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# Is 30 a factor of n? (1) 30 is a factor of n^2 (2) 30 is a

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Senior Manager
Joined: 14 Jul 2005
Posts: 402
Followers: 1

Kudos [?]: 12 [0], given: 0

Is 30 a factor of n? (1) 30 is a factor of n^2 (2) 30 is a [#permalink]  22 Aug 2006, 21:25
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Is 30 a factor of n?

(1) 30 is a factor of n^2
(2) 30 is a factor of 2n

A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D) Each statement alone is sufficient to answer the question.
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

Kudos [?]: 121 [0], given: 0

C

St1:
True for n^2 = 900
False for n^2 = 60: INSUFF

St2:
True for 2n = 60
False for 2n = 30: INSUFF

Together:
n must be an integer. So n could be 15,30,45,60......
But squares of odd values are not divisible by 30. So n is 30,60,90.....
Hence 30 is a factor of n.: SUFF
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
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Kudos [?]: 181 [0], given: 2

OK I am with C as well..but my approach is slightly different

the question is are the prime factors of n=2,3 and 5?

1) n^2= has factors 2,3 and 5...but we dont know anything about n...Insuff
2) 2n= has prime factors 2, 3 and 5..well we can just cancel out the 2s...so we know n has prime factors 3 and 5...for sure..insuff

combining...well n^2= has a prime factor of 2, so n must have 2 (we got that from st1) and we know that n has prime factors (3 and 5) from st.2...Sufficient..
Manager
Joined: 09 Jul 2006
Posts: 85
Location: India
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right fresinha12. I took the same approach .. got C as the answer.
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Cheers!
Prashrash.

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