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476** 0 is Divisible by Both 3 and 11. the Non-zero Digits in the Hundred'S and Ten'S Places Are Respectively - Mathematics

MCQ

476** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively

Options

  • 7 and 4

  • 7 and 5

  • 8 and 5

  • Cannot be determined

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Solution

Cannot be determined

Explanation

Let the given number be 476 xy 0.

Then, (4 + 7 + 6 + x + y + 0)

= (17 + x + y) must be divisible by 3 and

(0 + x + 7) - (y + 6 + 4) = (x - y - 3) must be either 0

or multiple of 11.

x - y - 3 = 0 ⇒ y = x - 3

Then, (17 + x + y) = (17 + x + x - 3)

= (2x+ 14) ⇒ x = 2 or x = 8 or x = 5

∴ x = 8 and y = 5 or x = 5 and y = 2
Hence, option Cannot be determined is correct.

Concept: Number System (Entrance Exam)
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