evillasis wrote:
susheelh wrote:
jachavez06 wrote:
I understand how you get to 75, but how can you be sure x doesn't also have prime factors that are in neither 225 or 300?
To rephrase, I can see how it could be 75, but why does it have to be 75 and not something like 75*11?
HI,
This is how it is
S1: Possible values = 25 or 75 or 125 : insuff
S2: Possible Values = 75 or 150 or 300 : insuff
s1+ S2 : Only one common value = 75 : Suff
Answer choice : C
We of course don't need to know the value is 75. Just knowing there is a unique common value between S1 and S2 is enough.
Hope this helps.
In S1: I don't see 225 as 125 as LCM of 25 and 225.
Hi,
Thanks for pointing it out. I have corrected the Typo in earlier response. Same is highlighted.
The concept being tested here is Prime factorization. Also, it tests how the LCM of two numbers is derived. Let me attempt to solve this long hand.
S1:
Prime Factors of 45 (One of the two numbers) = \(3^2\),\(5^1\)
Prime factors of 225 (LCM of the two numbers) = \(3^2\), \(5^2\)
If the LCM of X and 45 is 225, what are different possible prime factors of X?
* X HAS to have \(5^2\) as one of its factors
* X COULD have \(3^0\),\(3^1\) or \(3^2\) as its other factors
* Possible values of X are -
-> \(5^2*3^0 = 25\)
-> \(5^2*3^1 = 75\)
-> \(5^2*3^2 = 225\)
Three Answers for X and hence Insufficient.
S2:
Prime Factors of 20 (One of the two numbers) = \(2^2\),\(5^1\)
Prime factors of 300 (LCM of the two numbers) = \(2^2\),\(3^1\), \(5^2\)
If the LCM of X and 20 is 300, what are different possible prime factors of X?
* X HAS to have \(5^2\) as one of its factors
* X has to have \(3^1\) as one of its factors
* X COULD have \(2^0\),\(2^1\) or \(2^2\) as its other factors
* Possible values of X are -
-> \(5^2*3^1*2^0 = 75\)
-> \(5^2*3^1*2^1 = 150\)
-> \(5^2*3^1*2^2 = 300\)
Three Answers for X and hence Insufficient.
S1+S2
The only common values between S1 and S2 = \(5^2*3^1*2^0 = 75\)
Hence the Answer choice C
I hope this helps.
PS:
Recommendation: Please read the
MGMAT Number properties guide on prime factors. This approach is discussed thoroughly there. It will go a long way in clearing your concepts on Prime numbers - among others.
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