Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Is the 6-digit positive integer abc000 divisible by 24?

1) The 3-digit integer abc is divisible by 8.
2) The 3-digit integer abc is divisible by 3.

$$\frac{{\left\langle {abc000} \right\rangle }}{{3 \cdot 8}}\,\,\mathop = \limits^? \,\,\,\operatorname{int} \,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\frac{{\,1000 \cdot \left\langle {abc} \right\rangle }}{{3 \cdot 8}}\,\,\mathop = \limits^? \,\,\,\operatorname{int} \,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\frac{{125 \cdot \left\langle {abc} \right\rangle }}{3}\,\,\,\mathop = \limits^? \,\,\,\operatorname{int} \,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,\,\,\frac{{\left\langle {abc} \right\rangle }}{3}\,\,\,\mathop = \limits^? \,\,\,\operatorname{int} \,\,\,\,\,\left( {a \ne {\text{0}}} \right)\,\,}$$
$$\left( 1 \right)\,\,\,{{\left\langle {abc} \right\rangle } \over 8}\,\, = \,\,\,{\mathop{\rm int}} \,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left\langle {abc} \right\rangle = \left\langle {160} \right\rangle \,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\left[ {\sum\nolimits_{3\,\,{\rm{digits}}} { = 7\,\,{\rm{not}}\,\,{\rm{divisible}}\,\,{\rm{by}}\,\,3} } \right] \hfill \cr
\,{\rm{Take}}\,\,\left\langle {abc} \right\rangle = \left\langle {168} \right\rangle \,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\,\left[ {\sum\nolimits_{3\,\,{\rm{digits}}} { = 15\,\,\,{\rm{divisible}}\,\,{\rm{by}}\,\,3} } \right]\,\, \hfill \cr} \right.\,$$
$$\left( 2 \right)\,\,\,{{\left\langle {abc} \right\rangle } \over 3}\,\, = \,\,\,{\mathop{\rm int}} \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since the last three digits 000 is a multiple of 8 and abc000 is a multiple of 8, the question "is abc000 divisible by 24?" is equivalent to "is abc000 divisible by 3?" or "is a + b + c divisible by 3?".
Thus, condition 2) is sufficient.

Condition 1) is not sufficient as 8 is not divisible by 3.

Therefore, the correct answer is B.
Answer: B