Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 30 Nov 2013
Posts: 19
Location: India
Concentration: Finance, General Management
GPA: 3.5
WE: Information Technology (Computer Software)

If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
[#permalink]
Show Tags
Updated on: 17 May 2016, 21:48
Question Stats:
41% (00:51) correct 59% (00:56) wrong based on 442 sessions
HideShow timer Statistics
If \((a^{(\frac{1}{2})}*b^{(\frac{1}{3})})^6=2000\), what is the value of ab? (1) a = 5 (2) a and b are positive integers
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Kudos is the best way to say Thank you. Believe in yourself! Practice more and good score in GMAT is for sure
Originally posted by madhavsrinivas on 23 Dec 2013, 11:18.
Last edited by Bunuel on 17 May 2016, 21:48, edited 2 times in total.
Edited the question.




Manager
Joined: 19 Apr 2013
Posts: 74
Concentration: Entrepreneurship, Finance
GMAT Date: 06052015
GPA: 3.88
WE: Programming (Computer Software)

Re: If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
[#permalink]
Show Tags
23 Dec 2013, 19:09
madhavsrinivas wrote: If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
1) a = 5 2) a and b are positive integers
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient D) EACH statement ALONE is sufficient to answer the question asked E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed ({a^1/2}*{b^1/3})^6=2000 ==>a^3*b^2 = 2000 from statement 1 : a = 5 125*b^2 = 2000 b^2 == 2000/125 b^2 == 16 b =4,4 So ab will be 20,20. from statement 2 a,b are +ve a^3*b^2 = 2000 this will be factorise in above only  125*16 so answer from this will be only 20. So answer will be B. Thanks AB +1 Kudos if you like and understand.
_________________
Thanks, AB
+1 Kudos if you like and understand.




Intern
Joined: 05 Dec 2013
Posts: 13
Location: United States
GPA: 3.53

Re: If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
[#permalink]
Show Tags
24 Dec 2013, 06:49
shouldn't the answer be C, considering the fact that it hasn't been given that a & b are integers? there can be endless values of a&b satisfying the second statement.



Intern
Joined: 30 Nov 2013
Posts: 19
Location: India
Concentration: Finance, General Management
GPA: 3.5
WE: Information Technology (Computer Software)

Re: If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
[#permalink]
Show Tags
24 Dec 2013, 11:37
asethi100 wrote: shouldn't the answer be C, considering the fact that it hasn't been given that a & b are integers? there can be endless values of a&b satisfying the second statement. Hi asethi, Simplifying the original equation gives us a^3 * b^2 = 2000 We can write 2000 as 125 * 16 or 1000 *2 or 40 * 50 etc etc. But if you see statement 2, which says a and b are integers then only 125 and 16 can be expressed in the form of a^3 and b^2, i.e 5^3 and 4^2. The other values such as 1000*2 or 40*50 can be expressed in the form of a^3 and b^2, but either of a and b or both, will not be of integer values. So, if you consider statement 2 alone, you will get the answer straight away. I hope this helps !
_________________
Kudos is the best way to say Thank you. Believe in yourself! Practice more and good score in GMAT is for sure



Manager
Joined: 13 Dec 2013
Posts: 161
Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
[#permalink]
Show Tags
28 Apr 2017, 21:10
madhavsrinivas wrote: asethi100 wrote: shouldn't the answer be C, considering the fact that it hasn't been given that a & b are integers? there can be endless values of a&b satisfying the second statement. Hi asethi, Simplifying the original equation gives us a^3 * b^2 = 2000 We can write 2000 as 125 * 16 or 1000 *2 or 40 * 50 etc etc. But if you see statement 2, which says a and b are integers then only 125 and 16 can be expressed in the form of a^3 and b^2, i.e 5^3 and 4^2. The other values such as 1000*2 or 40*50 can be expressed in the form of a^3 and b^2, but either of a and b or both, will not be of integer values. So, if you consider statement 2 alone, you will get the answer straight away. I hope this helps ! This is helpful. Is there any way to concretely prove that only a and b can only take the values of 5 and 4 respectively?



