Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Mar 2012
Posts: 45
GPA: 3.7

Is (7x)^1/2 an integer?
[#permalink]
Show Tags
Updated on: 05 Jun 2013, 03:49
Question Stats:
30% (01:44) correct 70% (01:40) wrong based on 1514 sessions
HideShow timer Statistics
Is \(\sqrt{7x}\) an integer? (1) \(\sqrt{\frac{x}{7}}\) is an integer (2) \(\sqrt{28x}\) is an integer Can someone please explain why point 2 is not correct? What I did is that 28 is factored into => 2*2*7 so therefore I concluded x must have at least one 7. so if x has one seven then \sqrt{7x} must be an integer. Am I doing something wrong here?
Thanks! Alex
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by alex1233 on 13 Jan 2013, 08:22.
Last edited by Bunuel on 05 Jun 2013, 03:49, edited 3 times in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 59039

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
13 Jan 2013, 08:58
Is \(\sqrt{7x}\) an integer?Notice that we are not told that x is an integer. (1) \(\sqrt{\frac{x}{7}}\) is an integer. Given that \(\sqrt{\frac{x}{7}}=integer\) > square it: \(\frac{x}{7}=integer^2\) > \(x=7*integer^2\). So, \(\sqrt{7x}=\sqrt{7*(7*integer^2)}=7*integer=integer\). Sufficient. (2) \(\sqrt{28x}\) is an integer. If \(x=\frac{1}{28}\), then \(\sqrt{7x}=\frac{1}{2}\neq{integer}\) BUT if \(x=0\), then \(\sqrt{7x}=0=integer\). Not sufficient. Answer: A.
_________________




Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 584

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
05 Jun 2013, 23:53
alex1233 wrote: Is \(\sqrt{7x}\) an integer?
(1) \(\sqrt{\frac{x}{7}}\) is an integer
(2) \(\sqrt{28x}\) is an integer
From F.S 1 , we know that \(\sqrt{\frac{x}{7}}\) = Integer(I)> \(\sqrt{\frac{x*7}{7*7}}\) = \(\sqrt{7x}*\frac{1}{7}\) = I> \(\sqrt{7x}\) = 7*I. Thus, an integer. Sufficient. From F.S 2, we know that \(\sqrt{28x}\) = Integer(I) > \(\sqrt{7*4x}\) = 2*\(\sqrt{7x}\) = I. Thus, \(\sqrt{7x}\) =\(\frac{I}{2}\). Depending on I being odd/even, the given expression will be a noninteger/integer. Insufficient. A.
_________________




Retired Moderator
Joined: 05 Jul 2006
Posts: 1383

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
13 Jan 2013, 09:01
[quote="alexpavlos"]Is \(\sqrt{7x}\) an integer?
(1) \(\sqrt{\frac{x}{7}}\) is an integer
(2) \(\sqrt{28x}\) is an integer
for sqt 7x to be an integer , x has to have the form 7^a*z^b, where a is an odd integer and z is an integer and b a an even intiger.
from 1
x is in the form 7^a*z^b
from 2 2sqt 7x is an integer....this means that sqt 7x is in the form k/2 however , it says nothing about the form of x itself... thus insuff
A



Intern
Joined: 18 Mar 2012
Posts: 45
GPA: 3.7

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
13 Jan 2013, 09:16
Bunuel wrote: Is \(\sqrt{7x}\) an integer?
Notice that we are not told that x is an integer.
(1) \(\sqrt{\frac{x}{7}}\) is an integer. Given that \(\sqrt{\frac{x}{7}}=integer\) > square it: \(\frac{x}{7}=integer^2\) > \(x=7*integer^2\). So, \(\sqrt{7x}=\sqrt{7*(7*integer^2)}=7*integer=integer\). Sufficient.
(2) \(\sqrt{28x}\) is an integer. If \(x=\frac{1}{28}\), then \(\sqrt{7x}=\frac{1}{2}\neq{integer}\) BUT if \(x=0\), then \(\sqrt{7x}=0=integer\). Not sufficient.
Answer: A. Thanks sorry for asking again... But could you please explain if my method/ logic was completely wrong? ie if we break out 28 int primes we see that it has 2,2,7 so x must have at least one 7? therefore we can assume that \sqrt{7x} should be integer? Thanks again! Alex



