Which of the following is the largest?
Solution
Correct Answer: Option E
Let's simplify each option to comparable base powers:
A) 227 already in base 2
B) 1253 = (53)3 = 59
C) 518 already in base 5
D) 44 × 1024=(22)4× 210 = 28× 210 = 218
E) 279 = (33)9 = 327
Now observe:
518 is clearly much larger than 59
227 is larger than 218
But base 3 raised to 27 (i.e, 327) grows faster than all
Since 327 increases faster than any of the others, option E is the largest.
A) 227 already in base 2
B) 1253 = (53)3 = 59
C) 518 already in base 5
D) 44 × 1024=(22)4× 210 = 28× 210 = 218
E) 279 = (33)9 = 327
Now observe:
518 is clearly much larger than 59
227 is larger than 218
But base 3 raised to 27 (i.e, 327) grows faster than all
Since 327 increases faster than any of the others, option E is the largest.
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