CEO
Joined: 12 Sep 2015
Posts: 2848
Location: Canada

Re: If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
[#permalink]
Show Tags
29 Apr 2017, 07:22
madhavsrinivas wrote: If \((a^{(\frac{1}{2})}*b^{(\frac{1}{3})})^6=2000\), what is the value of ab?
(1) a = 5 (2) a and b are positive integers Target question: What is the value of ab? Given: \((a^{(\frac{1}{2})}*b^{(\frac{1}{3})})^6=2000\) Simplify to get: (a³)(b²) = 2000 Statement 1: a = 5 Take (a³)(b²) = 2000 and replace a with 5 to get: (5³)(b²) = 2000 Simplify: (125)(b²) = 2000 Divide both sides by 125 to get: b² = 16 So, EITHER b = 4 OR b = 4 Case a: if b = 4, then ab = (5)(4) = 20Case b: if b = 4, then ab = (5)(4) = 20Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: a and b are positive integers We're told that (a³)(b²) = 2000We also know that 2000 = (5)(5)(5)(2)(2)(2)(2) = (5)(5)(5)(4)(4) = (5³)(4²) Since we're told that a and b are positive integers, we can conclude that a = 5 and b = 4, which means ab = (5)(4) = 20Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails



Intern
Joined: 27 May 2015
Posts: 12
Location: Venezuela
GPA: 3.76

If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
[#permalink]
Show Tags
24 May 2017, 12:04
My approach, in case it helps:
Question stem: \((a^{1/2}*b^{1/3})^6=2000\)
Simplify it first:
\({(a^{1/2})}^{6}*{(b^{1/3})}^{6}=2000 \rightarrow a^{3}*b^{2}=2000\)
Now do the prime factorization of \(2000\) to see that \(2000=2^{4}*5^{3}\), which we can transform, using exponent properties, to \(2000=4^{2}*5^{3}\). Now we have an expression similar to that of the question stem. Therefore, \(a\) should be \(5\).
From here, we should pay attention to the odd/even nature of the exponents. For base \(5\), the exponent is odd (\(3\)). Since \(2000\) is positive and the exponent of base \(4\) is even (\(2\)), we know that \(5\) must be positive. However, since the exponent of \(4\) is even, \(4\) could actually be \(4\) or \(4\). The output of \(4^{2}\) is the same as of \(4^{2}\), which is \(16\). Therefore, \(b\) could be \(4\) or \(4\).
So we must focus on the sign of that \(4\), or in the problem's language, the sign of \(b\).
Statement 1) \(a=5\). We already knew this. Not sufficient.
Statement 2) \(a\) and \(b\) are positive integers. We know that \(a=5\) and that \(b\) is positive, so \(b\) is \(4\). From here, we know that \(a*b=20\). Sufficient.
Hope this approach helps.



Intern
Joined: 10 Sep 2017
Posts: 5

If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab?
[#permalink]
Show Tags
17 Sep 2017, 21:22
0 → see question 1 → \(a^3 * b^2 = 2000\) 2 → \((ab)^2 * a = 2000\) 3 → \((ab)^2 = 2000 / a\)
Statement #1: \(a = 5\) From 3 → \((ab)^2 = 2000 / 5 = 400\) So \(ab = \sqrt{(400)} = ± 20\), but GMAT doesn't like ± (unlike my grade school algebra teacher) So Statement #1 is insufficient.
Statement #2: a and b are positive integers From 3 → \((ab)^2 = 2000 / a\) So \(ab = \sqrt{(2000 / a)} = 2 * 2 * 5 * \sqrt{(5 / a)} → a = 5, b = 2 * 2\) since both are integers > 0 So Statement #2 is sufficient
Since a = 5, can be determined from Statement #2 alone, I will answer B for BOOM




If ({a^1/2}*{b^1/3})^6=2000, what is the value of ab? &nbs
[#permalink]
17 Sep 2017, 21:22






