Bunuel
All of the following have the same value EXCEPT?
A. \(\frac{1 + 2 + 3 + 4 + 5}{3}\)
B. \(\frac{1}{3}(1 + 1 + 1 + 1 +1)\)
C. \(\frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3}\)
D. \(\frac{2}{3}(\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2})\)
E. \(\frac{1}{3} + \frac{2}{6} + \frac{3}{9} + \frac{4}{12} + \frac{5}{15}\)
If we use the distributive law in choices B and D and simplify each term in choice E, we see that each term is 1/3 in choices B, C, D, and E. However, if we distribute in choice A, we have: 1/3 + 2/3 + 3/3 + 4/3 + 5/3. All the terms are not equal to 1/3. So the answer is A.
Alternate Solution:
Choice A becomes 1/3 + 2/3 + 3/3 + 4/3 + 5/3.
Choice B becomes 1/3 + 1/3 + 1/3 + 1/3 + 1/3.
Choice C is already 1/3 + 1/3 + 1/3 + 1/3 + 1/3.
Since we are looking for the answer choice that is unlike the others, we see, without going any further with our analysis of the answer choices, that Choice A will not yield the same value as B or C (or D or E). Thus, A is the correct answer.
Answer: A