Author 
Message 
TAGS:

Hide Tags

Director
Joined: 03 Sep 2006
Posts: 871

Is root{x} a prime number? [#permalink]
Show Tags
26 Jan 2012, 06:41
2
This post received KUDOS
8
This post was BOOKMARKED
Question Stats:
48% (01:57) correct
52% (01:01) wrong based on 595 sessions
HideShow timer Statistics
Is \(\sqrt{x}\) a prime number? (1) \(3x7=2x+2\) (2) \(x^2=9x\)
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 26 Jan 2012, 07:29, edited 1 time in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 39588

Is root{x} a prime number? [#permalink]
Show Tags
17 Oct 2012, 15:17
5
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
abikumar wrote: You guys have taken Sqrt(9) as 3 where as it should be plus or minus 3. In this case, statements (1) and (2) taken together wont be sufficient hence the answer should be E. Please explain. I know OA is C but it may be wrong.
Note that from statement 1: x>7/3 but root of x is not required to be greater than 7/3 or in fact sqrt(x) has no conditions on it so that logic wont work too. The red part is not correct. The point here is that square root function cannot give negative result > \(\sqrt{some \ expression}\geq{0}\), for example \(\sqrt{25}=5\) (not +5 and 5). In contrast, the equation \(x^2=25\) has TWO solutions, +5 and 5, because both 5^2 and (5)^2 equal to 25. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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



Manager
Joined: 13 Oct 2012
Posts: 70
Concentration: General Management, Leadership

Re: Is root{x} a prime number? [#permalink]
Show Tags
03 Jan 2013, 23:12
2
This post received KUDOS
solving 3x7 = 2x + 2 > x = 1 or 9 > Not Suff solving x^2 = 9x > x = 0 or 9 > Not Suff Together suff



Math Expert
Joined: 02 Sep 2009
Posts: 39588

Re: Square root is prime? [#permalink]
Show Tags
26 Jan 2012, 07:28
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
LM wrote: Is \(\sqrt{x}\)
(1) \(3x7=2x+2\)
(2) \(x^2=9x\) Is \(\sqrt{x}\) a prime number? 1) \(3x7=2x+2\) > we have one check point 7/3 (check point  the value of x for which an expression in absolute value equals to zero): A. \(x\leq{\frac{7}{3}}\) > \(3x7\leq{0}\) hence \(3x7=(3x7)\) > \((3x7)=2x+2\) > \(x=1\) > \(\sqrt{1}=1\neq{prime}\). B. A. \(x>{\frac{7}{3}}\) > \(3x7>0\) hence \(3x7=3x7\) > \(3x7=2x+2\) > \(x=9\) > \(\sqrt{9}=3=prime\). Two different answer. Not sufficient. 2) \(x^2=9x\) > \(x(x9)=0\) > \(x=0\) or \(x=9\) > \(\sqrt{0}=0\neq{prime}\) or \(\sqrt{9}=3=prime\). Not sufficient. (1)+(2) Intersection of values from (1) and (2) is \(x=9\) > \(\sqrt{9}=3=prime\). Sufficient. Answer: C.
_________________
New to the Math Forum? Please read this: 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
Joined: 07 Aug 2012
Posts: 40
GMAT 1: 690 Q49 V34 GMAT 2: 750 Q51 V40

Re: Is root{x} a prime number? [#permalink]
Show Tags
17 Oct 2012, 14:11
1
This post received KUDOS
You guys have taken Sqrt(9) as 3 where as it should be plus or minus 3. In this case, statements (1) and (2) taken together wont be sufficient hence the answer should be E. Please explain. I know OA is C but it may be wrong.
Note that from statement 1: x>7/3 but root of x is not required to be greater than 7/3 or in fact sqrt(x) has no conditions on it so that logic wont work too.



Math Expert
Joined: 02 Sep 2009
Posts: 39588

Re: Is root{x} a prime number? [#permalink]
Show Tags
21 Oct 2012, 04:25
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India

Re: Is root{x} a prime number? [#permalink]
Show Tags
17 Jan 2013, 20:58
Apex231 wrote: prinkashar wrote: As from the first statement x >1 so it can be 0 too. Second statement gives values 0 and 3
Even after combining both statements, As we are not sure of answer ( 0 or 3 ) i.e why I concluded E.
I know am skipping few imp. concepts here please help. any explanation for this? x > 1 implies that whatever value of x will satisfy this equation, it will be greater than 1. It does not mean that every value greater than 1 will satisfy it. You cannot take one part of an equation in isolation and solve from it. 3x7=2x+2 Point is that no value of x less than 1 can satisfy this equation. But, it doesn't mean that every value greater than or equal to 1 will satisfy it. When you solve this equation, you get x = 1 or 9 (both greater than 1). No other value of x satisfies this equation. If you put x = 0, you get 7 = 2 which is not true. So x cannot be 0.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Senior Manager
Joined: 03 Dec 2012
Posts: 339

