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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