I'm happy to help.

This is a somewhat offbeat question, but then again, that's just what the GMAT will throw at you.

So, from the prompt, we know we are picking X different single digit numbers: X must be greater than two and less than 9 (or 10, if we are counting zero as a "single digit number" ----- let's ignore that complication). Order doesn't matter. We know nothing about what constitutes winning.

Statement #1: Players must match at least two numbers to win.
Now, at least we know what constitutes winning. The trouble is --- we don't know the how many digits are picked. If X = 9 ---- the lottery picks all the digits from 1-9, then I also pick all the digits from 1-9 --- then I have 100% chance of matching at least two digits and winning. That wouldn't be much of a lottery. If X = 3 --- the lottery picks three, and then I pick three --- well, that's harder. Clearly the probability of winning depends on the value of X, and we don't know that in Statement #1. This statement, alone and by itself, is insufficient.

Statement #2: X = 4
Now, we know how many digits are picked ---- lottery picks 4, then I pick 4 --- but now I have no idea what constitutes "winning". (This is an example of a DS question in which it's crucially important to forget all about Statement #1 when we are analyzing Statement #2 on its own.) In Statement #2, we know how many digits are picked, but we have absolutely no idea what constitutes winning. This statement, alone and by itself, is insufficient.

Combined statements:
Now, we know --- the lottery picks 4 digits, then I pick 4 digits, and if at least two of my digits match two of the lottery's cards, I win. This is now a well defined math problem, and if we wanted, we could calculate the numerical value of the probability. Of course, since this is DS, it would be a big mistake to waste time with that calculation. We have enough information now. Combined, the statements are sufficient.

Answer = C

Does all this make sense?

Mike
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Mike McGarry
Magoosh Test Prep

It's tagged as a grockit problem, so I would guess that this is not an official question. It is also tagged as a 600-700 lvl question, which seems high to me for this question...I don't have any experience with Grockit, but MGMAT questions that are in the 600-700 range tend to be more difficult for me to solve.

Hi Mike,

In general I agree with everything that you're saying. Just to clarify, I think that .008 is a three digit number with 2 unique digits and so would be excluded. The numbers in question are .1, .2, .3, .4, .5, .6, .7, .8, and .9. They are numbers that have only one digit and hence are "single digit numbers". I have never seen this distinction be an actual issue on a GMAT question but am curious as to what the general consensus is.

HG.
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