar wrote: Viserion99 wrote: If n is a positive integer greater than 1, is \(\sqrt{n+11} = \sqrt{n} + 1\)?
(1) n is a perfect square (2) n + 11 is a perfect square. The data is sufficient if we can determine whether the equation holds good with the information in the statements. n is a positive integer. Properties of perfect squares. The difference between squares of consecutive positive integers will increase by 2. For instance, 2^2  1^2 = 3; 3^2  2^2 = 5; 4^2  3^2 = 7; 5^2  4^2 = 9; 6^2  5^2 = 11 and so on. Statement 1: n is a perfect square. If n = 4; \(\sqrt{4+11} \neq \sqrt{4} + 1\) If n = 25; \(\sqrt{25+11} = \sqrt{25} + 1\) Cannot determine whether the equality will hold good. Statement 1 alone is not sufficient. Statement 2: n + 11 is a perfect square If n = 14; n + 11 = 25, which is a perfect square. \(\sqrt{14+11} \neq \sqrt{14} + 1\) If n = 25; n + 11 = 36, which is a perfect square. \(\sqrt{25+11} = \sqrt{25} + 1\) Combining the two statements: n is a perfect square and (n + 11) is also a perfect square. If the equation were to hold good, the two numbers n and (n + 11) will have to be squares of two consecutive numbers. From the properties of difference between square of positive integers, there can exist only one set of values where the difference between squares of consecutive numbers is 11. The difference between 6^2 and 5^2 is 11 and we cannot find any other set of two consecutive integers that will satisfy this condition. i.e., the only value that satisfies is when n = 25 and (n + 11) = 36. Choice C is the answer. Dear Bunuel, Shouldn't the answer be E? I see a lot of my friends have said C, considering that n=25 and n+11 = 36, would solve the problem. I say that because \sqrt{36} would be +/ 6 and not just =6. Similarly, the \sqrt{25}, will be +/5 and not just +5. Given this, I believe the ans to be E. I note that the restriction to be a positive integer is for n, not on \sqrt{n}. Requesting your expertise! Thanks a lot. When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the nonnegative 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 \(x=\sqrt{9}=3\).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Status: GMAT in August 2018
Joined: 05 Mar 2018
Posts: 46
Location: India
Concentration: Leadership, Strategy
WE: Law (Consulting)

Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2)
[#permalink]
Show Tags
10 Jun 2018, 21:54
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the nonnegative 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 \(x=\sqrt{9}=3\).[/quote] Thanks so much Bunuel, this was very helpful! Very kind of you. Much appreciated




Re: If n is a positive integer greater than 1, is (n + 11)^(1/2) = n^(1/2) &nbs
[#permalink]
10 Jun 2018, 21:54






