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Two circular paper sheets, each of area 154 square cm, are laid on a table so that they overlap. The region common to both sheets measures 40 square cm. What is the area of the table, in square cm, that is covered by at least one sheet?

Competition practiceMensuration
  • A308
  • B228
  • C114
  • D268

Step-by-Step Solution

The covered region = first sheet + second sheet - the overlap, because the overlap has been counted twice: 154 + 154 - 40 = 268 sq cm. The trap 308 simply adds the two sheets and counts the shared strip twice; 228 subtracts the overlap twice, 308 - 80, but it was only double-counted once; 114 = 154 - 40 covers just one sheet's exclusive part and drops the other sheet altogether.
Answer: D) 268

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