CAT Practice : Number System

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Divisibility of powers

    Q.9: A number 416 + 1 is divisible by x. Which among the following is also divisible by x?
    1. 496 + 1
    2. 432 + 1
    3. 48 + 1
    4. 448 + 1


  • Correct Answer
    Choice D. 448 + 1

Detailed Solution

We know a3 + b3 = (a + b)3 – 3ab(a + b)
If (a + b) is divisible by x, then a3 + b3 is also divisible by x.
If 416 + 1 is divisible by x, then (416)3 + 13 is also divisible by x
Or 448 + 1 is divisible by x

Correct Answer: Choice D

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More questions from Number System

  1. Product of digits
  2. Sum of first n natural numbers
  3. Perfect Square
  4. Last two digits
  5. Multiples
  6. Greatest integer function
  7. Medians, Number
  8. 44th digit of a number
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