Math Expert
Joined: 02 Sep 2009
Posts: 59039

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
13 Jan 2013, 09:29
alexpavlos wrote: Bunuel wrote: Is \(\sqrt{7x}\) an integer?
Notice that we are not told that x is an integer.
(1) \(\sqrt{\frac{x}{7}}\) is an integer. Given that \(\sqrt{\frac{x}{7}}=integer\) > square it: \(\frac{x}{7}=integer^2\) > \(x=7*integer^2\). So, \(\sqrt{7x}=\sqrt{7*(7*integer^2)}=7*integer=integer\). Sufficient.
(2) \(\sqrt{28x}\) is an integer. If \(x=\frac{1}{28}\), then \(\sqrt{7x}=\frac{1}{2}\neq{integer}\) BUT if \(x=0\), then \(\sqrt{7x}=0=integer\). Not sufficient.
Answer: A. Thanks sorry for asking again... But could you please explain if my method/ logic was completely wrong? ie if we break out 28 int primes we see that it has 2,2,7 so x must have at least one 7? therefore we can assume that \sqrt{7x} should be integer? Thanks again! Alex If x is NOT an integer you cannot make its prime factorization. If we were told that x IS an integer, then \(\sqrt{28x}=2\sqrt{7x}=integer\). Thus x must be of the form \(7^{odd}*integer^2\), so in this case \(\sqrt{7x}=\sqrt{7*(7^{odd}*integer^2)}=\sqrt{7^{even}*integer^2}=integer\). Hope it's clear.
_________________



Manager
Joined: 07 May 2012
Posts: 52
Location: United States

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
26 May 2013, 21:17
alex1233 wrote: Is \(\sqrt{7x}\) an integer?
(1) \(\sqrt{\frac{x}{7}}\) is an integer
(2) \(\sqrt{28x}\) is an integer
Can someone please explain why point 2 is not correct? What I did is that 28 is factored into => 2*2*7 so therefore I concluded x must have at least one 7. so if x has one seven then \sqrt{7x} must be an integer. Am I doing something wrong here?
Thanks! Alex Quote: \(\sqrt{7x}\) = integer ? or 7x= int^2 ? ( 1) \(\sqrt{\frac{x}{7}}\) is an integer  lets say b x/7 = b^2 > where b is an integer x= 7 *b^2 7x = (7*b) ^2 hence 7x=int^2 sufficient (2) \(\sqrt{28x}\) is an integer  lets say c 28x= c^2 7x=c^2/4 = (c/2)^2 If C is odd , then ans is No and if C is even then yes . ( If you knew that x was an integer , then this would have sufficed) Insufficient.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59039

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
05 Jun 2013, 03:55
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Intern
Joined: 12 Apr 2013
Posts: 3
Location: Viet Nam
GPA: 3.3

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
21 Dec 2013, 06:09
(1) \(\sqrt{7x}\) = 7\(\sqrt{\frac{x}{7}}\)
7 and \(\sqrt{\frac{x}{7}}\) are integers so \(\sqrt{7x}\) is an integerSufficient
(2) \(\sqrt{7x}\) = \(\sqrt{28x}/2\)
We know that \(\sqrt{28x}\) is an integer but not sure if it is divisible by 2 or notInsufficient
Hence the answer is A



Manager
Joined: 25 Oct 2013
Posts: 141

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
03 Feb 2014, 06:29
(1) \(\sqrt{\frac{x}{7}}\) is integer. Let this integer be p. then \(\sqrt{\frac{x}{7}} = p\) \(\frac{x}{7} = p^2\) \(x=7*p^2\) \(7x=7^2*p^2\) \(\sqrt{7x}=7*p\) an integer. (1) is sufficient(2) \(\sqrt{28x}\) is integer. Let this integer be q. \(\sqrt{28x} = q\) \(\sqrt{4*7x} = q\) \(2*\sqrt{7x} = q\) \(\sqrt{7x} = \frac{q}{2}\) It is given that q is integer, but \(\frac{q}{2}\) may or may not be an integer. not sufficient. A is the soln.
_________________
Click on Kudos if you liked the post!
Practice makes Perfect.



