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What is the three-digit number which is 2 more than a perfect square and 2 less than a perfect cube?
A123
B627
C402
D350
Answer & Solution
Correct answer: A. 123
1. Check 123: subtract 2 to get 121, and 121 = 11², a perfect square.
2. Add 2 to 123 to get 125, and 125 = 5³, a perfect cube.
3. Both conditions hold, so the number is 123.
_Source: RRB Group D (RRC) PYQ, held 27-10-2013, Q.33._
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