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20 Apr 2010, 13:28
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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18%
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1. Is n an integer?
(1) n^3 + 3n is an integer.
(2) n^4 + 4n is an integer.
2. If m and n are positive integers, then is 5m + 2n divisible by 3m + n ?
(1) m is divisible by n
(2) m is divisible by 15 and n is divisible by 2
Please explain...
The OA in my opinion is debatable:
(1) n^3 + 3n is an integer.
(2) n^4 + 4n is an integer.
2. If m and n are positive integers, then is 5m + 2n divisible by 3m + n ?
(1) m is divisible by n
(2) m is divisible by 15 and n is divisible by 2
Please explain...
The OA in my opinion is debatable:
1. D 2. B
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20 Apr 2010, 16:12
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h2polo
1. Is n an integer?
I think this question is beyond GMAT scope.
(1) \(n^3+3n=a\), for some integer \(a\). This is a cubic equation and \(n\) (the root of this equation) could be an integer (eg \(a=0\), \(n=0\)) as well as non-integer. For example \(n^3+3n=10\) has one real root: \(n\approx{1.7}\) (some irrational number, so not an integer). Not sufficient.
(2) \(n^4 + 4n=b\), for some integer \(b\). This is a quartic equation and \(n\) (the root of this equation) could be an integer (eg \(b=0\), \(n=0\)) as well as non-integer. For example \(n^4+4n=20\) has two real roots: \(n\approx{1.88}\) and \(n\approx{2.33}\) (some irrational number, so not an integer). Not sufficient.
(1)+(2) Obviously \(n\) can be an integer. Can it be non-integer? Can the non-integer root(s) of equation \(n^3+3n=a\) be at the same time the root(s) of \(n^4 + 4n=b\)?
2. If m and n are positive integers, then is 5m + 2n divisible by 3m + n ?
This is also a strange question.
Q: is \(\frac{5m+2n}{3m+n}=integer\)? --> \(\frac{5m+2n}{3m+n}=\frac{3m+n+2m+n}{3m+n}=1+\frac{2m+n}{3m+n}=integer\)? Now as m and n are positive integers, in fraction \(\frac{2m+n}{3m+n}\), denominator is more than numerator, so \(\frac{2m+n}{3m+n}\) is not an integer. Hence \(1+\frac{2m+n}{3m+n}\neq{integer}\). We don't need statements to answer the question. Don't know if this is possible in real GMAT, but if it is, then answer should be D.
(1) m is divisible by n
(2) m is divisible by 15 and n is divisible by 2
h2polo
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20 Apr 2010, 17:13
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Thanks Bunuel... I think you are right to say that these questions are probably not within the scope of GMAT.
