NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 20:55 It is currently 23 Apr 2024, 20:55
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

M15-35

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [5]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
M15-35 [#permalink] New post   16 Sep 2014, 00:57
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

63% (01:43) correct 37% (01:49) wrong based on 87 sessions
Hide Show timer Statistics
If \(x^2 y^3 = 200\), what is the value of \(xy\)?


(1) \(y\) is an integer

(2) \(\frac{x}{y} = 2.5\)
ShowHide Answer
Official Answer
B
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [2]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re M15-35 [#permalink] New post   16 Sep 2014, 00:57
2
Kudos
Expert Reply
Official Solution:


If \(x^2 y^3 = 200\), what is the value of \(xy\)?

(1) \(y\) is an integer.

\(y\) can be any positive integer, and for each value of \(y\), there will be two corresponding values of \(x\) to satisfy the equation \(x^2y^3=200\). For instance, if \(y=10\), then \(x^2y^3=x^2*1000=200\). This results in \(x=\frac{1}{\sqrt{5} }\) or \(x=-\frac{1}{\sqrt{5} }\). Consequently, there are infinite possible values for \(xy\). Not sufficient.

(2) \(\frac{x}{y}=2.5\).

Upon cross-multiplying, we get \(x=2.5y\). Plugging this into our original equation, we have \((2.5y)^2*y^3=6.25y^5=200\). Simplifying, we get \(y^5=32\), which implies \(y=2\). Then, \(x=2.5y=5\). Therefore, \(xy=10\). Sufficient.


Answer: B
avatar
B
priyatomar
Intern
Intern
Joined: 01 Aug 2017
Posts: 9
Own Kudos [?]: 2 [1]
Given Kudos: 11
GMAT 1: 680 Q42 V41
GPA: 4
Send PM
Re: M15-35 [#permalink] New post   14 Dec 2019, 21:41
1
Kudos
Bunuel wrote:
If \(x^2 y^3 = 200\), what is the value of \(xy\)?


(1) \(y\) is an integer

(2) \(\frac{x}{y} = 2.5\)



In this question if the first one would have said that both x and y are integers, would it then be sufficient?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [1]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: M15-35 [#permalink] New post   15 Dec 2019, 02:53
1
Kudos
Expert Reply
priyatomar wrote:
Bunuel wrote:
If \(x^2 y^3 = 200\), what is the value of \(xy\)?


(1) \(y\) is an integer

(2) \(\frac{x}{y} = 2.5\)



In this question if the first one would have said that both x and y are integers, would it then be sufficient?


No. Because x = ± 5 and y = 2 satisfy x^2 y^3 = 200, so xy can be 10 or -10. If we were told that x and y are positive integers, then yes, it would be sufficient.
User avatar
Senthil7
Senior Manager
Senior Manager
Joined: 31 Mar 2016
Posts: 325
Own Kudos [?]: 195 [0]
Given Kudos: 197
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
Send PM
GMAT ToolKit User
Re: M15-35 [#permalink] New post   22 Aug 2016, 05:24
I think this is a high-quality question and I agree with explanation.
User avatar
B
nandakumars05
Intern
Intern
Joined: 27 Nov 2019
Posts: 6
Own Kudos [?]: 2 [0]
Given Kudos: 35
Location: India
Schools: S.P.Jain Institute (I)
GMAT 1: 500 Q43 V17 (Online)
GMAT 2: 570 Q42 V26 (Online)
GPA: 4
Send PM
Re: M15-35 [#permalink] New post   18 Sep 2020, 22:21
I think this is a high-quality question and I agree with explanation.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: M15-35 [#permalink] New post   20 Oct 2023, 01:51
Expert Reply
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
User avatar
B
Rebaz
Manager
Manager
Joined: 14 Feb 2014
Posts: 76
Own Kudos [?]: 16 [0]
Given Kudos: 3626
Send PM
CAT Tests
Re: M15-35 [#permalink] New post   07 Nov 2023, 07:13
Bunuel,

How should someone simplify (6.25) (y^5)=200 just to know that 200 is multiple of 6.25? Is there anyway to know that?

I know when i divide 200 by 6.25, the result is 32.

Thanks in advance!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: M15-35 [#permalink] New post   07 Nov 2023, 07:25
Expert Reply
Rebaz wrote:
Bunuel,

How should someone simplify (6.25) (y^5)=200 just to know that 200 is multiple of 6.25? Is there anyway to know that?

I know when i divide 200 by 6.25, the result is 32.

Thanks in advance!


You can express 6.25 as \(6.25=6\frac{1}{4}=\frac{25}{4}\). With this representation, it's evident that both the left-hand side and the right-hand side, which is 200, can be divided by 25. After this simplification, the calculation becomes straightforward.
User avatar
B
Rebaz
Manager
Manager
Joined: 14 Feb 2014
Posts: 76
Own Kudos [?]: 16 [0]
Given Kudos: 3626
Send PM
CAT Tests
Re: M15-35 [#permalink] New post   08 Nov 2023, 02:26
Bunuel wrote:
Rebaz wrote:
Bunuel,

How should someone simplify (6.25) (y^5)=200 just to know that 200 is multiple of 6.25? Is there anyway to know that?

I know when i divide 200 by 6.25, the result is 32.

Thanks in advance!


You can express 6.25 as \(6.25=6\frac{1}{4}=\frac{25}{4}\). With this representation, it's evident that both the left-hand side and the right-hand side, which is 200, can be divided by 25. After this simplification, the calculation becomes straightforward.


Ofcourse converting the decimal into fraction makes the calculation way more easier.

Brilliant explanation and very straightforward!

Thank you!
GMAT Club Bot
gmatclubot
Re: M15-35 [#permalink]
08 Nov 2023, 02:26
Moderator:
Bunuel
Math Expert
92883 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions