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Bunuel
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Bunuel
If m, n and p are all digits greater than 1 and their sum is also a digit, what is the value of m?

(1) m, n and p are all distinct.
(2) m is the largest of the three numbers.

Hey Bunuel!
Could you please provide explanation for the question, i've tried this question so many times with different perspective but i'm not still confused.
Thank you

If m, n and p are all digits greater than 1 and their sum is also a digit, what is the value of m?

What do we know from the stem?

    ...m, n and p are all digits greater than 1...:
      m, n, and p belong to {2, 3, 4, 5, 6, 7, 8, 9}

    ...their sum is also a digit...
      \(6 \leq m + n + p \leq 9\) (the least value of m, n and p is 2, so the least value of their sum is 6)

From the above, there are not that many case we can have. m, n and p can be (in any order):
    {2, 2, 2};
    {2, 2, 3};
    {2, 2, 4};
    {2, 2, 5};
    {2, 3, 3};
    {2, 3, 4};
    {3, 3, 3}.

(1) m, n and p are all distinct.

    We are left with {2, 3, 4} case only but we don't know which is which. Not sufficient.

(2) m is the largest of the three numbers.

    We are left with:
    {2, 2, 3};
    {2, 2, 4};
    {2, 2, 5};
    {2, 3, 4}.

    Not sufficient: m can be 3, 4, or 5.

(1)+(2) (1) rules out all cases but the last one from (2) ({2, 3, 4}), thus m = 4. Sufficient.

Answer: C.

Hope it's clear.
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I got confused with a DIGIT. I didn't understand that the question meant it as single digit.
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