Re: Square root is prime? [#permalink]
Show Tags
29 Nov 2013, 23:52
1
This post received KUDOS
Bunuel wrote: LM wrote: Is \(\sqrt{x}\)
(1) \(3x7=2x+2\)
(2) \(x^2=9x\) Is \(\sqrt{x}\) a prime number? 1) \(3x7=2x+2\) > we have one check point 7/3 (check point  the value of x for which an expression in absolute value equals to zero): A. \(x\leq{\frac{7}{3}}\) > \(3x7\leq{0}\) hence \(3x7=(3x7)\) > \((3x7)=2x+2\) > \(x=1\) > \(\sqrt{1}=1\neq{prime}\). B. A. \(x>{\frac{7}{3}}\) > \(3x7>0\) hence \(3x7=3x7\) > \(3x7=2x+2\) > \(x=9\) > \(\sqrt{9}=3=prime\). Two different answer. Not sufficient. 2) \(x^2=9x\) > \(x(x9)=0\) > \(x=0\) or \(x=9\) > \(\sqrt{0}=0\neq{prime}\) or \(\sqrt{9}=3=prime\). Not sufficient. (1)+(2) Intersection of values from (1) and (2) is \(x=9\) > \(\sqrt{9}=3=prime\). Sufficient. Answer: C. Bunuel, I have a question. Usually while solving modulus questions we take two cases 1) x>0 2) x<0. According to the first statement when x>0 we get x=9 which is valid, but when x<0 we get x=1 (which is not valid). Now, in some of the earlier questions when x<0 and if we got a positive value for it we neglected it and considered that x had only one valid value. In this question why hasn't something similar been done



Intern
Joined: 07 Aug 2012
Posts: 40
GMAT 1: 690 Q49 V34 GMAT 2: 750 Q51 V40

Re: Is root{x} a prime number? [#permalink]
Show Tags
17 Oct 2012, 22:34
ohh yes. Thanks Bunuel. I read other articles and realized what you have said is followed by GMAT. Anyways, i appreciate the explanation, thanks for the information.



Intern
Joined: 28 Sep 2012
Posts: 9
Concentration: General Management, International Business
GMAT Date: 01252013
GPA: 3.38

Re: Is root{x} a prime number? [#permalink]
Show Tags
20 Oct 2012, 18:49
Please correct me if i am wrong x\sqrt{2}=9x if we divide both sides by x then we get x= 9 which makes B sufficient. isnt it??



Intern
Joined: 28 Sep 2012
Posts: 9
Concentration: General Management, International Business
GMAT Date: 01252013
GPA: 3.38

Re: Is root{x} a prime number? [#permalink]
Show Tags
21 Oct 2012, 10:12
Bunuel wrote: manjusu wrote: Please correct me if i am wrong x\sqrt{2}=9x if we divide both sides by x then we get x= 9 which makes B sufficient. isnt it?? Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.So, if you divide (reduce) \(x^2=9x\) by \(x\), you assume, with no ground for it, that \(x\) does not equal to zero thus exclude a possible solution (notice that both x=9 AND x=0 satisfy the equation). Hope it's clear. got it!!! Thanks



Intern
Joined: 25 Jul 2012
Posts: 40
Concentration: Organizational Behavior, General Management
GMAT 1: 610 Q47 V26 GMAT 2: 640 Q49 V27
GPA: 4

Re: Is root{x} a prime number? [#permalink]
Show Tags
18 Nov 2012, 22:46
Hi Bunuel, There is one confusion .In many of your posts you have suggested whenever we have modulus at one side (Foreg: LHS in the first statement here). Why can't we compare the RHS as below 2x +2 >=0(LHS absolute value so always above or equal zero) x >1 In this case answer could be different ie E Please suggest where I am doing wrong
_________________
PLAN >>> EXECUTE >>> MEASURE



Math Expert
Joined: 02 Sep 2009
Posts: 39588

Re: Is root{x} a prime number? [#permalink]
Show Tags
19 Nov 2012, 04:00



Intern
Joined: 25 Jul 2012
Posts: 40
Concentration: Organizational Behavior, General Management
GMAT 1: 610 Q47 V26 GMAT 2: 640 Q49 V27
GPA: 4

Re: Is root{x} a prime number? [#permalink]
Show Tags
20 Nov 2012, 09:09
As from the first statement x >1 so it can be 0 too. Second statement gives values 0 and 3 Even after combining both statements, As we are not sure of answer ( 0 or 3 ) i.e why I concluded E. I know am skipping few imp. concepts here please help.
_________________
PLAN >>> EXECUTE >>> MEASURE



Current Student
Joined: 27 Jun 2012
Posts: 411
Concentration: Strategy, Finance

Re: Is root{x} a prime number? [#permalink]
Show Tags
17 Jan 2013, 01:21
Apex231 wrote: prinkashar wrote: As from the first statement x >1 so it can be 0 too. Second statement gives values 0 and 3
Even after combining both statements, As we are not sure of answer ( 0 or 3 ) i.e why I concluded E.
I know am skipping few imp. concepts here please help. any explanation for this? From statement 1, you only have two roots, x = 1 or 9. Its not a range of numbers.
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Manager
Joined: 03 Oct 2009
Posts: 62

