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06 Jul 2017, 07:29
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
57% (01:35) correct
43%
(01:47)
wrong
based on 313
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If x is a prime number, what is the number of different factors of 18x?
1) x^2 has 3 factors
2) x>3
1) x^2 has 3 factors
2) x>3
29 Jul 2018, 01:58
Kudos
Bookmarks
KarthikvsGMAT
OA: B
\(x\) is prime, how many different factors are of \(18x\)?
\(18x = 2*3^2*x\)
Case 1: if \(x =2\), then \(18x =36=2^2*3^2\)
then number of factors \((2+1)(2+1)=9\)
Case 2: if \(x =3\), then \(18x =54=2*3^3\)
then number of factors \((1+1)(3+1)=8\)
Case 3: if \(x >3\), then \(18x=2*3^2*x^1\)
then number of factors \((1+1)(2+1)(1+1)=12\)
Statement 1 :\(x^2\) has 3 factors
Square of every prime number has 3 factors: \(1,x,x^2\)
\(18 x\) can have \(9,8\) or \(12\) factors depending on whether \(x =2,3\) or \(x>3\)
So Statement 1 alone is not sufficient.
Statement 2: \(x>3\)
If \(x>3\), then \(18x\) will have \(12\) factors.
So Statement 2 alone is sufficient.
General Discussion
06 Jul 2017, 09:01
Kudos
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If x is a prime number, what is the number of different factors of 18x?
18x can be written as 2 * 3^2 * x
Case 1: If x=2, then 18x = 2^2 * 3^2 , total number of factors = 3*3 = 9
Case 2: If x=3, then 18x = 2 * 3^3 , total number of factors = 2*4 = 8
Case 3: If x= a prime number other than 2 and 3, then 18x = 2 * 3^2 * x , total number of factors = 2*3*2 = 12
So we need to find out what is the value of x?
Statement 1) x^2 has 3 factors
Square of any Prime number will have 3 factors. Eg. 2^2, 3^2, 5^2. As this statement gives no new information. This statement is not sufficient.
Statement 2) x>3
This statement clearly tells us that x is greater than 3, which means the third case is applicable here.So the total number of factors = 12. This statement is sufficient.
Answer is B
18x can be written as 2 * 3^2 * x
Case 1: If x=2, then 18x = 2^2 * 3^2 , total number of factors = 3*3 = 9
Case 2: If x=3, then 18x = 2 * 3^3 , total number of factors = 2*4 = 8
Case 3: If x= a prime number other than 2 and 3, then 18x = 2 * 3^2 * x , total number of factors = 2*3*2 = 12
So we need to find out what is the value of x?
Statement 1) x^2 has 3 factors
Square of any Prime number will have 3 factors. Eg. 2^2, 3^2, 5^2. As this statement gives no new information. This statement is not sufficient.
Statement 2) x>3
This statement clearly tells us that x is greater than 3, which means the third case is applicable here.So the total number of factors = 12. This statement is sufficient.
Answer is B
