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Updated on: 13 Aug 2021, 03:16
Originally posted by MathRevolution on 20 Jan 2019, 18:39.
Last edited by MathRevolution on 13 Aug 2021, 03:16, edited 1 time in total.
Last edited by MathRevolution on 13 Aug 2021, 03:16, edited 1 time in total.
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MathRevolution
=>
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.
You should remember that the inequality \(|x+y| < |x| + |y|\) is equivalent to the inequality \(xy < 0.\)
Condition 2) tells us that \(|a+b| + 1 = |a| + |b|.\) Thus, \(|a + b| < |a| + |b|\) and \(ab < 0\).
Thus, condition 2) is sufficient.
Condition 1)
If \(a = -2\) and \(b = 1\), then the answer is ‘yes’.
If \(a = -1\) and \(b = -1\), then the answer is ‘no’.
Since it does not yield a unique solution, condition 1) is not sufficient.
Therefore, the answer is B.
Answer: B
21 Jan 2019, 01:14
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[Math Revolution GMAT math practice question]
(number properties) \(n\) is a \(3\) digit integer of the form \(ab6\). Is \(n\) divisible by \(4\)?
1) \(a+b\) is an even integer
2) \(ab\) is an odd integer.
(number properties) \(n\) is a \(3\) digit integer of the form \(ab6\). Is \(n\) divisible by \(4\)?
1) \(a+b\) is an even integer
2) \(ab\) is an odd integer.
21 Jan 2019, 05:24
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MathRevolution
\(n = \left\langle {ab6} \right\rangle \,\,\,\, \Rightarrow \left\{ \matrix{\\
\,n > 0\,\,\,\left( {{\rm{implicitly}}} \right) \hfill \cr \\
\,a \in \left\{ {1,2,3, \ldots ,9} \right\} \hfill \cr \\
\,b \in \left\{ {0,1,2,3, \ldots ,9} \right\} \hfill \cr} \right.\)
\({{\left\langle {ab6} \right\rangle } \over 4}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}}\)
\(\left( 1 \right)\,\,\,a + b = {\rm{even}}\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {2,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.\)
\(\left( 2 \right)\,\,ab = {\rm{odd}}\,\,\, \Rightarrow \,\,\,b = {\rm{odd}}\,\,\, \Rightarrow \,\,\,\left\langle {b6} \right\rangle \in \left\{ {16,36,56,76,96} \right\}\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\)
The correct answer is therefore (B).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
