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14 Mar 2019, 07:56
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
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Question Stats:
48% (02:08) correct
52%
(02:09)
wrong
based on 65
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GMATH practice exercise (Quant Class 16)
If N is a positive two-digit integer, is N+1 prime?
(1) The sum of the digits of N is equal to 11.
(2) N-1 is divisible by 7.
If N is a positive two-digit integer, is N+1 prime?
(1) The sum of the digits of N is equal to 11.
(2) N-1 is divisible by 7.
14 Mar 2019, 09:22
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For stat 1.
we have, 29,38,47,56,65,74,83,92
so N+1 is always divisible by some number , So N+1 is not a prime ,
sufficient
statement 2 ,
possible numbers ,
15, 22, 29, 36,43,50 ...
So N+1 = 16 , 23, ...
so 16 is not prime and 23 is prime
Not sufficient
Award kudos if helpful ..
Posted from my mobile device
we have, 29,38,47,56,65,74,83,92
so N+1 is always divisible by some number , So N+1 is not a prime ,
sufficient
statement 2 ,
possible numbers ,
15, 22, 29, 36,43,50 ...
So N+1 = 16 , 23, ...
so 16 is not prime and 23 is prime
Not sufficient
Award kudos if helpful ..
Posted from my mobile device
14 Mar 2019, 13:55
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fskilnik
\(N = \left\langle {AB} \right\rangle\)
\(N + 1\,\,\mathop = \limits^? \,\,{\rm{prime}}\)
\(\left( 1 \right)\,\,A + B = 11\,\,\,\,\left\{ \matrix{\\
\,B\,\,{\rm{odd}}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\left[ {N + 1\,\,{\rm{even}}\,\, > 2\,\,} \right] \hfill \cr \\
\,B\,\,{\rm{even}}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\left[ {N + 1\,\, \in \left\{ {92 + 1,74 + 1,56 + 1,38 + 1} \right\}\,\,\, \Rightarrow \,\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,3\,\,\, > 3} \right]\,\, \hfill \cr} \right.\)
\(\left( 2 \right)\,\,{{N - 1} \over 7} = {\mathop{\rm int}} \,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,N = 15\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,N = 22\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)
The correct answer is (A).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
P.S. (to the careful reader): there is at least one number N that satisfies the question stem (pre-statements) and both statements together (92). This is expected to avoid "internal contradictions".
