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.
Answer
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
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