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A number consists of two digits whose sum is 10. If the digits of the number are reversed, then the number decreased by 36. Which of the following is/are correct?

I. The number is divisible by a composite number.

II. The number is a multiple of a prime number.

Correct Answer:

I. The number is divisible by a composite number.

II. The number is a multiple of a prime number.

A) Only I |
B) Only II |

C) Both 1 and H |
D) Neither I nor II |

Correct Answer:

B) Only II |

Description for Correct answer:

Let the two-digit number be 10x + y.

Now, according to the question,

x + y = 10 ...(i)

and \( \Large \left(x+10y\right)+36 = \left(y+10x\right) \)

=> \( \Large -9y + 9x = 36 \)

=> \( \Large -y + x = 4 \) ...(ii)

On adding Eqs. (i) and (ii), we get

2x = 14 = x = 7

Therefore, x = 7 and y = 3

Therefore, Required number is 73.

So, the number is a multiple of a number.

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