Intern
Joined: 13 Apr 2014
Posts: 11

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
15 Apr 2014, 08:04
(1) \sqrt{\frac{x}{7}} is integer. Let this integer be p. then \sqrt{\frac{x}{7}} = p \frac{x}{7} = p^2 x=7*p^2 7x=7^2*p^2 \sqrt{7x}=7*p an integer. (1) is sufficient (2) \sqrt{28x} is integer. Let this integer be q. \sqrt{28x} = q \sqrt{4*7x} = q 2*\sqrt{7x} = q \sqrt{7x} = \frac{q}{2} It is given that q is integer, but \frac{q}{2} may or may not be an integer. not sufficient. A is the soln. tnx for this
_________________
http://www.gmatacademy.ir best for iranian



Math Expert
Joined: 02 Sep 2009
Posts: 59039

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
15 Apr 2014, 08:09
gmatonline wrote: (1) \sqrt{\frac{x}{7}} is integer.
Let this integer be p. then
\sqrt{\frac{x}{7}} = p
\frac{x}{7} = p^2
x=7*p^2
7x=7^2*p^2
\sqrt{7x}=7*p an integer. (1) is sufficient
(2) \sqrt{28x} is integer.
Let this integer be q.
\sqrt{28x} = q
\sqrt{4*7x} = q
2*\sqrt{7x} = q
\sqrt{7x} = \frac{q}{2}
It is given that q is integer, but \frac{q}{2} may or may not be an integer. not sufficient.
A is the soln.
tnx for this I think this is the post you are looking for: rulesforpostingpleasereadthisbeforeposting133935.html#p1096628 Hope it helps.
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15447
Location: United States (CA)

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
16 Apr 2015, 11:54
Hi All, This question can be solved by TESTing VALUES, but you have to really be thorough with your TESTs (and think about what X COULD be given the information in the Facts). We're asked if Root(7X) is an integer. This is a YES/NO question. Fact 1: Root(X/7) is an integer. This Fact tells us that X has to be a specific type of multiple of 7.... IF.... X = 7 the Root(7/7) = 1 and is an integer Root(49) = 7 and the answer to the question is YES IF.... X = 28 the Root(28/7) = 2 and is an integer Root(196) = 14 and the answer to the question is YES This hints at the pattern that X will be a "perfect square times a multiple of 7', which means that the answer to the question is ALWAYS YES. You can also use primefactorization to prove that this is the case. Fact 1 is SUFFICIENT Fact 2: Root(28X) is an integer. This Fact tells us that X has to be a specific type of multiple of 7.... IF.... X = 7 the Root(196) = 14 and is an integer Root(49) = 7 and the answer to the question is YES IF.... X = 1/28 the Root(1) = 1 and is an integer Root(7/28) = 1/2 and the answer to the question is NO Fact 2 is INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 25 Nov 2015
Posts: 5
Location: India

Is [m][square_root](7x)[/square_root][/m] an integer?
[#permalink]
Show Tags
15 May 2016, 09:36
Is \(\sqrt{(7x)}\) an integer?
(1) \(\sqrt{(x/7)}\) is an integer.
(2) \(\sqrt{(28x)}\)is an integer.
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. EITHER statement BY ITSELF is sufficient to answer the question. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.



Math Expert
Joined: 02 Sep 2009
Posts: 59039

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
15 May 2016, 09:41
sahilhanda wrote: Is \(\sqrt{(7x)}\) an integer?
(1) \(\sqrt{(x/7)}\) is an integer.
(2) \(\sqrt{(28x)}\)is an integer.
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. EITHER statement BY ITSELF is sufficient to answer the question. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem. Merging topics. Please refer to the discussion above.
_________________



Math Expert
Joined: 02 Aug 2009
Posts: 8164

Re: Is [m][square_root](7x)[/square_root][/m] an integer?
[#permalink]
Show Tags
15 May 2016, 09:45
sahilhanda wrote: Is \(\sqrt{(7x)}\) an integer?
(1) \(\sqrt{(x/7)}\) is an integer.
(2) \(\sqrt{(28x)}\)is an integer.
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. EITHER statement BY ITSELF is sufficient to answer the question. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem. Hi lets see the what info Q has.. Is \(\sqrt{(7x)}\) an integer?.. possible  a) if x ia an integer and of type y^2*7.. b) if x is a fraction of type y^2/7.. lets see the statements (1) \(\sqrt{(x/7)}\) is an integer. this tells us that x = y^2*7, where y is an integer, SAME as case (a) above Suff (2) \(\sqrt{(28x)}\)is an integer. this tells us that \(\sqrt{(4*7*x)}\)is an integer. so x = y^2/28.. if y is multiple of 2, ans is YES if y is not a multiple of 2, ans is No Insuff A
_________________



