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Lengthy Question

by ronnie1985 » Wed Apr 18, 2012 6:09 am
Got the question from web forum. Can you tell me the shortest method to solve? Also can we expect such lengthy questions in GMAT?
Thanks in advance.
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by aneesh.kg » Wed Apr 18, 2012 6:59 am
from the inequality,
3 =< n =< 8

y = (n4 + 4n3 + 64n + 56)/ (n + 4)^2
= (n4 - 32n2 + 56)/(n+4)^2 + 4n
= [(n2 + 8n + 16)(n2 - 8n + 32) - 456]/(n+4)2 + 4n
= (n2 - 4n + 32) - 456/(n+4)2
Substituting n = 3,
y = 29 - 9 (approx)
= 20
Substituting n = 8,
y = 64 - 3 (approx)
= 61

So, I am getting y approximately between 20 and 61.

I am interested to know a better way to solve this; and I don't think you should expect such a question in GMAT.
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by Cheerios » Thu Apr 19, 2012 1:21 pm
The question is wrong, unless n4 doesn't mean n^4. Try n=3:

y=[81+56+12(16+9)]/[9+24+16]
=[137+300]/[49]
=437/49 -> approx. 9
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