Last visit was: 24 Jul 2024, 10:44 It is currently 24 Jul 2024, 10:44
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
avatar
Intern
Intern
Joined: 25 Mar 2018
Posts: 2
Own Kudos [?]: 27 [26]
Given Kudos: 0
Send PM
Most Helpful Reply
Manager
Manager
Joined: 03 Oct 2016
Posts: 96
Own Kudos [?]: 156 [5]
Given Kudos: 64
Send PM
General Discussion
Tutor
Joined: 08 May 2018
Affiliations: All Day Test Prep
Posts: 98
Own Kudos [?]: 92 [3]
Given Kudos: 1
Location: United States (IL)
Schools: Booth '20 (A)
GMAT 1: 770 Q51 V49
GRE 1: Q167 V167
GPA: 3.58
Send PM
avatar
Intern
Intern
Joined: 25 Mar 2018
Posts: 2
Own Kudos [?]: 27 [1]
Given Kudos: 0
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
1
Kudos
I agree. And I am considering x to be positive (8). However the question asks for sqrt of x. It doesn't suggest that sqrt of x is positive. hence it can be +- 2(2)^1/2. Am I missing something?
Manager
Manager
Joined: 08 Sep 2008
Posts: 105
Own Kudos [?]: 98 [1]
Given Kudos: 17
Location: India
Concentration: Operations, General Management
Schools: ISB '20
GPA: 3.8
WE:Operations (Transportation)
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
1
Kudos
When the GMAT gives you a square root symbol, it’s referring to one specific value: the positive square root. 

So from statement 1: x=2^3=8. Sufficient.
Statement 2: x^2=64
IxI=8; x can be +8 or,-8.
As per question stem x is positive. So only x=8 satisfied.
Hence sufficient

Ans: D

Sent from my ASUS_Z010D using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 94606
Own Kudos [?]: 643589 [3]
Given Kudos: 86737
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
3
Bookmarks
Expert Reply
vhsneha wrote:
If x is positive, what is the value of \(\sqrt{x}\)


(1) \(\sqrt[3]{x}=2\)

(2) x^2=64

Comment: The official answer is D. However, since the question stem doesn't state anything about the sign of x^1/2 (only that x is positive), i am not convinced that there is a unique answer since x^1/2 can be +- 2 {(2)^1/2}

PS: I tried using the math formula buttons. Didnt work for me. Apologize for the format


If x is positive, what is the value of \(\sqrt{x}\)?


(1) \(\sqrt[3]{x}=2\) --> take to the third power: x = 8 --> \(\sqrt{x}=\sqrt{8}\). Sufficient.

(2) x^2=64 --> x = 8 or x = -8. Since we are told that x is positive, then x = 8 and \(\sqrt{x}=\sqrt{8}\). Sufficient.

Answer: D.

vhsneha wrote:
Comment: The official answer is D. However, since the question stem doesn't state anything about the sign of x^1/2 (only that x is positive), i am not convinced that there is a unique answer since x^1/2 can be +- 2 {(2)^1/2}

PS: I tried using the math formula buttons. Didnt work for me. Apologize for the format


First of all, we are told that x is positive, so x cannot be \(-2\sqrt{2}\). Next, the square root cannot give a negative result, that is \(\sqrt{4}=2\) NOT +2 and -2. (In contrast the equation x^2 = 4 has TWO solutions x = 2 and x = -2).

arosman wrote:
You can't have the square root of a negative number. Irrational numbers are way beyond the scope of GMAT. If a question ask for \(\sqrt{x}\) you can assume x is positive or zero.


Yes, even roots from negative numbers are not defined for the GMAT (\(\sqrt[even]{negative}\) is undefined). So, you don't need complex numbers for the GMAT.

GMAT deals with only real numbers: integers (-3, -2, -1, 0, 1, 2, 3, ...), fractions/decimals (3/2, 4/3, 0.7, 17.5, ...) and irrational numbers (\(\sqrt{3}\), \(\sqrt{2}\), \(\pi\), ...).

