GMAT Changed on April 16th - Read about the latest changes here

 It is currently 21 Apr 2018, 17:47

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If a and b are positive integer,is (ab)^(1/3) an integer?

Author Message
TAGS:

### Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 556
GPA: 2.81
If a and b are positive integer,is (ab)^(1/3) an integer? [#permalink]

### Show Tags

24 Jun 2016, 12:16
15
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

54% (00:58) correct 46% (01:23) wrong based on 287 sessions

### HideShow timer Statistics

If a and b are positive integer, is $$\sqrt[3]{ab}$$ an integer?

(1) $$\sqrt{a}$$ is an integer

(2) $$b=\sqrt{a}$$

OG Q 2017(Book Question: 300)
[Reveal] Spoiler: OA

_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Senior Manager
Joined: 22 Jun 2016
Posts: 250
Re: If a and b are positive integer,is (ab)^(1/3) an integer? [#permalink]

### Show Tags

24 Jun 2016, 13:32
1
KUDOS
1
This post was
BOOKMARKED
Statement 1: It is clearly insufficient as there is no information about b.

Statement 2: It is given in the question that a and b are integers. So, b=sqrt(a) is an integer.
(a*b)^1/3 = (a ^ (1+1/2))^(1/3) = (a^3/2)^(1/3) = a^(1/2) = sqrt (a) = b (b is an integer)
So, Statement 2 is sufficient.

------------------------------------

P.S. Don't forget to give kudos
_________________

P.S. Don't forget to give Kudos

Manager
Joined: 22 Feb 2016
Posts: 101
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Re: If a and b are positive integer,is (ab)^(1/3) an integer? [#permalink]

### Show Tags

14 Oct 2016, 08:23
In this case:
3sqrt(ab)= integer, we need to know if the product of a and b is a cube of either a or b or any other number.

Case1: nothing is mentioned about one variable NS
Case2: B=sqrt(a)
hence B^2=A

Putting it in the given equation we have b^2*B= B^3.
Hence the cube root is an interger.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3391
Location: India
GPA: 3.5
Re: If a and b are positive integer,is (ab)^(1/3) an integer? [#permalink]

### Show Tags

15 Oct 2016, 07:54
AbdurRakib wrote:
If a and b are positive integer,is $$\sqrt[3]{ab}$$ an integer?

(1) $$\sqrt{a}$$ is an integer

(2) b=$$\sqrt{a}$$

OG Q 2017(Book Question: 300)

FROM STATEMENT - I

We will be unable to comment on $$\sqrt[3]{ab}$$ from one variable $$\sqrt{a}$$, we need information on the other variable $$b$$ to ascertain the value.

FROM STATEMENT - II

This statement is sufficient , because we have the relationship between the two variable...

Hence , correct answer will be Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

PS : Feel free to revert in case of any doubt..
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Manager
Joined: 17 Aug 2015
Posts: 102
Re: If a and b are positive integer,is (ab)^(1/3) an integer? [#permalink]

### Show Tags

17 Jan 2017, 22:16
Abhishek009 wrote:
AbdurRakib wrote:
If a and b are positive integer,is $$\sqrt[3]{ab}$$ an integer?

(1) $$\sqrt{a}$$ is an integer

(2) b=$$\sqrt{a}$$

OG Q 2017(Book Question: 300)

FROM STATEMENT - I

We will be unable to comment on $$\sqrt[3]{ab}$$ from one variable $$\sqrt{a}$$, we need information on the other variable $$b$$ to ascertain the value.

FROM STATEMENT - II

This statement is sufficient , because we have the relationship between the two variable...

Hence , correct answer will be Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

PS : Feel free to revert in case of any doubt..

Thanks ..do you mean the specific relationship or just any relationship in your analysis of statement 2?
If we have the specific relationship which is described above, then shoud we not check by subsitituting in the prompt expression?

