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GMATmission
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x Updated on: 16 Nov 2025, 01:06
Originally posted by GMATmission on 24 Aug 2011, 23:41.
Last edited by Bunuel on 16 Nov 2025, 01:06, edited 4 times in total.
Renamed the topic, edited the question and added the OA.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

51% (01:47) correct 49% (01:44) wrong based on 419 sessions

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Is \(\sqrt{x}\) a prime number?

(1) |3x - 7| = 2x + 2
(2) x^2 = 9x
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C
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 25 Aug 2011, 00:05
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the answer is C

1 |3x-7|=2x+2

--> -(3x-7)=2x+2
on solving this we get x=1
--> +(3x-7)=2x+2
on solving this we get x=9
so insufficient

B ) x^2=9x
x^2-9x=0
x(x-9)=0
hence x=0,9
insuff

combining both will give x=9
hence sqroot(9) will give 3 which is a prime number
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 25 Aug 2011, 04:28
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(1) mod (3x-7) = 2x+2
3x-7=2x+2
x=9

-3x+7=2x+2
x=1
x can be 9 or 1, 9^1/2 is 3 (prime) while 1^1/2 is 1 (not prime)
INSUFFICIENT

(2) x^2 = 9x
x(x-9)=0
x can only have two solutions 0 or 9
INSUFFICIENT

But combining the two statements we have 9 in both so the answer is 9
9^1/2 = 3, which is prime
So the answer is C
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 26 Aug 2011, 08:45
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the answer is C

1 |3x-7|=2x+2

--> -(3x-7)=2x+2
on solving this we get x=1
--> +(3x-7)=2x+2
on solving this we get x=9
so insufficient

B ) x^2=9x
x^2-9x=0
x(x-9)=0
hence x=0,9
insuff

combining both will give x=9
hence sqroot(9) will give 3 which is a prime number
Show more

OA is C. I was wondering whether we should consider negative values. Sq root of 9 = +/-3. +3 is prime and -3 is not. What do you say?
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 26 Aug 2011, 09:15
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When we take the square root of a number in the GMAT the answer is always positive.
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 27 Aug 2011, 14:42
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GMATmission
OA is C. I was wondering whether we should consider negative values. Sq root of 9 = +/-3. +3 is prime and -3 is not. What do you say?
Show more

nammers
When we take the square root of a number in the GMAT the answer is always positive.
Show more


x has 2 roots i.e. sqrt(x) and - sqrt(x).

The question is asking about positive root i.e. sqrt(x). so sqrt(x) has always a +ve value.

Similarly sqrt(9) = 3.
-sqrt(9) = -3.
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 10 Jul 2014, 01:40
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Is x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) x^2 = 9x
Show more

Hi Bunnel,

Could you please provide your comments on this?

I am using following logic

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5
x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x= 0 or 9

here we are getting 2 values so not sufficient.
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 10 Jul 2014, 02:04
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GMATmission
Is x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) x^2 = 9x

Hi Bunnel,

Could you please provide your comments on this?

I am using following logic

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5
x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x= 0 or 9

here we are getting 2 values so not sufficient.
Show more

2 questions:

1. Does x=9 satisfy the equation?
2. Why do you say that when x>=-1, then |3x-7| = -(3x-7)?
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 10 Jul 2014, 03:14
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Bunuel
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GMATmission
Is x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) x^2 = 9x

Hi Bunnel,

Could you please provide your comments on this?

I am using following logic

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5
x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x= 0 or 9

here we are getting 2 values so not sufficient.

2 questions:

1. Does x=9 satisfy the equation?
2. Why do you say that when x>=-1, then |3x-7| = -(3x-7)?
Show more

Hi Bunnel,

1. Yes x=9 satisfy the equation.
2. I told x>= -1 because in st1 it is given that |3x-7| = 2x+2. Here LHS. is in modulus so it is >=0. so RHS should be >=0 2x+2>= 0 --> 2x>=-2-->x>=-1


Thanks
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 10 Jul 2014, 03:56
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Hi Bunnel,

Could you please provide your comments on this?

I am using following logic

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5
x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x= 0 or 9

here we are getting 2 values so not sufficient.

