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What is the two-digit number? (I) Its tens digit is twice its units digit. (II) It is a perfect square whose digits add up to 13.

Competition practiceData Sufficiency
  • ABoth statements together are needed (neither alone is sufficient)
  • BEither statement alone is sufficient
  • CStatement I alone is sufficient but Statement II alone is not
  • DStatement II alone is sufficient but Statement I alone is not

Step-by-Step Solution

II: the two-digit squares are 16, 25, 36, 49, 64, 81 and only 49 has digit sum 13, so II alone fixes the number. I allows 21, 42, 63 or 84, so I alone is not sufficient.
Answer: D) Statement II alone is sufficient but Statement I alone is not

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