Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 May 2016, 03:17

### 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 x and y are positive integers, is the following cube root

Author Message
TAGS:

### Hide Tags

Intern
Joined: 14 Mar 2012
Posts: 28
GMAT 1: 590 Q32 V30
GMAT 2: 700 Q48 V37
GPA: 3.6
Followers: 0

Kudos [?]: 63 [1] , given: 28

If x and y are positive integers, is the following cube root [#permalink]

### Show Tags

09 Jun 2012, 07:22
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

66% (02:13) correct 34% (01:36) wrong based on 200 sessions

### HideShow timer Statistics

If x and y are positive integers, is the following cube root an integer?

(x + y^2)^(1/3)

(1) x = y^2(y-1)
(2) x = 2
[Reveal] Spoiler: OA

_________________

Give kudos if you find my post helpful

Intern
Joined: 14 Mar 2012
Posts: 28
GMAT 1: 590 Q32 V30
GMAT 2: 700 Q48 V37
GPA: 3.6
Followers: 0

Kudos [?]: 63 [0], given: 28

Re: If x and y are positive integers, is the following cube root [#permalink]

### Show Tags

09 Jun 2012, 07:23
[quote="solarzj"]If x and y are positive integers, is the following cube root an integer?

(x + y^2)^(1/3)

1. x = y^2(y-1)
2. x = 2

So if I understand correctly.

In 1.) if I expand x = y^2 * (y-1) to x = y^3 - y ^2 and substitute in

cubeRoot(x + y^2) => i get cubeRoot(y^3 - y ^2 + y^2)
because both y^2 cancel out.

After this I can say, based on the information of the question (x and Y are positive integers) that y is a positive INTEGER

and because cubeRoot(y^3) => y ... the answer is yes, cubeRoot(x + y^2) = y = a positive INTEGER
_________________

Give kudos if you find my post helpful

Math Expert
Joined: 02 Sep 2009
Posts: 32965
Followers: 5749

Kudos [?]: 70431 [2] , given: 9844

Re: If x and y are positive integers, is the following cube root [#permalink]

### Show Tags

09 Jun 2012, 07:45
2
KUDOS
Expert's post
If x and y are positive integers, is the following cube root an integer?

$$\sqrt[3]{x + y^2}$$

(1) x = y^2(y-1) --> $$x=y^3-y^2$$ --> $$\sqrt[3]{x+y^2}=\sqrt[3]{y^3-y^2+y^2}=\sqrt[3]{y^3}=y=integer$$. Sufficient.

(2) x = 2 --> if $$y=1$$ then the answer is NO but if $$y=5$$ then the answer is YES. Not sufficient.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9617
Followers: 465

Kudos [?]: 120 [0], given: 0

Re: If x and y are positive integers, is the following cube root [#permalink]

### Show Tags

27 Aug 2015, 08:22
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x and y are positive integers, is the following cube root   [#permalink] 27 Aug 2015, 08:22
Similar topics Replies Last post
Similar
Topics:
Is the positive square root of x an integer? 1 29 Dec 2013, 02:13
10 If y is a positive integer, is square_root of y 10 30 Jun 2012, 03:46
2 Is the positive square root of x an integer? 2 28 Nov 2011, 10:31
14 If y is a positive integer is root(y) an integer? 10 26 Jan 2011, 06:17
10 If x is a positive integer, is root(x) an integer? 10 20 Feb 2010, 14:49
Display posts from previous: Sort by