GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 03:34

### 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

# If x is a positive integer, which of the following CANNOT be expressed

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

### Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 114
If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

Updated on: 09 Dec 2017, 06:39
10
32
00:00

Difficulty:

75% (hard)

Question Stats:

53% (01:45) correct 47% (01:39) wrong based on 332 sessions

### HideShow timer Statistics

If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?

A. $$x^5$$

B. $$x^2 − 1$$

C. $$\sqrt{x^8}$$

D. $$x^2 + 1$$

E. $$\sqrt{x^5}$$

_________________
Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Originally posted by emmak on 11 Feb 2013, 11:09.
Last edited by Bunuel on 09 Dec 2017, 06:39, edited 2 times in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 55273
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

11 Feb 2013, 15:13
8
10
emmak wrote:
If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?

A. x^5
B. x^2 − 1
C. $$\sqrt{x^8}$$
D. x^2 + 1
E. $$\sqrt{x^5}$$

The question basically asks: if x is a positive integer, which of the following CANNOT be a perfect square.

Now, if x=1, then options A, B, C and E ARE perfect squares, therefore by POE the correct answer must be D.

_________________
##### General Discussion
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1812
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

06 Mar 2014, 00:06
2
If we take x = 2 & calculate, we cant get the answers;
seems that x has to be taken 1 to execute all the options
_________________
Kindly press "+1 Kudos" to appreciate
SVP
Joined: 06 Sep 2013
Posts: 1660
Concentration: Finance
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

27 Mar 2014, 17:12
emmak wrote:
If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?

A. x^5
B. x^2 − 1
C. $$\sqrt{x^8}$$
D. x^2 + 1
E. $$\sqrt{x^5}$$

So I guess zero does count as a perfect square then

Cheers
J
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9237
Location: Pune, India
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

27 Mar 2014, 21:21
7
6
PareshGmat wrote:
If we take x = 2 & calculate, we cant get the answers;
seems that x has to be taken 1 to execute all the options

Any random value of x will not help you get the answer. Even if you do not try x = 1, you can use reasoning to solve this question.

A. $$x^5$$
If x is a number with an even power, such as $$x = a^4$$ (a is an integer), then $$x^5 = a^{20} = n^2$$
n will be $$a^{10}$$, an integer here.

B. $$x^2 - 1$$
$$x^2 - 1 = n^2$$
You need two consecutive perfect squares. Only 0 and 1 are consecutive perfect squares. Thereafter, the distance between perfect squares keeps increasing. x needs to be a positive integers so if x = 1, n = 0 (an integer)

C. $$\sqrt{x^8}$$
$$\sqrt{x^8} = x^4 = n^2$$
n will be $$x^2$$, an integer here.

D. $$x^2 + 1$$
x is a positive integer so it must be at least 1. After 1, there are no two consecutive integers. n cannot be an integer.

E. $$\sqrt{x^5}$$
If x is a number with an even power which is a multiple of 4, such as $$x = a^4$$ (a is an integer), then $$\sqrt{x^5} = \sqrt{a^{20}} = a^{10} = n^2$$
n will be $$a^5$$, an integer here.

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Joined: 14 Jan 2013
Posts: 136
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

29 Mar 2014, 02:38
Even though Bunuel and karishma have answered this question, I am not able to digest any fundamental of this ....

Not sure how to crack this one... as I got this question in my Veritas prep exam today...
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9237
Location: Pune, India
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

30 Mar 2014, 19:01
6
3
Mountain14 wrote:
Even though Bunuel and karishma have answered this question, I am not able to digest any fundamental of this ....

Not sure how to crack this one... as I got this question in my Veritas prep exam today...

Look, the question simply asks which option CANNOT be a perfect square. In the options, x is a positive integer.

Can x^5 be a perfect square? Can x take some value such that x^5 is a perfect square? Say, x = 4. Then x^5 = 4^5 = 2^10
This is a perfect square. Hence for some value of x, x^5 could be a perfect square. Hence this is not our answer.
How do we find a value for which x^5 will be a perfect square? Perfect squares have even powers. We have x^5 which is an odd power. To get an even power, we could select x such that it already has an even power - we selected x = 2^2. Similarly, x could be 1^2 or 3^2 or 4^2 or 5^2 or 3^4 etc

Now think, can x^2 - 1 be a perfect square?
The reasoning for all the options is given in the post above.

A more intuitive approach is putting x = 1 as given by Bunuel. When x = 1, all options except option (D) results in a perfect square. So we know that all options CAN be perfect squares except (D). By elimination, answer must be (D).
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Joined: 03 Aug 2012
Posts: 19
Location: United States (OR)
Concentration: Finance, International Business
GPA: 3.53
WE: Analyst (Entertainment and Sports)
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

30 Mar 2014, 21:18
VeritasPrepKarishma wrote:
Mountain14 wrote:
Even though Bunuel and karishma have answered this question, I am not able to digest any fundamental of this ....

Not sure how to crack this one... as I got this question in my Veritas prep exam today...

Look, the question simply asks which option CANNOT be a perfect square. In the options, x is a positive integer.

Can x^5 be a perfect square? Can x take some value such that x^5 is a perfect square? Say, x = 4. Then x^5 = 4^5 = 2^10
This is a perfect square. Hence for some value of x, x^5 could be a perfect square. Hence this is not our answer.
How do we find a value for which x^5 will be a perfect square? Perfect squares have even powers. We have x^5 which is an odd power. To get an even power, we could select x such that it already has an even power - we selected x = 2^2. Similarly, x could be 1^2 or 3^2 or 4^2 or 5^2 or 3^4 etc

Now think, can x^2 - 1 be a perfect square?
The reasoning for all the options is given in the post above.

