GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 Jan 2020, 04:44

### 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

# Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60778
Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

04 Nov 2019, 02:02
00:00

Difficulty:

85% (hard)

Question Stats:

34% (01:53) correct 66% (01:46) wrong based on 102 sessions

### HideShow timer Statistics

Is x an odd number?

(1) $$1 < x < 8$$
(2) $$7x^2$$ has four positive factors

Are You Up For the Challenge: 700 Level Questions

_________________
Senior Manager
Joined: 25 Jul 2018
Posts: 493
Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

Updated on: 05 Nov 2019, 10:45
3
Is x an odd number??

(Statement1) 1< x < 8
x could be odd or even number in the range from 1 to 8.

Insufficient

(Statement2):
7x^{2} has four positive number factors

If the value of x is equal to 7, statement2 will have 4 positive factors
—> x=7 —> 7*7^{2}= 7^{3}
(3+1)= 4 ( 1, 7,49, 343)
—> x is odd (YES)

If $$x= 3^{1/2}$$, then 7*3 has also 4 positive factors (—> 1,3,7,21)
x is not odd ( NO)

Insufficient

Taken together 1&2,
—> x could be $$3^{1/2}$$ or 7 in the range from 1 to 8.

Insufficient

Posted from my mobile device

Originally posted by lacktutor on 04 Nov 2019, 02:18.
Last edited by lacktutor on 05 Nov 2019, 10:45, edited 1 time in total.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5751
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

Updated on: 04 Nov 2019, 02:38
Bunuel wrote:
Is x an odd number?

(1) $$1 < x < 8$$
(2) $$7x^2$$ has four positive factors

Are You Up For the Challenge: 700 Level Questions

#1
$$1 < x < 8$$
x can be odd or even
insufficient
#2
$$7x^2$$ has four positive factors
x can be prime integer ; 7*2^2 ;yes
or x can be a fraction ; 7*(1/7)^2 ; 4 factors
from 1 &2
nothing in common
IMO E

Originally posted by Archit3110 on 04 Nov 2019, 02:23.
Last edited by Archit3110 on 04 Nov 2019, 02:38, edited 1 time in total.
Intern
Joined: 28 Mar 2013
Posts: 12
GMAT 1: 680 Q49 V32
Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

Updated on: 04 Nov 2019, 02:28

A - Itself not sufficient . We don't know that X is integer or not .
B -

since we X^2 has to be a prime for 4 total factors and X^0.5 will not be an integer . - No

Or
if X = 7 , then 7^3 will have 4 factors total . Ans - Yes .

Not sufficient ..
Taking both A and B , also not sufficient .

Originally posted by DasAshish1 on 04 Nov 2019, 02:24.
Last edited by DasAshish1 on 04 Nov 2019, 02:28, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 60778
Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

04 Nov 2019, 02:28
Just a note: this is a 700+ question from our new collection Are You Up For the Challenge: 700 Level Questions. Aren't you missing something there?
_________________
Manager
Joined: 23 Nov 2018
Posts: 246
GMAT 1: 650 Q49 V28
GPA: 4
Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

05 Nov 2019, 02:47
Is x an odd number?

(1) 1<x<8
(2) 7*X^2 has four positive factors

evaluating option A:
X=2 no
X=3 yes
insufficient

evaluation option B
to have 4 factors the power must be 3
to make the power 3; X=7

therefore 7^3 = 4 factors; X=7

option B is sufficient!
_________________
Manager
Joined: 20 Jul 2019
Posts: 55
Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

05 Nov 2019, 10:22
1
lacktutor wrote:
Is x an odd number??

(Statement1) 1< x < 8
x could be odd or even number in the range from 1 to 8.

Insufficient

(Statement2):
7x^{2} has four positive number factors

Only if the value of x is equal to 7, statement2 will have 4 positive factors
—> x=7 —> 7*7^{2}= 7^{3}
(3+1)= 4 ( 1, 7,49, 343)
—> x is odd

Suffficient

Posted from my mobile device

In st 2 what if x=√3
Senior Manager
Joined: 25 Jul 2018
Posts: 493
Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

05 Nov 2019, 10:35
Peddi wrote:
lacktutor wrote:
Is x an odd number??

(Statement1) 1< x < 8
x could be odd or even number in the range from 1 to 8.

