Question of The Day23-05-2022

If x and y are two missing digits of the numbers x304 and y5317 such that the numbers are divisible by 17 and 29 respectively then find the value of x + y.

Correct Answer : c ) 7

Explanation :

It is given that,

x304 is divisible by 17 and y5317 is divisible by 29.

Finding the value of x:

Using the divisibility rule of 17 and applying it on x304:

Multiply the last digit with 5 and subtract it from the remaining number

⇒ x30 – 5*4 = x10

⇒ x1 - 5*0 = x1

⇒ x - 5*1

Now, x – 5 should be divisible by 17.

Since x – 5 will result in a single-digit number, x – 5 should give 0 to be divisible by 17.

Here, x = 5 is the only possible case for the number to be divisible by 17.

Hence, x = 5

Finding the value of y:

Using the divisibility rule of 29 and applying it on y5317:

Multiply the last digit with 3 and add it to the remaining number.

⇒ y531 + 3*7 = y552

⇒ y55 + 3*2 = y61

⇒ y6 + 3*1 = y9

⇒ y + 3*9

Now, y + 27 should be divisible by 29.

Since, y + 27 will range from 27 to 36, y + 27 should give 29 to be divisible by 29.

Here, y = 2 is the only possible case for the number to be divisible by 29.

Hence, y = 2

Therefore, x + y= 7

Hence, (c) is the correct answer 0 