Question

A two-digit number is 4 times the sum of its digits. If the digits are reversed, the new number is 18 more than the original. What is the number?

• A. 24
• B. 30
• C. 36
• D. 32

Answer 1

Answer:

A. 24

Let the two-digit number be (10a+b), where:

• (a) = tens digit

• (b) = units digit

Step 1: Use the first condition

The number is 4 times the sum of its digits:

10a+b = 4(a+b)

10a+b = 4a+4b
6a = 3b
b = 2a

Step 2: Use the second condition

When the digits are reversed, the new number is 18 more than the original:

10b+a = (10a+b)+18
9b-9a = 18
b-a = 2

Substitute (b=2a):

2a-a = 2
a = 2

Therefore,

b = 4

Step 3: Find the number

10a+b = 10(2)+4 = 24

The number is 24