Insufficient

(Statement2):
7x^{2} has four positive number factors

Only if the value of x is equal to 7, statement2 will have 4 positive factors
—> x=7 —> 7*7^{2}= 7^{3}
(3+1)= 4 ( 1, 7,49, 343)
—> x is odd

Suffficient

Posted from my mobile device

In st 2 what if x=√3

Yes, you’re right.
Senior Manager
Joined: 21 Jun 2017
Posts: 399
Location: India
Concentration: Finance, Economics
Schools: IIM
GMAT 1: 620 Q47 V30
GPA: 3
WE: Corporate Finance (Commercial Banking)
Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

26 Dec 2019, 09:45
in order to make the no of factors to equal 4 , we can do either of the two things.

1> make the no a cube....... let x=7 so 7x^2 = 7^3 ...... therefore 7x^2 will have 2*2 factors = 4
2> make it an irrational square---- ex x=sqrt(2) ---> x^2 = 2 .... therefore 7x^2 will have 2*2 factors = 4

E
Intern
Joined: 05 Nov 2015
Posts: 14
Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

05 Jan 2020, 08:18
lacktutor wrote:
Is x an odd number??

(Statement1) 1< x < 8
x could be odd or even number in the range from 1 to 8.

Insufficient

(Statement2):
7x^{2} has four positive number factors

If the value of x is equal to 7, statement2 will have 4 positive factors
—> x=7 —> 7*7^{2}= 7^{3}
(3+1)= 4 ( 1, 7,49, 343)
—> x is odd (YES)

If $$x= 3^{1/2}$$, then 7*3 has also 4 positive factors (—> 1,3,7,21)
x is not odd ( NO)

Insufficient

Taken together 1&2,
—> x could be $$3^{1/2}$$ or 7 in the range from 1 to 8.

Insufficient

Posted from my mobile device

Can you please guide how to think of the Exception like you have thought of 3^(1/2) a the value of x here.... how did you choose amonst so many values....Please guide
Senior Manager
Joined: 25 Jul 2018
Posts: 493
Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

### Show Tags

05 Jan 2020, 09:34
avirup2018 wrote:
lacktutor wrote:
Is x an odd number??

(Statement1) 1< x < 8
x could be odd or even number in the range from 1 to 8.

Insufficient

(Statement2):
$$7x^{2}$$ has four positive number factors

If the value of x is equal to 7, statement2 will have 4 positive factors
—> x=7 —> $$7*7^{2}= 7^{3}$$
(3+1)= 4 ( 1, 7,49, 343)
—> x is odd (YES)

If $$x= 3^{1/2}$$, then 7*3 has also 4 positive factors (—> 1,3,7,21)
x is not odd ( NO)

Insufficient

Taken together 1&2,
—> x could be $$3^{1/2}$$ or 7 in the range from 1 to 8.

Insufficient

Posted from my mobile device

Can you please guide how to think of the Exception like you have thought of 3^(1/2) a the value of x here.... how did you choose amonst so many values....Please guide

Hi, avirup2018
Firstly, nothing tells us whether x is integer or not in the question stem. Well, we need to check non-integer values of x too.
Secondly, statement2 says there are 4 factors of $$7x^{2}$$.
—> there are two cases of finding factors (formula)
Case1: (1+1)(1+1) = 4
$$7x^{2}$$ => $$7^{1}$$— Ok. $$x^{2}$$ should be equal to any prime number except 7.
—> $$x^{2}= 5$$ —> $$x= 5^{1/2}$$
—> $$7x^{2} = 7^{1}*5^{1}$$ —> (1+1)(1+1) = 4 ( x is not an integer)

Case2: 3+1= 4
$$7x^{2}$$ = should be equal to $$7^{3}$$
—> x= 7 (x is an integer)
Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors   [#permalink] 05 Jan 2020, 09:34
Display posts from previous: Sort by