If |2 3/4 - 3 4/5 - 4 5/6+ 5 6/7| = p/q where and if (p, q) = 1, then p + q =

AP ICET 2019 Shift 2 Paper

Question : 86 of 200

Marks: +1, -0

|2 3/4 - 3 4/5 - 4 5/6+ 5 6/7|

p/q

where and if (p, q) = 1, then p + q =

Solution:

Given,

|2 \;{3}/{4}-3 \;{4}/{5}-4 \;{5}/{6}+5 \;{6}/{7}|=\;{p}/{q}

⇒|2-3-4+5+\;{3}/{4}-\;{4}/{5}-\;{5}/{6}+\;{6}/{7}|=\;{p}/{q}

⇒|-11/420|=\;{ p }/{ q }

⇒ \;{p}/{q}=\;{11}/{420}

⇒ p + q =11 k +420 k

=11(1)+420(1)=431

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