CAT 2009 | Question: 36

Question

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. $p = 110$

• A. Statement $(1)$ ALONE is sufficient, but statement $(2)$ alone is not sufficient.
• B. Statement $(2)$ ALONE is sufficient, but statement $(1)$ alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
• D. EACH statement ALONE is sufficient.

Answer 1

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