Consider the following statements in respect of three 3-digit numbers XYZ, YZX and ZXY: 1) The sum of the numbers is divisible by (X + Y + Z) 2) The sum of the numbers is divisible by 111 Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 3 : Both 1 and 2

We can write,

⇒ XYZ = 100X + 10Y + Z

⇒ YZX = 100Y + 10Z + X

⇒ ZXY = 100Z + 10X + Y

Sum of the numbers

= 100X + 10Y + Z + 100Y + 10Z + X + 100Z + 10X + Y

= 111X + 111Y + 111Z

= 111(X + Y + Z)

Hence, the sum of the numbers is divisible by both 111 and (X + Y + Z)

∴ Statement 1 and 2, both are correct.

4 views Answered 2022-09-04 04:29

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