6th Class Mathematics Factors and Multiples Question Bank Factors & Multiples

  • question_answer If \[{{P}_{1}}\] and \[{{P}_{2}}\] are two odd primes numbers such that \[{{P}_{1}}>{{P}_{2}}\]then \[P_{1}^{2}-P_{2}^{2}\] is

    A)  an Even number

    B)  an odd number

    C)  an odd prime number            

    D)  a prime number

    Correct Answer: A

    Solution :

    \[{{P}_{1}}^{2}-{{P}_{2}}^{2}=:\left( \underset{\begin{smallmatrix}  \downarrow - \\  odd \end{smallmatrix}}{\mathop{{{p}_{1}}}}\,-\underset{odd}{\mathop{\underset{\downarrow }{\mathop{{{p}_{2}}}}\,}}\, \right)\left( \underset{\begin{smallmatrix}  \downarrow  \\  odd \end{smallmatrix}}{\mathop{{{p}_{1}}}}\,+\underset{odd}{\mathop{\underset{-\downarrow }{\mathop{{{p}_{2}}}}\,}}\, \right)\] (\[\because \]odd - odd = Evan) \[(5-3=2)\] \[Even\times Even=Even\]

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