Question : If the six-digit number 479xyz is exactly divisible by 7, 11, and 13, then {(y + z) ÷ x} is equal to:
Option 1: $4$
Option 2: $\frac{11}{9}$
Option 3: $\frac{7}{13}$
Option 4: $\frac{13}{7}$
Correct Answer: $4$
Solution :
A 6-digit number in which a 3-digit repeat xyzxyz is divisible by 1001 and 1001 is divisible by 7, 11, and 13.
⇒ 479479 is divisible by 7, 11 and 13.
Comparing 479479 with 479xyz.
we get, $x = 4, y = 7 \text{ and }z = 9$
Now,
{(y + z) ÷ x}
= (7 + 9) ÷ 4
=$\frac{16}{4}$
= 4
Hence, the correct answer is 4.
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