LCM of x and y is 36 and HCF of x and y is 4. If x = 4 then which of the…

2023

LCM of x and y is 36 and HCF of x and y is 4. If x = 4 then which of the following is definitely not true ?

  1. A.

    Y is divisible by 3

  2. B.

    Y is divisible by 6

  3. C.

    Y is divisible by 9

  4. D.

    X + Y is divisible by

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Correct answer: D

Correct approach: use the relation x × y = LCM(x,y) × HCF(x,y).

  • Step 1: Compute the product x × y = 36 × 4 = 144.

  • Step 2: Given x = 4, find y = 144 ÷ 4 = 36.

  • Step 3: Compute x + y = 4 + 36 = 40.

Check each statement using y = 36 and x + y = 40:

  1. Y is divisible by 3: 36 ÷ 3 = 12, so this is true.

  2. Y is divisible by 6: 36 ÷ 6 = 6, so this is true.

  3. Y is divisible by 9: 36 ÷ 9 = 4, so this is true.

  4. X + Y is divisible by: This statement is incomplete because no divisor is specified. Since x + y = 40, divisibility depends on the (missing) divisor; as written the claim cannot be evaluated and is therefore not a valid true statement.

Conclusion: the only statement that is definitely not true (as written) is the incomplete "X + Y is divisible by" statement.

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