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Re: If the three-digit integer x=”abc”, where a, b, and c [#permalink]
04 May 2012, 07:55

1

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Expert's post

If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b. Not sufficient, since no info about c. (2) b>= 3c. Not sufficient, since no info about a.

(1)+(2) We have that a>= 3b and b>= 3c. Now, since each represent a nonzero single digit then c can only be 1, b can only be 3 and a can only be 9. Because if c=2 (or more) then the least value of b is 6 and in this case the least value of a is 18, so it's no more a single digit. Sufficient.

1+2) If we combine both inequalities together we end up with a/3>=b>=3c, thus the only values a can assume are 3 and 9, if a=3 the inequality does not hold true. Pick a=9 at this point we must minimize c, which will be 1, and b will be 3. Thus the value of abc is 931.

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Re: If the three-digit integer x=”abc”, where a, b, and c
[#permalink]
21 Jan 2014, 14:22