CAT 2003 Slot 2 — QA Question 31
MiscellaneousEasy
Passage / Data
Answer the following question based on the information given below.
Two binary operations ⊕ and * are defined over the set {a, e, f, g, h} as per the following tables:
âââââââ
âââââââ
Thus, according to the first table f ⊕ g = a, while according to the second table g * h = f, and so on.
Also, let f2 = f * f, g3 = g * g * g, and so on.
Upon simplification, (a10 * (f10 ⊕ g9)} ⊕ e8 equals
Answer & solution
e
- B
f
- C
g
- D
h
Solution
a10 = a ...(âµ a * a = a)
f10 = (f2)5 = h5 = h * (h2)2 = h * e2 = h * e = h
g9 = g * (g2)4 = g * h4 = g * e = g
e8 = e .....(âµ e2 = e)
∴ {a10 * (f10 ⊕ g9)} ⊕ e8 = {a * (h ⊕ g)} ⊕ e = {a * f} ⊕ e = a ⊕ e = e