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GRE
GRE Quantitative Reasoning Section

Integer Relation Between x and its Digit Sum

Hard Arithmetic Integers

Let the integer $x$ be three times the sum of its digits when written in decimal notation, and let the sum of its digits be denoted as $S(x)$. If the integer $x$ is between 100 and 999, which of the following equations is true?

In other words, if $x = 100a + 10b + c$, where $a$, $b$, and $c$ are the digits of $x$, then how does this relate to $S(x) = a + b + c$?

Hint

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