Last visit was: 27 May 2024, 00:41 It is currently 27 May 2024, 00:41
Toolkit
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

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.

# Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2)

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93470
Own Kudos [?]: 627014 [12]
Given Kudos: 81958
Senior Manager
Joined: 13 Feb 2018
Posts: 385
Own Kudos [?]: 386 [1]
Given Kudos: 50
GMAT 1: 640 Q48 V28
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 7982
Own Kudos [?]: 4128 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18909
Own Kudos [?]: 22324 [4]
Given Kudos: 285
Location: United States (CA)
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
2
Kudos
2
Bookmarks
Archit3110 wrote:
Bunuel wrote:
Is x an integer?

(1) $$x^3 = 8$$
(2) $$x = \sqrt{4}$$

DS22602.01
OG2020 NEW QUESTION

Statement One Alone:

x^3 = 8

Since x^3 = 8, x = 2, then x is an integer.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

x = √4

Since x = √4, x = 2, then x is an integer. (Recall that the square root symbol means to take the principal square root of a number, which is only the positive square root.)

Statement two alone is sufficient to answer the question.

GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11697 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
2
Kudos
1
Bookmarks
Hi All,

We're asked if X is an INTEGER. This is a YES/NO question. This question is built around some standard math rules and Number Properties.

(1) X^3 = 8

With Fact 1, we're cubing the value of X and ending with a POSITIVE value - thus, X MUST be positive. Here, the value of X = +2 and the answer to the question is YES.
Fact 1 is SUFFICIENT

(2) X =√4

With Fact 1, we have a number that's square-rooted for the value of X. The square root of a number has just ONE solution: a POSITIVE one. Here, we're dealing with the positive square-root of 4, so the value of X = +2 and the answer to the question is YES.
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich
Retired Moderator
Joined: 31 May 2017
Posts: 748
Own Kudos [?]: 672 [0]
Given Kudos: 53
Concentration: Technology, Strategy
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
X is an Integer?

Statement 1:$$X^3 = 8$$
This gives , X=2. Option A alone is sufficient

Statement 2: X = √4
This gives x=2 , Option B alone is sufficient

Ans: D
Intern
Joined: 06 May 2019
Posts: 24
Own Kudos [?]: 5 [0]
Given Kudos: 132
Location: India
Concentration: General Management, Marketing
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
Bunuel. option B. according to Gmat, can we say that x!=2?
Math Expert
Joined: 02 Sep 2009
Posts: 93470
Own Kudos [?]: 627014 [0]
Given Kudos: 81958
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
ShivamoggaGaganhs wrote:
Bunuel. option B. according to Gmat, can we say that x!=2?

Not sure I understand what yo mean but $$x = \sqrt{4}$$ means that x = 2 only, nothing else.
Manager
Joined: 30 Jan 2020
Posts: 167
Own Kudos [?]: 79 [0]
Given Kudos: 528
Location: India
WE:Accounting (Accounting)
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
Bunuel wrote:
Is x an integer?

(1) $$x^3 = 8$$
(2) $$x = \sqrt{4}$$

DS22602.01
OG2020 NEW QUESTION

Statement 1: x^3=8 > x has to be 2 which is an integer, note: x cannot be -2 as x^3 is equal to 8. SUFFICIENT
Statement 2: x=squareroot 4. Square root of 4 is (+)(-) 2, i.e it can be both positive and negative therefore integer. SUFFICIENT

Hope that helps!
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11697 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
1
Kudos
1
Bookmarks
hemantbafna wrote:
Bunuel wrote:
Is x an integer?

(1) $$x^3 = 8$$
(2) $$x = \sqrt{4}$$

DS22602.01
OG2020 NEW QUESTION

Statement 1: x^3=8 > x has to be 2 which is an integer, note: x cannot be -2 as x^3 is equal to 8. SUFFICIENT
Statement 2: x=squareroot 4. Square root of 4 is (+)(-) 2, i.e it can be both positive and negative therefore integer. SUFFICIENT

Hope that helps!

