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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.

A certain stadium is currently full to $\frac{13}{16}$ of its maximum seating capacity. What is the maximum seating capacity of the stadium?

  1. If $1,250$ people were to enter the stadium, the stadium would be full to $\frac{15}{16}$ of its maximum seating capacity.
  2. If $2,500$ people were to leave the stadium, the stadium would be full to $\frac{9}{16}$ of its maximum seating capacity.

 

  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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let $x$ be max capacity

acc to statement $1$

$13/16x+1250=15/16 x$

acc to statement  $2$

$13/16 x-2500=9/16 x$

so either $1$ and $2$ can be used to calculate $x$

so option$:\text{D}$
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