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Each of the following problems consists of a question and the statements labelled $(1)$ and $(2).$ You must decide whether the data given for the statements are sufficient to answer the questions.

If both $\text{ABDC}$ and $\text{CDFE}$ are parallelograms. what is $q + r ?$

  1. $r = 70$             
  2. $p = 110$

  1. Statement $(1)$ ALONE is sufficient, but statement $(2)$ alone is not sufficient.
  2. Statement $(2)$ ALONE is sufficient, but statement $(1)$ alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
  4. EACH statement ALONE is sufficient.
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two properties to be used

1)consecutive angles of parallelogram are supplementary (ie in above eg p+q $=180$)

2)angles forming linear pair are supplementary(p+r $= 180$)

so we can find q if r is given

and also we can find q,r if p is given

so q+r can be easily found out if either p or r is given

so ans is d
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