If for example I take another relationship ..say a= b/2..
cubroot(ab) = cubroot(b^2/2)
now let us take b = 4 .. b^2 = 16 and cubroot(b^2/2) = cubroot(8) = 2.. so here we get a yes answer ..

if we take b = 3 b^2 = 9 cubroot(9/2) is not an integer.. so we get a no answer.

I am finding it difficult to understand how just knowing that a relationship exists is sufficient to answer the question..
Manager
Joined: 17 May 2015
Posts: 222
Re: If a and b are positive integer,is (ab)^(1/3) an integer? [#permalink]

### Show Tags

17 Jan 2017, 22:52
1
KUDOS
2
This post was
BOOKMARKED
ajdse22 wrote:
Abhishek009 wrote:
AbdurRakib wrote:
If a and b are positive integer,is $$\sqrt[3]{ab}$$ an integer?

(1) $$\sqrt{a}$$ is an integer

(2) b=$$\sqrt{a}$$

OG Q 2017(Book Question: 300)

FROM STATEMENT - I

We will be unable to comment on $$\sqrt[3]{ab}$$ from one variable $$\sqrt{a}$$, we need information on the other variable $$b$$ to ascertain the value.

FROM STATEMENT - II

This statement is sufficient , because we have the relationship between the two variable...

Hence , correct answer will be Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

PS : Feel free to revert in case of any doubt..

Thanks ..do you mean the specific relationship or just any relationship in your analysis of statement 2?
If we have the specific relationship which is described above, then shoud we not check by subsitituting in the prompt expression?

If for example I take another relationship ..say a= b/2..
cubroot(ab) = cubroot(b^2/2)
now let us take b = 4 .. b^2 = 16 and cubroot(b^2/2) = cubroot(8) = 2.. so here we get a yes answer ..

if we take b = 3 b^2 = 9 cubroot(9/2) is not an integer.. so we get a no answer.

I am finding it difficult to understand how just knowing that a relationship exists is sufficient to answer the question..

Hi ajdse22,

You have correctly pointed out that not any relation will work. But, the relationship given in statement 2 will work. Let's analyze it.

(2) b=$$\sqrt{a}$$

$$\sqrt[3]{ab} = \sqrt[3]{a \sqrt{a}} = \sqrt[3]{a^{3/2}} =$$ $$a^{\frac{3}{2} \times \frac{1}{3}$$ = $$a^{\frac{1}{2}$$ = b

b is an integer; hence definite answer.

Hope this helps.
Intern
Joined: 18 Jan 2017
Posts: 36
Re: If a and b are positive integer,is (ab)^(1/3) an integer? [#permalink]

### Show Tags

18 Jan 2017, 11:13
Got this one wrong. On closer scrutiny, statement (2) actually includes the information in statement (1).
Senior Manager
Joined: 02 Apr 2014
Posts: 469
If a and b are positive integer,is (ab)^(1/3) an integer? [#permalink]

### Show Tags

21 Dec 2017, 13:09
Question : $$(ab)^{1/3}$$ integer ?

Statement 1: $$\sqrt{a}$$ is integer
Let $$\sqrt{a}$$ = m
=> $$a = m^2$$
$$(ab)^{1/3}$$ = (m^2 * b)^ {1/3}
=> if b = m => $$(m^2 * m)^ {1/3}$$ => $$(m^3)^{1/3}$$ = m => integer
=> if b not equals m, then $$(m^2 * b)^{1/3}$$ , may not be integer , say b = 1, then $$(m^2)^{1/3}$$ => not an integer
=> Insufficient

Statement 2: b = $$\sqrt{a}$$
=> $$b^2 = a$$
=> $$(ab)^{1/3}$$ = $$(b^2 * b)^{1/3}$$ => integer => sufficient => Answer (B)
If a and b are positive integer,is (ab)^(1/3) an integer?   [#permalink] 21 Dec 2017, 13:09
Display posts from previous: Sort by