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

It is currently 19 Aug 2018, 03:09

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

If x ≠ 0, does x have an odd number of factors?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
If x ≠ 0, does x have an odd number of factors?  [#permalink]

Show Tags

New post 31 Jul 2018, 22:00
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

62% (00:57) correct 38% (01:04) wrong based on 45 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6554
Re: If x ≠ 0, does x have an odd number of factors?  [#permalink]

Show Tags

New post 31 Jul 2018, 22:28
If x ≠ 0, does x have an odd number of factors?

ODD number of factors :- Only perfect square have odd factors
so the question is :- Is x a perfect square?

(1) √x is an integer.
let √x=y, where y is an integer
so \(x=y^2\), thus x is a perfect square
sufficient

(2) x^2 is an integer.
if x is an integer, ans is YES
but if x is not an integer, or example \(x^2=3......x=\sqrt{3}\)... ans is NO
insuff

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Senior Manager
Senior Manager
User avatar
B
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 434
Location: India
Premium Member
Re: If x ≠ 0, does x have an odd number of factors?  [#permalink]

Show Tags

New post 01 Aug 2018, 00:27
Hi,

This question, if you know below properties of perfect square numbers then its just a twenty second problem.

1). A perfect square will always have an odd number of factors

2). A square of a prime number will always have exactly 3 factors

3). A perfect square will have an odd number of odd factors and even number of even factors.

Let’s say if one student could not recollect this during the exam,then its always good to try some numbers.

Let’s say for an example,

If x = 2,3 then it has even number of factors. Infact all the prime numbers as even number of factors.

If x is an odd number (not prime), let’s say x = 15, then x has 1,3,5,15 four factors.

If x is an even number (not prime), let’s say x = 20, then x has 1,2,4,5,10 and 20 six factors.

Now lets x is 4 or 9, then the factors are 1,2, 4 and for 9 we have 1,3,9.

We can see that, perfect square numbers have odd number of factors.

This is infact because,

When we prime factorize as perfect square number, always the power of primes is even.

Then the number of factors would be odd.

For example, 36 = 2^2 * 3^2

So, the number of factors is equal to (2+1) * (2+1) = 9 factors.

During the exam, it won’t take more than 40 or 50 secs to check the possibilities(But I would still recommend to know the properties as these are commonly asked questions in GMAT).

Statement I is sufficient:

√x is an integer.

So, x is a perfect square number.

So sufficient.

Statement II is insufficient:

x^2 is an integer.

First thing is “x” here may or may not be an integer.

Let’s say x = √2 is not an integer. But x^2 is not an integer.

Even if we consider “x” is an integer, we are not still sure whether “x” is a perfect square number or not.

So not sufficient.

So the answer is A here.
_________________

GMAT Mentors
Image

Re: If x ≠ 0, does x have an odd number of factors? &nbs [#permalink] 01 Aug 2018, 00:27
Display posts from previous: Sort by

If x ≠ 0, does x have an odd number of factors?

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.