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

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

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New post 04 Nov 2019, 02:02
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A
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E

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Question Stats:

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

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

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New post 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

The answer is E

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

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New post 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.
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Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

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New post Updated on: 04 Nov 2019, 02:28
Answer is E ,

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 .
So answer is E.

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.
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Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

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New post 04 Nov 2019, 02:28
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Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

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New post 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!
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Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

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New post 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

The answer is B

Posted from my mobile device

In st 2 what if x=√3
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Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

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New post 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

The answer is B

Posted from my mobile device

In st 2 what if x=√3


Yes, you’re right.
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Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

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New post 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


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Re: Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors  [#permalink]

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New post 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

The answer is E

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

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New post 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

The answer is E

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)
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Is x an odd number? (1) 1 < x < 8 (2) 7x^2 has four positive factors   [#permalink] 05 Jan 2020, 09:34
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