Check for more below:

2. Properties of Integers



For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
Intern
Intern
Joined: 20 Sep 2020
Posts: 10
Own Kudos [?]: 1 [0]
Given Kudos: 93
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
1) x^1/3=2
which means x=2^3= 8
therefore x=8 and root x = root 8
(sufficient)

2) x^2=64
which means x=root 64, ie, 8
therefore, x=8 and root x= root 8
(sufficient)
Manager
Manager
Joined: 22 Apr 2021
Posts: 130
Own Kudos [?]: 11 [0]
Given Kudos: 409
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
KarishmaB

Madam, I did not get the answer. How could the answer be D? As per statement 2, x^2 = 64 which means x=8 and x^(1/2) could be +/- 2*(2)^(1/2). I would use another simple example to explain this, if x = 4 then square root of x could be +/-2.

Much to my surprise this question is of 5% difficulty level. Please help me with this concept. Thanks a lot in advance Madam!
Math Expert
Joined: 02 Sep 2009
Posts: 94606
Own Kudos [?]: 643589 [0]
Given Kudos: 86737
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
Expert Reply
waytowharton wrote:
KarishmaB

Madam, I did not get the answer. How could the answer be D? As per statement 2, x^2 = 64 which means x=8 and x^(1/2) could be +/- 2*(2)^(1/2). I would use another simple example to explain this, if x = 4 then square root of x could be +/-2.

Much to my surprise this question is of 5% difficulty level. Please help me with this concept. Thanks a lot in advance Madam!


I think you are missing the crucial info from the stem

If x is positive, what is the value of \(\sqrt{x}\)?

So, from x^2=64, when you get that x = 8 or x = -8, you should discard x = -8 because we are explicitly given that x is positive and you'll get only one value: x = 8, thus \(\sqrt{x}=\sqrt{8}=2\sqrt{2}\).

Does this make sense?
Manager
Manager
Joined: 22 Apr 2021
Posts: 130
Own Kudos [?]: 11 [0]
Given Kudos: 409
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
Bunuel wrote:
waytowharton wrote:
KarishmaB

Madam, I did not get the answer. How could the answer be D? As per statement 2, x^2 = 64 which means x=8 and x^(1/2) could be +/- 2*(2)^(1/2). I would use another simple example to explain this, if x = 4 then square root of x could be +/-2.

Much to my surprise this question is of 5% difficulty level. Please help me with this concept. Thanks a lot in advance Madam!


I think you are missing the crucial info from the stem

If x is positive, what is the value of \(\sqrt{x}\)?

So, from x^2=64, when you get that x = 8 or x = -8, you should discard x = -8 because we are explicitly given that x is positive and you'll get only one value: x = 8, thus \(\sqrt{x}=\sqrt{8}=2\sqrt{2}\).

Does this make sense?


Thanks Bunuel for your reply. I did not miss the condition that x is positive. But i would like to highlight that we are not given that x^(1/2) will be positive. It could be both positive and negative. Since square of neg is also positice. For example, If we are given x=4 then square root of x is +2 and -2.

Please do let me know flaw in my reasoning. Thanks in advance!

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 94606
Own Kudos [?]: 643589 [1]
Given Kudos: 86737
Send PM
If x is positive, what is the value of x^(1/2)? [#permalink]
1
Kudos
Expert Reply
waytowharton wrote:
Bunuel wrote:
waytowharton wrote:
KarishmaB

Madam, I did not get the answer. How could the answer be D? As per statement 2, x^2 = 64 which means x=8 and x^(1/2) could be +/- 2*(2)^(1/2). I would use another simple example to explain this, if x = 4 then square root of x could be +/-2.

Much to my surprise this question is of 5% difficulty level. Please help me with this concept. Thanks a lot in advance Madam!


I think you are missing the crucial info from the stem

If x is positive, what is the value of \(\sqrt{x}\)?

So, from x^2=64, when you get that x = 8 or x = -8, you should discard x = -8 because we are explicitly given that x is positive and you'll get only one value: x = 8, thus \(\sqrt{x}=\sqrt{8}=2\sqrt{2}\).

Does this make sense?


Thanks Bunuel for your reply. I did not miss the condition that x is positive. But i would like to highlight that we are not given that x^(1/2) will be positive. It could be both positive and negative. Since square of neg is also positice. For example, If we are given x=4 then square root of x is +2 and -2.

