If the number 517X324 is completely divisible by 3, then the smallest whole…
2024
If the number 517X324 is completely divisible by 3, then the smallest whole number in the place of X will be :
- A.
0
- B.
1
- C.
2
- D.
none of these
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Correct answer: C
Key idea: A number is divisible by 3 if and only if the sum of its digits is divisible by 3.
Write the digit sum of 517X324 in terms of X:
5 + 1 + 7 + X + 3 + 2 + 4 = 22 + X.
For the number to be divisible by 3, 22 + X must be divisible by 3.
Since 22 leaves a remainder of 1 when divided by 3, X must leave a remainder of 2 when divided by 3 so that 22 + X is a multiple of 3.
Digits that leave remainder 2 when divided by 3 are 2, 5, and 8. Among these, the smallest whole number is 2.
Therefore, the smallest whole number that can replace X so that 517X324 is divisible by 3 is 2.