If the five-digit number 235 xy is divisible by 3, 7 and 11, then what

1.	If the five-digit number 235 xy is divisible by 3, 7 and 11, then what is the value of (3x - 4y)?1. 92. 53. 84. 10
Answer» Correct Answer - Option 4 : 10 Given: Five-digit number 235xy is divisible by 3, 7 and 11 Concept used: Divisibility rule of 3- The sum of its digit is divisible by 3. Divisibility rule of 7- To make a pair of 3 from unit digit than subtract left over pair, The result is divisible by 7. Divisibility rule of 11- The difference of the sum of odd place and even place is zero or multiples of 11. The result is divisible by 11. Calculation: 235xy For 3, x + y = 2, 5, 8, 11 For 11, (7 + y) - (3 + x) = 0 or 11 y = 2 then x = 6, x + y = 8 For 7, 562 - 023 = 539 it is also divisible by 7 number = 23562 and x = 6, y = 2 now, 3x - 4y = 18 - 8 = 10 ∴ The value of 3x - 4y is 10.

If the five-digit number 235 xy is divisible by 3, 7 and 11, then what is the value of (3x - 4y)?1. 92. 53. 84. 10

Answer» Correct Answer - Option 4 : 10

Given:

Five-digit number 235xy is divisible by 3, 7 and 11

Concept used:

Divisibility rule of 3- The sum of its digit is divisible by 3.

Divisibility rule of 7- To make a pair of 3 from unit digit than subtract left over pair,

The result is divisible by 7.

Divisibility rule of 11- The difference of the sum of odd place and even place is zero or multiples of 11.

The result is divisible by 11.

Calculation:

235xy

For 3, x + y = 2, 5, 8, 11

For 11, (7 + y) - (3 + x) = 0 or 11

y = 2 then x = 6, x + y = 8

For 7, 562 - 023 = 539

it is also divisible by 7

number = 23562 and x = 6, y = 2

now,

3x - 4y = 18 - 8 = 10

∴ The value of 3x - 4y is 10.

Discussion

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