Re: Is root{x} a prime number? [#permalink]
Show Tags
17 Jan 2013, 19:26
PraPon wrote: Apex231 wrote: prinkashar wrote: As from the first statement x >1 so it can be 0 too. Second statement gives values 0 and 3
Even after combining both statements, As we are not sure of answer ( 0 or 3 ) i.e why I concluded E.
I know am skipping few imp. concepts here please help. any explanation for this? From statement 1, you only have two roots, x = 1 or 9. Its not a range of numbers. I am referring to one of the posts above which mentions following for stmt 1 2x +2 >=0(LHS absolute value so always above or equal zero) x >1 In this case answer could be different ie E



Intern
Joined: 16 Jun 2012
Posts: 5
Concentration: General Management, Finance
GPA: 3.22

Re: Is root{x} a prime number? [#permalink]
Show Tags
20 Jan 2013, 22:24
VeritasPrepKarishma wrote: Apex231 wrote: prinkashar wrote: As from the first statement x >1 so it can be 0 too. Second statement gives values 0 and 3
Even after combining both statements, As we are not sure of answer ( 0 or 3 ) i.e why I concluded E.
I know am skipping few imp. concepts here please help. any explanation for this? x > 1 implies that whatever value of x will satisfy this equation, it will be greater than 1. It does not mean that every value greater than 1 will satisfy it. You cannot take one part of an equation in isolation and solve from it. 3x7=2x+2 Point is that no value of x less than 1 can satisfy this equation. But, it doesn't mean that every value greater than or equal to 1 will satisfy it. When you solve this equation, you get x = 1 or 9 (both greater than 1). No other value of x satisfies this equation. If you put x = 0, you get 7 = 2 which is not true. So x cannot be 0. simply... for condition 1...square both sides... x=9 or x=1 we get two solutions for cndition 2..we get x=9 therefore, both statements are reqd.



Math Expert
Joined: 02 Sep 2009
Posts: 39588

Re: Square root is prime? [#permalink]
Show Tags
30 Nov 2013, 04:12
mohnish104 wrote: Bunuel wrote: LM wrote: Is \(\sqrt{x}\)
(1) \(3x7=2x+2\)
(2) \(x^2=9x\) Is \(\sqrt{x}\) a prime number? 1) \(3x7=2x+2\) > we have one check point 7/3 (check point  the value of x for which an expression in absolute value equals to zero): A. \(x\leq{\frac{7}{3}}\) > \(3x7\leq{0}\) hence \(3x7=(3x7)\) > \((3x7)=2x+2\) > \(x=1\) > \(\sqrt{1}=1\neq{prime}\). B. A. \(x>{\frac{7}{3}}\) > \(3x7>0\) hence \(3x7=3x7\) > \(3x7=2x+2\) > \(x=9\) > \(\sqrt{9}=3=prime\). Two different answer. Not sufficient. 2) \(x^2=9x\) > \(x(x9)=0\) > \(x=0\) or \(x=9\) > \(\sqrt{0}=0\neq{prime}\) or \(\sqrt{9}=3=prime\). Not sufficient. (1)+(2) Intersection of values from (1) and (2) is \(x=9\) > \(\sqrt{9}=3=prime\). Sufficient. Answer: C. Bunuel, I have a question. Usually while solving modulus questions we take two cases 1) x>0 2) x<0. According to the first statement when x>0 we get x=9 which is valid, but when x<0 we get x=1 (which is not valid). Now, in some of the earlier questions when x<0 and if we got a positive value for it we neglected it and considered that x had only one valid value. In this question why hasn't something similar been done Both x=1 and x=9 are valid for (1). Please elaborate what you mean?
_________________
New to the Math Forum? Please read this: 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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15912

Re: Is root{x} a prime number? [#permalink]
Show Tags
24 Dec 2015, 06:20
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 03 Aug 2015
Posts: 64
Concentration: Strategy, Technology

Re: Is root{x} a prime number? [#permalink]
Show Tags
25 Dec 2015, 00:24
Bunuel, I have a question. Usually while solving modulus questions we take two cases 1) x>0 2) x<0. According to the first statement when x>0 we get x=9 which is valid, but when x<0 we get x=1 (which is not valid). Now, in some of the earlier questions when x<0 and if we got a positive value for it we neglected it and considered that x had only one valid value. In this question why hasn't something similar been done[/quote]
Both x=1 and x=9 are valid for (1). Please elaborate what you mean?[/quote]
Bunel, I too have the same doubt in my mind. I will try to explain it.
By taking condition, X>0, i got the value of X as 9
And by taking the condition X<0, I have got the solution as X=1, Which is not a valid solution with the given condition.
So i took X=9 only and got the answer as A.
Pls explain how X=1 with the condition X<0 is valid.
Thanks in advance




Re: Is root{x} a prime number?
[#permalink]
25 Dec 2015, 00:24



Go to page
1 2
Next
[ 25 posts ]




