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I wonder whether following sentence is grammatically correct?

"It could have been that I wouldn't have been able to solve even one of these two problems, let alone both of them."

I'm talking here about a past exam that I took. It had 2 problems and I was able to solve both of them. What I'm trying to say is that it was by no means guaranteed that I would have been able to solve either of the 2 problems, and even less so that I'd solve not just one but both of them.

In general, I want to talk about a hypothetical in the past without the "if" conditional and by starting the sentence with "it could have been that...".

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    I'll let others comment on/answer the conditional question. But you have your let alone construct the wrong way round. Let alone always compares a lesser result with a greater one: "I wouldn't have been able to solve one of the problems, let alone both of them!" That is, the first result is improbable; the second practically impossible. – Andrew Leach Oct 21 '16 at 8:33
  • Thanks Andrew! I now see what you mean. I think I'll edit the sentence to reverse the order. – Daniel Oct 21 '16 at 8:36
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It looks like you've updated the sentence to reflect Andrew's comment about your usage of the "let alone" phrase. However, if you're still looking for alternate ways to state the conditional at the beginning of your sentence, some good options might include:

  • "It was entirely possible that I wouldn't have been able to solve even one of these two problems, let alone both of them."

Or if you wanted to add a prepositional phrase, your meaning might become clearer:

  • "When I took the exam, it was entirely possible that I wouldn't have been able to solve even one of these two problems, let alone both of them."

You could also use a negative statement, with or without the prepositional phrase, to say essentially the same thing:

  • "When I took the exam, I was unsure if I would have been able to solve even one of these two problems, let alone both of them."

I hope this helps!

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You wanted to say that "it was by no means guaranteed that I would have been able to solve either of these two problems". You could simply say it!

Or keeping Andrew's remark into account, you could express your idea clearly and to its full extent:

"It was by no means guaranteed that I would have been able to solve these two problems, let alone one of them."

or perhaps:

"There was no guarantee that I would have been able to solve these two problems, let alone one of them."

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