MathRevolution wrote:
[
Math Revolution GMAT math practice question]
If \(p\) and \(q\) are prime numbers, is \(pq+1\) an odd number?
\(1) p – q = 5\)
\(2) p = 7\)
\(p,q\,\,{\rm{primes}}\,\,\,\,\left( * \right)\)
\(pq + 1\,\,\mathop = \limits^? \,\,{\text{odd}}\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\boxed{\,?\,\,\,:\,\,\,\,p = 2\,\,\,{\text{or}}\,\,\,q = 2\,\,\,}\)
\(\left( 1 \right)\,\,p - q = 5\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\)
\(\left( {**} \right)\,\,p \ne 2\,\,{\rm{and}}\,\,q \ne 2\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,p,q\,\,\,{\rm{odd}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {5 = } \right)\,\,p - q\,\,{\rm{even}}\,\,,\,\,\,{\rm{impossible}}\)
\(\left( 2 \right)\,\,p = 7\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {p,q} \right) = \left( {7,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {p,q} \right) = \left( {7,3} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.\,\,\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net