Please do let me know flaw in my reasoning. Thanks in advance!

Posted from my mobile device


So, you are saying that \(\sqrt{8}\) could be \(2\sqrt{2}\) or \(-2\sqrt{2}\). That's not true.

\(\sqrt{...}\) 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 \(x=\sqrt{9}=3\).


Thus, \(\sqrt{8}=2\sqrt{2}\) only.

Hope it helps.
Manager
Manager
Joined: 22 Apr 2021
Posts: 130
Own Kudos [?]: 11 [0]
Given Kudos: 409
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
Thanks a lot Bunuel! This is really very helpful.
Intern
Intern
Joined: 30 Jan 2022
Posts: 40
Own Kudos [?]: 7 [0]
Given Kudos: 28
Location: Canada
Concentration: Finance
GMAT 1: 670 Q49 V32
GMAT 2: 690 Q46 V40
GMAT 3: 680 Q49 V34
GMAT 4: 710 Q48 V39
GPA: 3.7
WE:Operations (Investment Banking)
Send PM
If x is positive, what is the value of x^(1/2)? [#permalink]
Bunuel wrote:
vhsneha wrote:
If x is positive, what is the value of \(\sqrt{x}\)


(1) \(\sqrt[3]{x}=2\)

(2) x^2=64

Comment: The official answer is D. However, since the question stem doesn't state anything about the sign of x^1/2 (only that x is positive), i am not convinced that there is a unique answer since x^1/2 can be +- 2 {(2)^1/2}

PS: I tried using the math formula buttons. Didnt work for me. Apologize for the format


If x is positive, what is the value of \(\sqrt{x}\)?


(1) \(\sqrt[3]{x}=2\) --> take to the third power: x = 8 --> \(\sqrt{x}=\sqrt{8}\). Sufficient.

(2) x^2=64 --> x = 8 or x = -8. Since we are told that x is positive, then x = 8 and \(\sqrt{x}=\sqrt{8}\). Sufficient.

Answer: D.

vhsneha wrote:
Comment: The official answer is D. However, since the question stem doesn't state anything about the sign of x^1/2 (only that x is positive), i am not convinced that there is a unique answer since x^1/2 can be +- 2 {(2)^1/2}

PS: I tried using the math formula buttons. Didnt work for me. Apologize for the format


First of all, we are told that x is positive, so x cannot be \(-2\sqrt{2}\). Next, the square root cannot give a negative result, that is \(\sqrt{4}=2\) NOT +2 and -2. (In contrast the equation x^2 = 4 has TWO solutions x = 2 and x = -2).

arosman wrote:
You can't have the square root of a negative number. Irrational numbers are way beyond the scope of GMAT. If a question ask for \(\sqrt{x}\) you can assume x is positive or zero.


Yes, even roots from negative numbers are not defined for the GMAT (\(\sqrt[even]{negative}\) is undefined). So, you don't need complex numbers for the GMAT.

GMAT deals with only real numbers: integers (-3, -2, -1, 0, 1, 2, 3, ...), fractions/decimals (3/2, 4/3, 0.7, 17.5, ...) and irrational numbers (\(\sqrt{3}\), \(\sqrt{2}\), \(\pi\), ...).

Check for more below:

2. Properties of Integers



For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread


Hey Bunuel, I still can't wrap my head around this question.

Although i DO agree that only x can be determined to be +8 based on the stem, how can we presume that the sqrt of +8 cannot be negative?

For example, given that x = +4, then sqrt of +4 can be +/-2.

multiplying -2*-2 will return the positive x value +4.


In the case of the question - why would this not apply..?

it could effectively be written as:

\([(-\sqrt{8})^2]^(1/3)\)

EDIT: i believe the confusing part about this questions is that the question is not asking you to TAKE the square root of x, but rather assume that the expression provided is already \(\sqrt{x}\), implying that the number will always be positive.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34067
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
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 Club Bot
Re: If x is positive, what is the value of x^(1/2)? [#permalink]
Moderator:
Math Expert
94606 posts