2 questions:

1. Does x=9 satisfy the equation?
2. Why do you say that when x>=-1, then |3x-7| = -(3x-7)?

Hi Bunnel,

1. Yes x=9 satisfy the equation.
2. I told x>= -1 because in st1 it is given that |3x-7| = 2x+2. Here LHS. is in modulus so it is >=0. so RHS should be >=0 2x+2>= 0 --> 2x>=-2-->x>=-1


Thanks
Show more

You did not understand my second question. Yes, from (1) x>=-1 BUT why does that mean that |3x-7| = -(3x-7)?

P.S. It's Bunuel not Bunnel. :-D
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Hey Bunuel I know I was using Bunnel bcz in my area where I live in india its mean wise. So I used this word for you.

i think i got confusion here |3x-7| = -(3x-7) as i thought putting -1 makes it negative in modulus |-3-7| . but I think this is not the case and it should be |3x-7| = 3x-7.

Thanks Bunuel for all your replies. Please clarify this
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 10 Jul 2014, 12:30
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Hey Bunuel I know I was using Bunnel bcz in my area where I live in india its mean wise. So I used this word for you.

i think i got confusion here |3x-7| = -(3x-7) as i thought putting -1 makes it negative in modulus |-3-7| . but I think this is not the case and it should be |3x-7| = 3x-7.

Thanks Bunuel for all your replies. Please clarify this
Show more

That's not correct.

|3x-7| = 3x-7, when x > 7/3.
|3x-7| = -(3x-7), when x <= 7/3.

x>=-1 is not sufficient info to say whether |3x-7| = 3x-7 or |3x-7| = -(3x-7). For example, if x=0<7/3, then |3x-7| = -(3x-7) but if x=100>7/3, then |3x-7| = 3x-7.

Hope it's clear.
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 01 Sep 2014, 03:25
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Hey bunuel, In Manhattan gmat book its written that absolute values have +ve or -ve value. For +ve value the sign after solving is positive then its a correct soln, same goes for -ve. But here when we solve for +ve value we get +9, thats a correct soln, but for -ve soln we get +1, which isnt negative, so its not a legitimte soln and hence should be ignored, acc to MGMAT. Plz help !
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 01 Sep 2014, 03:35
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sunaimshadmani
Hey bunuel, In Manhattan gmat book its written that absolute values have +ve or -ve value. For +ve value the sign after solving is positive then its a correct soln, same goes for -ve. But here when we solve for +ve value we get +9, thats a correct soln, but for -ve soln we get +1, which isnt negative, so its not a legitimte soln and hence should be ignored, acc to MGMAT. Plz help !
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Not sure I understand what you mean there.

As for the roots of |3x - 7| = 2x + 2: both x = 1 and x = 9 satisfy this equation, thus both are valid solutions.

Maybe if you could show your work, I'd be able to say more.
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 06 Sep 2014, 11:05
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abhi398
the answer is C

1 |3x-7|=2x+2

--> -(3x-7)=2x+2
on solving this we get x=1
--> +(3x-7)=2x+2
on solving this we get x=9
so insufficient

B ) x^2=9x
x^2-9x=0
x(x-9)=0
hence x=0,9
insuff

combining both will give x=9
hence sqroot(9) will give 3 which is a prime number
Show more



why cant we take x^2=9x as x.x=9.x
so x on both sides get cancelled
hence x=9
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 15 Nov 2025, 19:13
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Im confused here,

1) tells us x = 9 or 1.
2) tells us x = 9.

x^1/2 for x=9 can be -3 or 3.

Only √9 means x = 3.

Hence statement is insuff as answer can be -3 (not prime) or 3 (prime). Anyone clarify please?
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Is x^1/2 a prime number? (1) |3x - 7| = 2x + 2 (2) x^2 = 9x 16 Nov 2025, 01:07
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Rohanx9
Im confused here,

1) tells us x = 9 or 1.
2) tells us x = 9.

x^1/2 for x=9 can be -3 or 3.

Only √9 means x = 3.

Hence statement is insuff as answer can be -3 (not prime) or 3 (prime). Anyone clarify please?
Show more
Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

  • Word Problems
  • Work Problems
  • Distance Problems
  • Mixture Problems
  • Percent and Interest Problems
  • Overlapping Sets Problems
  • Statistics Problems
  • Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.­
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