Harshgmat wrote:
If a + (1/b) = 400, and a < -300, then which of the following must be true?
A) b > -700
B) b > 1/(-100)
C) b > 1/ 300
D) b > 700
E) b < 1/700
The
winning triad asks for
DATA connected to
FOCUS... but it is the
FOCUS the fundamental leg of the triad!
\(?\,\,\,:\,\,\,b\,\,{\rm{inequality}}\)
Hence:
\(a + {1 \over b} = 400\,\,\,\, \Rightarrow \,\,\,{1 \over b} = 400 - a = 400 + \left( { - a} \right)\mathop > \limits^{\left( * \right)} 700\)
\(\left( * \right)\,\,\,a < - 300\,\,\,\, \Rightarrow \,\,\, - a > 300\)
\({1 \over b} > 700\,\,\,\,\mathop \Rightarrow \limits^{{\rm{positives}}!} \,\,\,\,\,?\,\,:\,\,b < {1 \over {700}}\)
Do not forget the two "Golden rules": when numbers have the same signs, the greater has the lower reciprocal... Mathematically speaking:
\(x > y > 0\,\,\,\mathop \Rightarrow \limits^{:\,\,xy\, > \,0} \,\,\,{1 \over x} < {1 \over y}\)
\(q < w < 0\,\,\,\mathop \Rightarrow \limits^{:\,\,qw\, > \,0} \,\,\,{1 \over w} < {1 \over q}\)
\(\left( {x = {1 \over b}\,\,\,{\rm{and}}\,\,y = 700\,\,{\rm{in}}\,\,{\rm{our}}\,\,{\rm{case}}} \right)\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
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Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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