If O and ∆ are digits. What is the value of ∆.OOO + O. ∆∆∆?

Target question: What is the value of ∆.OOO + O. ∆∆∆?
This is a great candidate for rephrasing the target question

Let's start by making a few observations.
Notice that 0.222 = 2(0.111), 0.333 = 3(0.111), 0.444 = 4(0.111), etc.
Likewise, 0.∆∆∆ =∆(0.111) and 0.OOO = O(0.111) and

So, ∆.OOO + O. ∆∆∆ = [∆ + O(0.111)] + [O + ∆(0.111)]
= 1.111∆ + 1.111O
= 1.111(∆ + O)

REPHRASED target question: What is the value of 1.111(∆ + O)?

Aside: the video below has tips on rephrasing the target question

Statement 1: ∆ + O = 10
So, 1.111(∆ + O) = 1.111(10) = 11.11
Perfect!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: ∆ = O
This does not help us answer the REPHRASED target question.
Consider these two conflicting cases:
Case a: ∆ = O = 1. In this case, the answer to the REPHRASED target question is 1.111(∆ + O) = 1.111(1 + 1) = 1.111(2) = 2.222
Case a: ∆ = O = 3. In this case, the answer to the REPHRASED target question is 1.111(∆ + O) = 1.111(3 + 3) = 1.111(6) = 6.666
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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