Intern
Joined: 19 Sep 2015
Posts: 22

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
16 May 2016, 23:51
alex1233 wrote: Is \(\sqrt{7x}\) an integer? (1) \(\sqrt{\frac{x}{7}}\) is an integer (2) \(\sqrt{28x}\) is an integer Can someone please explain why point 2 is not correct? What I did is that 28 is factored into => 2*2*7 so therefore I concluded x must have at least one 7. so if x has one seven then \sqrt{7x} must be an integer. Am I doing something wrong here?
Thanks! Alex A: let's say \(\sqrt{\frac{x}{7}}\) = m \(\sqrt{\frac{x*7}{7*7}}\) = m \(\sqrt{7x}\)/7 = m => \(\sqrt{7x}\) = 7*m => \(\sqrt{7x}\) is an integer. (m is given to be an integer) A is sufficient. B: let's say \(\sqrt{28x}\) = k 2*\(\sqrt{7x}\) = k \(\sqrt{7x}\) = k/2 Here the answer depends on the parity (evenness or oddness) of k and parity of k is unknown. Hence B is not sufficient. Final answer: A



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4063
Location: Canada

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
14 Oct 2018, 16:34
alex1233 wrote: Is \(\sqrt{7x}\) an integer?
(1) \(\sqrt{\frac{x}{7}}\) is an integer
(2) \(\sqrt{28x}\) is an integer
Target question: Is \(\sqrt{7x}\) an integer? Statement 1: \(\sqrt{\frac{x}{7}}\) is an integer Let's say that √(x/7) = k, where k is an integer Square both sides to get: x/7 = k² Multiply both side by 7 to get: x = 7k² This means 7x = 7(7k²) = 49k² So, √(7x) = √(49k²) = 7k Since k is an integer, we know that 7k is an integer. So, the answer to the target question is YES, √(7x) IS an integerSince we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: \(\sqrt{28x}\) is an integerThere are several values of x that satisfy statement 2. Here are two: Case a: x = 28, which means, √(7x) = √(196) = 14. So, in this case , the answer to the target question is YES, √(7x) IS an integerCase b: x = 9/28, which means, √(7x) = √(63/28) = some noninteger. So, in this case , the answer to the target question is NO, √(7x) is NOT an integerSince we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Intern
Joined: 02 Jan 2019
Posts: 1

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
28 Jan 2019, 08:29
For statement 1, x=7 and x=343 both satisfy the condition, so how can the answer be A?
For statement 2, x= 1/28 and x=7 satisfy the condition,
But when both combined, x=1/28 is not valid. and x=7 is the unique answer.
So Answer is C, how is the answer A, can anyone guide how my method is incorrect?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15447
Location: United States (CA)

Re: Is (7x)^1/2 an integer?
[#permalink]
Show Tags
28 Jan 2019, 12:38
anoopdev wrote: For statement 1, x=7 and x=343 both satisfy the condition, so how can the answer be A?
For statement 2, x= 1/28 and x=7 satisfy the condition,
But when both combined, x=1/28 is not valid. and x=7 is the unique answer.
So Answer is C, how is the answer A, can anyone guide how my method is incorrect? Hi anoopdev, When dealing with DS questions, you have to make sure that you are answering the question that is ASKED (and define whether the answer is consistent  meaning that it stays the same OR that it is inconsistent  meaning that it changes). Based on the information in Fact 1, you listed two possible values for X. Both of those values lead to the SAME answer to the question (re: YES, you would end up with an integer). That is a consistent result. All of the other potential values for X that 'fit' the information in Fact 1 will lead to the SAME answer to the given question, so Fact 1 is SUFFICIENT. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★




Re: Is (7x)^1/2 an integer?
[#permalink]
28 Jan 2019, 12:38






