It is currently 14 Dec 2017, 07:25

Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135629 [0], given: 12705

If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal [#permalink]

Show Tags

New post 21 Nov 2017, 00:59
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

55% (01:39) correct 45% (01:11) wrong based on 72 sessions

HideShow timer Statistics

Kudos [?]: 135629 [0], given: 12705

Intern
Intern
avatar
B
Joined: 15 Oct 2017
Posts: 7

Kudos [?]: 5 [0], given: 50

Location: India
Concentration: Entrepreneurship, Marketing
Premium Member CAT Tests
Re: If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal [#permalink]

Show Tags

New post 21 Nov 2017, 01:41
By solving LHS, we get a^2*b^3=500
We know 500 = 2^2*5^3

Hence, a=2 b=5
a+b = 7 (Not in the options)

Kudos [?]: 5 [0], given: 50

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 598

Kudos [?]: 181 [0], given: 138

GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal [#permalink]

Show Tags

New post 21 Nov 2017, 01:43
1
This post was
BOOKMARKED
Bunuel wrote:
If a and b are integers and \((\sqrt[3]{a}*\sqrt{b})^6 = 500\), then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6


a^2 * b^3

now a =2 or -2 and b = 5 (125*4)
-2+5 = 3

B
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Kudos [?]: 181 [0], given: 138

Manager
Manager
avatar
B
Joined: 31 Jul 2017
Posts: 118

Kudos [?]: 17 [0], given: 325

Re: If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal [#permalink]

Show Tags

New post 21 Nov 2017, 02:36
Bunuel wrote:
If a and b are integers and \((\sqrt[3]{a}*\sqrt{b})^6 = 500\), then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6

a^2 * b^3 = (-2)^2 * 5^3 = 2^2 * 5^3

a + b = 3/7

Sent from my Lenovo P1a42 using GMAT Club Forum mobile app

Kudos [?]: 17 [0], given: 325

VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1126

Kudos [?]: 402 [0], given: 645

If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal [#permalink]

Show Tags

New post 21 Nov 2017, 18:13
Bunuel wrote:
If a and b are integers and \((\sqrt[3]{a}*\sqrt{b})^6 = 500\), then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6

\((\sqrt[3]{a}*\sqrt{b})^6 = 500\)

Do the prime factorization for 500: \(2^25^3\)

Rewrite
\((a^{\frac{1}{3}} * b^{\frac{1}{2}})^6 = 2^2*5^3\)

Distribute the exponent

\(a^{(\frac{1}{3}*6)} * b^{(\frac{1}{2}*6)} = 2^2*5^3\)

\(a^2 * b^3 = 2^2 * 5^3\)

\(a^2 = 2^2 = 4\)

\(\sqrt{a^2} =\sqrt{4}\)
\(a = 2\) OR
\(a = -2\)

\(b^3 = 5^3\)

\((\sqrt[3]{b^3}) = (\sqrt[3]{5^3}\))

\(b = 5\)

\(a + b\)?

\(2 + 5 = 7\) Not an answer choice
\(-2 + 5 = 3\)

Answer B

Kudos [?]: 402 [0], given: 645

Intern
Intern
avatar
B
Status: Prepping for GMAT
Joined: 06 Nov 2017
Posts: 16

Kudos [?]: 5 [0], given: 26

Location: France
GPA: 4
If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal [#permalink]

Show Tags

New post 22 Nov 2017, 04:49
Bunuel wrote:
If a and b are integers and \((\sqrt[3]{a}*\sqrt{b})^6 = 500\), then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6


Before people complain that the answer they have found is not in the suggestions of the problem prompt, they need to remember that an integer can be either positive and negative. This was, in my opinion, the main trap with this problem.

We have: \((\sqrt[3]{a}*\sqrt{b})^6 = 500\) (A)

This equality is too complex for my tastes, let's simplify it while keeping in mind that:

1/ \(\sqrt{x} = x^\frac{1}{2}\)
2/ \(\sqrt[y]{x} = x^\frac{1}{y}\)
3/ \((a*b)^c = a^c * b^c\)

Therefore, using the first 3 properties above, A becomes:
\((\sqrt[3]{a}*\sqrt{b})^6 = (a^\frac{1}{3} * b^\frac{1}{2})^6 = a^2 * b^3 = 500\) (B)

If we decompose 500 into its prime components, we get \(500 = 2^2*5^3\)

Thus B can be written as: \(a^2 * b^3 = 2^2*5^3\)

At this stage, we're tempted to say that \(a = 2\) and \(b = 5\) and thus complain that \(a+b = 7\) isn't in the choices.

Or, we can remember that even exponents remove the negative sign from negative integers and deduce that the only solution possible is \(a = -2\) and \(b = 5\) (since odd exponents keep the negative sign of negative integers and since 500 is positive, it follows that b can never be negative).

Thus, \(a + b = 3\) i.e. answer B.

Kudos [?]: 5 [0], given: 26

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1803

Kudos [?]: 981 [0], given: 5

Re: If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal [#permalink]

Show Tags

New post 27 Nov 2017, 10:49
Bunuel wrote:
If a and b are integers and \((\sqrt[3]{a}*\sqrt{b})^6 = 500\), then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6


We can rewrite the expression:

[(a^1/3) x (b^1/2)]^6 = 500

a^2 x b^3 = 500

a^2 x b^3 = 2^2 x 5^3

Thus a could be 2 and b could be 5, and a + b = 7. However, notice that a^2 = 2^2 = 4, so a could be -2 also. In that case, a + b = -2 + 5 = 3.

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 981 [0], given: 5

Re: If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal   [#permalink] 27 Nov 2017, 10:49
Display posts from previous: Sort by

If a and b are integers and (3√a*√b)^6 = 500, then a + b could equal

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.