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# A Two-digit Number is Such that the Products of Its Digits is 8. When 18 is Subtracted from the Number, the Digits Interchange Their Places. Find the Number? - Mathematics

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#### Question

A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?

#### Solution

Let the two digits be x and x - 2

Given that the product of their digits is 8.

⇒ x(x - 2) = 8

⇒ 𝑥2 - 2𝑥 - 8 = 0

⇒ 𝑥2 - 4𝑥 + 2𝑥 - 8 = 0

⇒ 𝑥(𝑥 - 4) + 2(𝑥 - 4) = 0

⇒ (𝑥 - 4)(𝑥 + 2) = 0

⇒ 𝑥 = 4 𝑜𝑟 𝑥 = -2

Considering the positive value x = 4, x - 2 = 2.

∴ The two digit number is 42.

Is there an error in this question or solution?
The text passage contains a mathematical word problem and its solution, where the problem is to find a two-digit number based on given conditions, and the solution is provided as 42.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# A Two-digit Number is Such that the Products of Its Digits is 8. When 18 is Subtracted from the Number, the Digits Interchange Their Places. Find the Number? - Mathematics

Course

#### Question

A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?

#### Solution

Let the two digits be x and x - 2

Given that the product of their digits is 8.

⇒ x(x - 2) = 8

⇒ 𝑥2 - 2𝑥 - 8 = 0

⇒ 𝑥2 - 4𝑥 + 2𝑥 - 8 = 0

⇒ 𝑥(𝑥 - 4) + 2(𝑥 - 4) = 0

⇒ (𝑥 - 4)(𝑥 + 2) = 0

⇒ 𝑥 = 4 𝑜𝑟 𝑥 = -2

Considering the positive value x = 4, x - 2 = 2.

∴ The two digit number is 42.

Is there an error in this question or solution?
user
The text passage contains a mathematical word problem and its solution, where the problem is to find a two-digit number based on given conditions, and the solution is provided as 42.

TYPE: SINGLE_QUESTION_WITH_ANSWER