A more intuitive approach is putting x = 1 as given by Bunuel. When x = 1, all options except option (D) results in a perfect square. So we know that all options CAN be perfect squares except (D). By elimination, answer must be (D).

So the one point where I get tripped up is the X^2 - 1. 0 is assumed to be a perfect square?

How can I tell from the verbage of the question that what they are asking for is determining whether or not something is a perfect square or not?

Thanks for the help.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9237
Location: Pune, India
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

30 Mar 2014, 22:59
dbiersdo wrote:
VeritasPrepKarishma wrote:
Mountain14 wrote:
Even though Bunuel and karishma have answered this question, I am not able to digest any fundamental of this ....

Not sure how to crack this one... as I got this question in my Veritas prep exam today...

Look, the question simply asks which option CANNOT be a perfect square. In the options, x is a positive integer.

Can x^5 be a perfect square? Can x take some value such that x^5 is a perfect square? Say, x = 4. Then x^5 = 4^5 = 2^10
This is a perfect square. Hence for some value of x, x^5 could be a perfect square. Hence this is not our answer.
How do we find a value for which x^5 will be a perfect square? Perfect squares have even powers. We have x^5 which is an odd power. To get an even power, we could select x such that it already has an even power - we selected x = 2^2. Similarly, x could be 1^2 or 3^2 or 4^2 or 5^2 or 3^4 etc

Now think, can x^2 - 1 be a perfect square?
The reasoning for all the options is given in the post above.

A more intuitive approach is putting x = 1 as given by Bunuel. When x = 1, all options except option (D) results in a perfect square. So we know that all options CAN be perfect squares except (D). By elimination, answer must be (D).

So the one point where I get tripped up is the X^2 - 1. 0 is assumed to be a perfect square?

How can I tell from the verbage of the question that what they are asking for is determining whether or not something is a perfect square or not?

Thanks for the help.

Yes, both 0 and 1 are perfect squares.

"Can you express 'this' as n^2 where n is an integer?" asks us whether we can write 'this' as square of an integer.
Square of an integer is a perfect square. So the question becomes "Can you express 'this' as a perfect square?"

Slightly convoluted verbiage is common in GMAT.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Status: Just redeemed Kudos for GMAT Club Test !!
Joined: 14 Sep 2013
Posts: 93
GMAT 1: 530 Q40 V23
GPA: 3.56
WE: Analyst (Commercial Banking)
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

20 Jul 2014, 01:05
Bunuel wrote:
emmak wrote:
If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?

A. x^5
B. x^2 − 1
C. $$\sqrt{x^8}$$
D. x^2 + 1
E. $$\sqrt{x^5}$$

The question basically asks: if x is a positive integer, which of the following CANNOT be a perfect square.

Now, if x=1, then options A, B, C and E ARE perfect squares, therefore by POE the correct answer must be D.

Please refer to option [b] where value comes 0.
Would you please clarify whether 0 is a perfect square?
_________________
______________
KUDOS please, if you like the post or if it helps
"Giving kudos" is a decent way to say "Thanks"

Master with structure - Numerical comparison [source: economist.com] https://gmatclub.com/forum/master-with-structure-numerical-comparison-233657.html#p1801987
Math Expert
Joined: 02 Sep 2009
Posts: 55273
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

20 Jul 2014, 04:16
musunna wrote:
Bunuel wrote:
emmak wrote:
If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?

A. x^5
B. x^2 − 1
C. $$\sqrt{x^8}$$
D. x^2 + 1
E. $$\sqrt{x^5}$$

The question basically asks: if x is a positive integer, which of the following CANNOT be a perfect square.

Now, if x=1, then options A, B, C and E ARE perfect squares, therefore by POE the correct answer must be D.

Please refer to option [b] where value comes 0.
Would you please clarify whether 0 is a perfect square?

Yes, 0 is a perfect square 0 = 0^2.
_________________
Board of Directors
Joined: 17 Jul 2014
Posts: 2551
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

16 Mar 2016, 18:12
I picked B, because I thought that 2 consecutive integers multiplied do not equal a perfect square...I did not take into consideration the possibility of 0...
Current Student
Joined: 20 Jan 2014
Posts: 39
Location: United States
GMAT 1: 720 Q47 V41
GPA: 3.71
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

21 May 2016, 15:21
1
I think the hardest part about this question is working out what is being asked.

Which of the following cannot be expressed as n^2 means which of the following cannot be perfect square when n is an integer.

Subbing in 1 for x in each example brings us to answer D.

1^2 + 1 = 2, which is not the square of any integer. D is your answer! Easy
Intern
Joined: 19 Feb 2019
Posts: 5
Re: If x is a positive integer, which of the following CANNOT be expressed  [#permalink]

### Show Tags

26 Mar 2019, 20:22
D.

x^2+1 = n^2 => x^2 = (n+1)(n-1) and n>0. This can never give a perfect square
Re: If x is a positive integer, which of the following CANNOT be expressed   [#permalink] 26 Mar 2019, 20:22
Display posts from previous: Sort by

# If x is a positive integer, which of the following CANNOT be expressed

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

 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®.