Question : If the number 8764x5 is divisible by 9, then find the least possible value of x where x is a two-digit number.
Option 1: 15
Option 2: 06
Option 3: 14
Option 4: 18
Correct Answer: 15
Solution : Given number: 8764x5 x = 2-digit number By using the divisibility rule of 9 Sum of the digits = 8 + 7 + 6 + 4 + x + 5 = 30 + x is divisible by 9 ⇒ 30 + x = 45 [since (30 + 15) = 45 is divisible by 9] ⇒ x = 15 Hence, the correct answer is 15.
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Question : If a 4-digit number x58y is exactly divisible by 9, then the least value of (x + y) is:
Option 1: 4
Option 2: 5
Option 3: 3
Option 4: 2
Question : If the 7-digit number $x$468$y$05 is divisible by 11, then what is the value of ($x$ + $y$)?
Option 1: 12
Option 2: 14
Option 3: 8
Option 4: 10
Question : If the six-digit number 5x2y6z is divisible by 7, 11 and 13, then the value of $(x-y+3 z)$ is:
Option 1: 7
Option 2: 4
Option 3: 0
Option 4: 9
Question : If a nine-digit number 785$x$3678$y$ is divisible by 72, then the value of ($x$ + $y$) is:
Option 1: 20
Option 2: 12
Option 3: 10
Option 4: 5
Question : Let $x$ be the least number which when divided by 8, 9, 12, 14 and 36 leaves a remainder of 4 in each case, but $x$ is divisible by 11. The sum of the digits of $x$ is
Option 1: 5
Option 2: 6
Option 3: 9
Option 4: 4
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