Hi hemantbafna,

You selected the correct answer, but there's a subtle rule here that you appear to have missed. On the GMAT, the result of a square root of a positive number can ONLY be positive. For example....

√4 = +2

However, a squared-term that equals a positive number can lead to a positive or negative result. For example...

X^2 = 4..... X = +2 or -2.

GMAT assassins aren't born, they're made,
Rich
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6003
Own Kudos [?]: 13519 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
Bunuel wrote:
Is x an integer?

(1) $$x^3 = 8$$
(2) $$x = \sqrt{4}$$

DS22602.01
OG2020 NEW QUESTION

Wanna make solving the Official Questions interesting???

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
Intern
Joined: 31 Jul 2021
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 42
GMAT 1: 700 Q50 V33
Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
x^3 = 8 actually has 3 solutions ;

$$x^3 - 8 =0$$
$$(x-2)(x^2+2x+4)=0$$
1 for the above equation $$x=2$$
other 2 solutions are imaginary $$[-1+i\sqrt{3}], [-1-i\sqrt{3}]$$

so we cant say x is an interger or imaginary,

Bunuel
EMPOWERgmatRichC
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11697 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
1
Kudos
Hi Kanna444,

Imaginary numbers are NOT a subject that the GMAT 'tests' - and that ultimately means that you are NOT expected to think in those terms when answering GMAT questions.

GMAT assassins aren't born, they're made,
Rich
Manager
Joined: 30 Nov 2018
Posts: 174
Own Kudos [?]: 149 [0]
Given Kudos: 79
Location: India
Concentration: Strategy, Marketing
GPA: 4
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
Is x an integer?

(1) x^3=8

Since 8 is a perfect cube, we can easily say x = 2 (INTEGER)

(2) x=√4

Since √4 = +2, we can say that X is an integer

OPTION D
Manager
Joined: 10 Jan 2023
Posts: 152
Own Kudos [?]: 106 [0]
Given Kudos: 58
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
Bunuel bb EMPOWERgmatRichC

can you please clarify this case?

Kanna444 wrote:
x^3 = 8 actually has 3 solutions ;

$$x^3 - 8 =0$$
$$(x-2)(x^2+2x+4)=0$$
1 for the above equation $$x=2$$
other 2 solutions are imaginary $$[-1+i\sqrt{3}], [-1-i\sqrt{3}]$$

so we cant say x is an interger or imaginary,

Bunuel
EMPOWERgmatRichC
Math Expert
Joined: 02 Sep 2009
Posts: 93470
Own Kudos [?]: 627014 [1]
Given Kudos: 81958
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
1
Kudos
vedha0 wrote:
Bunuel bb EMPOWERgmatRichC

can you please clarify this case?

Kanna444 wrote:
x^3 = 8 actually has 3 solutions ;

$$x^3 - 8 =0$$
$$(x-2)(x^2+2x+4)=0$$
1 for the above equation $$x=2$$
other 2 solutions are imaginary $$[-1+i\sqrt{3}], [-1-i\sqrt{3}]$$

so we cant say x is an interger or imaginary,

Bunuel
EMPOWERgmatRichC

On the GMAT, all numbers are assumed to be real numbers by default.
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11697 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
1
Kudos
vedha0 wrote:
Bunuel bb EMPOWERgmatRichC

can you please clarify this case?

Kanna444 wrote:
x^3 = 8 actually has 3 solutions ;

$$x^3 - 8 =0$$
$$(x-2)(x^2+2x+4)=0$$
1 for the above equation $$x=2$$
other 2 solutions are imaginary $$[-1+i\sqrt{3}], [-1-i\sqrt{3}]$$

so we cant say x is an interger or imaginary,

Bunuel
EMPOWERgmatRichC

Hi vedha0,

Imaginary numbers are NOT a subject that the GMAT 'tests' - and that ultimately means that you are NOT expected to think in those terms when answering GMAT questions.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com
Re: Is x an integer? (1) x^3 = 8 (2) x = 4^(1/2) [#permalink]
Moderator:
Math Expert
93470 posts