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If x is a positive integer, what is the number of different positive

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If x is a positive integer, what is the number of different positive  [#permalink]

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New post 16 Dec 2019, 01:39
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C
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Difficulty:

  65% (hard)

Question Stats:

46% (01:26) correct 54% (01:40) wrong based on 33 sessions

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If x is a positive integer, what is the number of different positive  [#permalink]

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New post Updated on: 16 Dec 2019, 09:04
#1
x is a two-digit number
24* x
many possible values
insufficient
#2
x^2 has 3 positive factors

only possible when x is prime ;
so factor of 24 * x ;
possible to determine different + factors of 24*x
2^3*3^1 * 2 ; 5*2 ; 10 or 2^3*3^2 *3 ; 4*4 ; 16
insufficient
from 1 &2
x= 11,13,. any prime no
total factors of 24*x ; 2^3*3^1*x^1 ; 8+2 ; 10
IMO C

Bunuel wrote:
If x is a positive integer, what is the number of different positive factors of 24x ?

(1) x is a two-digit number
(2) x^2 has 3 positive factors

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Originally posted by Archit3110 on 16 Dec 2019, 03:26.
Last edited by Archit3110 on 16 Dec 2019, 09:04, edited 1 time in total.
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Re: If x is a positive integer, what is the number of different positive  [#permalink]

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New post 16 Dec 2019, 08:57
Archit3110 wrote:
#1
x is a two-digit number
24* x
many possible values
insufficient
#2
x^2 has 3 positive factors

only possible when x is prime ;
so factor of 24 * x ;
possible to determine different + factors of 24*x
IMO B

Bunuel wrote:
If x is a positive integer, what is the number of different positive factors of 24x ?

(1) x is a two-digit number
(2) x^2 has 3 positive factors

Are You Up For the Challenge: 700 Level Questions

IMO C

Statement 1 alone insufficient

Statement 2 shows X prime
X can be 2 or 3
Hence Statement 2 not sufficient.

However, if Statement 1 + 2
X is prime different from 2 or 3.
Hence can determine number of positive factors.
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If x is a positive integer, what is the number of different positive  [#permalink]

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New post 16 Dec 2019, 10:57
If x is a positive integer, what is the number of different positive factors of 24x ?
(1) x is a two-digit number
(2) x^2 has 3 positive factors

Question: 24x =2^3 . 3 . x

statement 1: insufficient
statement 2: x^2 has 3 positive factors
We have to realize that here the questions is talking about factors and Not Prime Factors
This means that two of these 3 factors is 1 and the x^2 itself.
---> x must be a prime number because the square of prime is the only integer that has only 3 factors

24x = 2^3.3.P where P is any prime number
This is not sufficient because the answer is going to be different depending on wether P= 2 or 3 or some other P numbers

Statement 1 + Statement 2
Sufficient because now we now that the Prime number is different from 2 and 3, and now we can use the formulas for finding the number of
of factors of 2^3 . 3 . P = (3+1)(2)(2)

Answer C
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If x is a positive integer, what is the number of different positive   [#permalink] 16 Dec 2019, 10:57
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